摘要:

Coagulation of I Molten Lead Aerosols BYS. C. GRAHAM AND J. B. HOMER* Shell Research Ltd. Thornton Research Centre P.O. Box 1 Chester CHI 3SH Receioed 4th December 1972 A study is made of the kinetics by which particles in a high-temperature aerosol coagulate. The experimental method uses a light-scattering technique coupled to a shock tube and allows a con-tinuous record to be made of the changes in particle volume during the coagulation process. The theory of free-molecule coagulation of aerosols with a self-preserving size distribution has been developed to include the effects of dispersion forces and a comparison made between theoretical and observed rates of coagulation of a molten lead aerosol at temperatures around 940 K. Observed rates are found to be a factor of two faster than theory would predict.In this paper we describe a study of the coagulation of very finely dispersed aerosols that coagulate on a millisecond time-scale. We have developed an experi- mental method that enables a continuous record to be made of the changes in particle volume during such coagulation and the results afford a test of whether current coagulation is capable of predicting the coagulation rates of very small particles. The study is made specifically on lead aerosols at temperatures around 940 K and the work is an extension of our previous study on the rates of condensa- tion of lead vapour. The lead aerosols are generated in a shock tube by the thermal decomposition of tetramethyl-lead (TML) highly diluted with argon and " ideal " conditions are chosen where virtually all the lead condenses within 0.5 ms and remains at a constant particulate volume for the remaining 3 ms of available flow time.The molten lead particles collide and coalesce during this period and grow to diameters of 10-20nm before the end of the flow. Since such diameters are less than one-fifth of the mean free path of the argon diluent we may expect 3*7the coagulatioq process to have the characteristics of the free-molecule rather than the diffusion-controlled regime. Furthermore the observed change in particle volume is so high that we expect a self-preserving size distribution to be developed very early in the flow. We have therefore developed the theory of free-molecule coagulation of aerosols with a self-preserving size distribution to describe the rate of coagulation of these aerosoIs.The experimental method for measuring the change in particle volume during the flow is based on a light-scattering technique using an argon-ion laser as the light source. The rates of coagulation are recorded and compared with those predicted by the theory. THEORY COAGULATION The theory of aerosol coagulation is developed here to provide an appropriate equation relating the mean particle volume to-the coagulation time. Within the free-molecule regime coagulation theory defines the collision parameter [ref. (3) p. 3031 as 85 COAGULATION OF MOLTEN LEAD AEROSOLS For an isodisperse system in which the particles coalesce on every collision this leads [ref.(2) eqn (7) ref. (S) eqn (22)] to a coagulation rate of Using the relationship N,ij = 4 eqn (2) may be expressed in the alternative form dij 1 3 1/6 6kT 'I2 1/6 (q-= -(-) (4) 4J24. (3) dt 2 471 111 the above equations v is the volume of a particle k is Boltzmann's constant Tis the absolute temperature p is the density of the particulate phase N is the total particle number density at time t V is the mean particle volume at time t and 4 is the particulate volume fraction. A system of coagulating lead particles (droplets) in a stagnant gas in which gravitational effects and the loss of particulare material through particle wall collisions are negligible is one in which we may expect the particle size distribution to tend Whilst the nature of such self-preserving towards a " self-preserving " f~rrn.~*~ size distributions has been described by Friedlander and others 9*10 for coagulation in the Brownian diffusion regime it is only recently that approximations to the self- preserving distribution for the free-molecule regime have been published by Lai Friedlander et al.' and by Ulrich.2* The rate of coagulation for such systems is given by where and where q is the reduced particle volume and $(q) the reduced distribution function defined in eqn (7) of ref.(1) by As part of this work we derived the ordinary integro-differential equation (6) indepen-dently of Lai Friedlander et al.' and obtained a numerical solution to this equation which we believe to be more accurate for values of 21 20.15 than either of the published distributions.' p2 An important difference between our computed distribution and that of Lai Friedlander et al.' is that in our analysis the two fundamental constraints * Ulrich underestimated the rate density of collisions between equal-sized particles by a factor of two which may account for some of the difference between his computed distribution (fig.l(b))and ours (fig. l(c)). S. C. GRAHAM AND J. B. HOMER are both satisfied with a high degree of accuracy (1 part in lo4). Details of our numerical results will be published elsewhere l1 but the three distributions are illus- trated in fig. 1. Throughout this paper wherever numerical values of q are required they are calculated from our own computed distribution shown in fig.l(b). Of particular importance in these calculations are the integrals a and which values were derived from fig. 1(b)and to be 6.4 and 1.84 respectively. -3.0-2.6 -2.2 -1.8 -1.4 -1.0-0.6-0.2 0.2 0.8 1.0 log, 71 FIG.1 .-Results of computations of the self-preserving size distribution function for free-molecule aerosols (a)Lai Friedlander et d.’, (b) this work and (c)Ulrich.2 Eqn (4) can be modified to include the effect of inter-particle dispersion forces which for lead aerosols can be significant.12 We can take these forces into account if we assume that they modify the collision parameter according to P(u u) = (p)1i2G(~~u1/3++B”’)2(~+~) 6kT 1 1 li2. (i) Eqn (4) then becomes where COAGULATION OF MOLTEN LEAD AEROSOLS and where I,!I’(Y,I) is now a function of G(q/V)and satisfies the equation so that for every different function G(q/ij) there will be a correspondingly different self-preserving size distribution.Recently Fuchs and Sutugin 4913 have shown that interparticle dispersion forces substantially increase the rate of coagulation of sodium chloride aerosols in the free- molecule regime. They show that for collisions between spheres of equal size the coagulation rate is enhanced by a factor which is dependent only on the ratio (A/T) where A is the Hamaker 12* l4 constant and Tis the absolute temperature. We have extended their treatment to include collisions between unequal spheres and find that the collision cross-section is increased by a factor G being the value of F(a p) evaluated at M(a p)/h = 0.Here a = (rl +r2)/p’ and p = (r -r2)/(r1 +r2) where Y and r2 are the particle radii and p’ is the distance of closest approach of the two spheres during a near collision. F(a p) is given by -1 1 F(a p) = bi[ 1+-3&{ +(1-p2)a2[&+(I -pW) + I.(-=)]}]. 1-p2a2 (12) 2.5 2.0 I I I I n 3. vu I I I 1 I 1.5 - I I I I I I I I I I I.o I I I 1 I I I 1 0 0.2 0.4 0.6 0.8 I.o II FIG.2.-The dependence of the collision cross-section enhancement ratio C(p) on the difference in particle size for various values of the Hamaker constant A and for a temperature of 940K. p is (ri -r2)/(rl+r2)where rl and r2 are the radii of the two particles. G’ is the approximate coagulation rate enhancement due to dispersion forces for an aerosol with the self-preszfving size distribution as defined in eqn (6).S. C. GRAHAM AND J. B. HOMER Fortunately however G is only weakly dependent on p in the important region near p = 0 as shown by the plots of G(p) for various values of A/T in fig. 2 and thus for all reasonable values of the Hamaker constant for liquid lead (no reliable value being available the effect of G(p) on the form of the self-preserving size j6) distribution may be ignored. Within this approximation the dispersion forces increase the coagulation rate by the factor G' where and where l+p = G(p) and = (--). 1 -p The corresponding rate equation is obtained by insertion of G' into eqn (4) which on substituting 4/ij for N, gives on integration so that for fi 9 i$=o,to a good approximation (15) This is the required equation which describes the expected change of mean particle volume with time.LIGHT SCATTERING BY SMALL PARTICLES Because of their small size the lead particles are within the small-particle limit ' of Mie theory 17* l8 for visible radiation. Within this limit a spherical particle scatters light in proportion to the square of its v01urne.'~ The intensity of light scattered by an aerosol of such particles (Rayleigh scattering) is thus proportional to n(v) uz do where n(u)du is the number density of particles with volumes between 17 I and (u+du). For an aerosol with the self-preserving size distribution given in fig.l(b)this integral simplifies [see eqn (7)] to ra fa so that for an aerosol with a constant particulate volume fraction the scattered light intensity is directly proportional to the instantaneous mean particle volume. This relationship is one that allows a direct experimental check on the growth of mean particle volume during the coagulation process as described by eqn (15). Because of the essential similarity of particulate and molecular Rayleigh scatter- ing,I7 the measurement of the latter proves to be extremely useful in aligning and calibrating the optical detection system. In addition information on the shape of the aerosol particles can be obtained from the dependence of the scattered light intensity on the orientation of the plane of polarization of the incident light in the same way as such measurements on gases can be used to determine anisotropies of molecular polarizabilities.COAGULATION OF MOLTEN LEAD AEROSOLS EXPERIMENTAL Lead aerosols were generated in the shock tube by the decomposition of TML in dilute mixtures with argon in the manner previously described.6 The operation of the 76 mm i.d. shock tube and of the recording oscilloscopes is similar also to that previously reported.6 The optical system for the light scattering measurements was set up as indicated diagram-matically in fig. 3. A Laser Sciences Inc. 2-W argon-ion laser gave a monochromatic beam of 800 mW at 488.0 nm. The plane of polarization of the beam is rotated from the vertical to the horizontal by the polarization rotator and is then focused at the centre of the shock tube.The light scattered perpendicular to the beam and to the axis of the shock ARGON LASER 1 IPLIER PT FOLARIZATION ROIATGR CROSS - SECTION OF SHCKASHOU( TUBE FIG.3.-Schematic diagram of the optical system. tube by molecules or particles at this focus is collected by a lens and passes through an interference filter (band pass 1.O nm) to eliminate thermal radiation. The scattered light is focused to give an image at a slit S whose width is carefully matched to that of the image in order to prevent as far as possible the thermal radiation and stray laser light from reaching the detecting photomultiplier P, and the photomultiplier output is displayed and photographed on an oscilloscope.Alignment and calibration of the detection system were conducted before each shock in the followingmanner. The shock tube was filled with filtered argon to a pressure of 800 Torr and the slit S (fig. 3) was traversed in a horizontal plane until a position was found which gave a maximum in the detected signal. In this condition simultaneous measurements of the output voltages Vkr and Vtr of the two photomultipliers P and PT respectively were taken. These measurements were then repeated with the shock tube evacuated to give Vpcand Vpc. The scattered light signals from the lead aerosols are calibrated using the value of (Vfr/ V4')-(Vsvac/Vpc). The shock tube was then charged with a TML+ argon mixture and a shock fired without further adjustment to the optical sytem the values of V and VT during the shock flow being displayed and photographed on an oscilloscope.The sensitivity of the technique was such that when the apparatus was initially set up the ratios (Vfr/ V#r) and (VPc/Vpc)were themselves in the ratio 20 :1. During the initial setting-up of the apparatus a check was made on the validity of the detection system by measuring the relative scattering cross-sections of CCl and Ar and these were found to be in the ratio 34 :1 as against a ratio of 38 1 calculated from litera-ture l 9-2l values. S. C. GRAHAM AND J. B. HOMER RESULTS LIGHT-SCATTERING MEASUREMENTS ON LEAD AEROSOLS A quantitative treatment of the time variation of the intensity of light scattered by a coagulating aerosol is feasible only for the period that the aerosol has the self- preserving size distribution and a constant volume fraction of particulate lead.The extent to which this ideal condition is approached depends critically on the rate of formation of lead vapour via the decomposition of TML and on the rate of nucleation of this vapour. Ideally these rates should be very fast in comparison with the available observation time for only after the nucleation of lead is complete will the size distribution of the lead particles begin to approach the self-preserving form. In practice the two rates are highly temperature-dependent though in opposite ways.6 The rate-determining step in the formation of lead vapour is the initial step in the decomposition of TML and this decomposition has been shown to display first- order kinetics.In contrast the nucleation rate is critically dependent on the super- saturation ratio and as shown previously,6 this ratio must exceed -50 for rapid nucleation to occur during the available observation time. For a total lead concen- tration of 7 x 1015 atom/cm3 corresponding to a particulate volume fraction of 2.4 x near ideal coagulation can be expected to occur somewhere in the tempera- ture range 870-1010 K the lower temperature corresponding to a limiting TML half-life of -1.O ms the upper temperature corresponding to a limiting super- saturation ratio of -50. Experimentally for this lead concentration near ideal coagulation was observed within the much narrower temperature range 920-960 K.I I 2 4 t;= 0 tc = timelms FIG.4.-Oscilloscope trace of the scattered light signal for a shock recorded under " near ideal " conditions. The output voltage VF has been displayed simultaneously at the two different sensi- tivities 1 V/cm and 0.01 V/cm. Zero time is assigned to the time of arrival of the shock front at the point of observation. Zero coagulation time is indicated as tc = 0. For this shock T = 930 K [Pb] = 7 x 10'' atom/cm3 [Ar] = 1.4x 10'' atom/cm3. Fig. 4 shows an example of an oscilloscope trace recorded for such a condition and demonstrates the overall sensitivity of the technique. This trace records a change in V!b by a factor of -1000 during the shock flow corresponding to a tenfold increase in mean particle diameter.As required by eqn (15) the corresponding plot of logloV,Pbagainst log, t is linear with a slope of 9 as shown in fig. 5 and these results represent to our knowledge the first time that this relationship has been tested directly. A similar time-dependence was found for all aerosols with total lead concentrations of -7 x lOI5 atom/cm3 in the temperature range 920-960 K the COAGULATlON OF MOLTEN LEAD AEROSOLS observed slopcs ranging from 1. I8 to I .22. Outside this temperature rmge very different patterns of behaviour were observed. At temperatures progressively lower than 920 K the critical supersaturation ratio is reached at progressively lower lead vapour concentrations so that coagulation is initiated well before the decomposition of TM L is complete.Because condensation of lead vapour is rapid after nucleation a condition is quickly reached where the growth of the particulate volume fraction of lead is limited by the rate of decomposi- tion of TML. A record from a typical low-temperature shock is illustrated in fig. 6(a)where the“acce1eration”of VFb is clearly greater than that of a t6/’ dependence and arises at least in part because the rate of aerosol coagulation increases with increasing particulate volume fraction. At temperatures below 820 K no scattered light signals were observed confirming the absence of particles under these conditions. 1.0 0.5 0.2 ,z. /’ LINE OF 3 ,*-UNIT SLOPE 0.I 0.0 5 Lf I I I I II 0.15 0.3 0.5 1.0 2.0 3.0 4.0 coagulation time/ms FIG.5.-A plot of log, V.’” against loglor from the oscilloscope record of fig.4. At temperatures above 960 K the decomposition of TML is very fast but the “ ideal ” conditions of coagulation cease to be achieved because the nucleation process becomes the limiting factor. Whilst rapid homogeneous nucleation occurs at high supersaturation ratios of lead vapour at progressively lower supersaturations (higher temperatures) the induction period before significant nucleation occurs lengthens and if sufficient particulate impurities are present (e.g. dust or PbO) heterogeneous nucleation may take over as the dominant nucleation process. We may then expect that condensation of vapour on to a relatively small number of particles may become the dominant growth process of the aerosol rather than coagulation.Experimentally we have found that at temperatures above 960 K (corresponding to a supersaturation ratio of <250) the scattered light records showed increasingly erratic variations indicative of heterogeneous nucleation (fig. 6(b)) and on increasing delay between the arrival of the incident shock wave and the onset of a rapidly increasing light intensity in keeping with a decreasing homogeneous S. C. GRAHAM AND J. B. HOMER nucleation rate. No particulate scattering was detected for shocked gas temperatures above 1100K. An investigation of the shape of the coagulating lead particles was made by the dependence of the scattered light intensity on the angle between the plane of polariza-tion of the incident beam and the scattering plane.When the two planes were 0123 0 1 2 3 timelms FIG.6.4sci11oscope trace of the scattered light signals for shocks recorded at (a) T = 830 K [Pb] = 6.8 x lot5 atom/cm3 and [Ar] = 1.4x lot9atom/cm3 ; (6) T = 966 K [Pb] = 6.2 x loi5 atom/cm3 and [Ar]= 1.26~ IOl9 atom/cm3. parallel the pattern of the scattered light intensity for shocks in the near-ideal range was identical to that observed for the perpendicular configuration (fig. 4) but was uniformly weaker by a factor of 95. To within experimental error this is the same as the ratio of 100 1 which we observed for molecular Rayleigh scattering by SF6 and by CCl, and thus confirms the interpretation of the scattered light signals from the coagulating lead aerosols as Rayleigh scattering from spherical particles.DETERMINATION OF ABSOLUTE PARTICLE SIZES AND COAGULATION RATES So far the interpretation of the scattered light measurements has required only that the intensity of this light be proportional to the output voltage of the detecting photomultiplier. However these measurements are potentially capable of yielding absolute values of particle sizes and coagulation rates but to do so requires a calibration of the scattered light intensity. We used the calibration procedure based on the detection of molecular Rayleigh scattering which allows the determina- tion of the instantaneous differential cross-section per unit volume of aerosol c$b from the voltage YsPb. The value of a& is given by Here aAris the total scattering cross-section of the argon atom at 488.0 nm and NAr is the density of argon (atom/cin3) at which the voltages V$' and Y+' were recorded.VFb is the output voltage of the photomultiplier used to record the intensity of the transmitted beam after the plateau of constant absorption had been reached. R is the ratio of the photomultiplier gains used during the measurement of Vt' and V!b respectively. The cross-section a& is related to the particle size distribution and to the optical properties of liquid lead through the equations COAGULATION OF MOLTEN LEAD AEROSOLS a" = a",/v (19) -( fi2-a" = 3 -1). 4x fi2+2 Here a" is the polarizability of a lead particle (assumed spherical) of volume v a" is the volume polarizability of liquid lead and rfi is the complex refractive index of lead at 488.0 nm.Using eqn (16) the required relationship between v the instantaneous mean particle volume and Y,'b is given by ij = kcaljbv? (21) In this equation the value of J(rG2 -l)/(6i2 +2)12used was 1.22 and was calculated from Hodgson's 23 optical measurements on liquid lead at 1059 K. The value 6.45 x lo-" em2 used for the cross-section of argon at 488 nm was calculated from the measurements of Buckingham and Bridge 21 at 632.8 nm. 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -.-0 0 Y 2 5 0 a 0 0 0 timelms FIG.7.-Variation in mean particle volume V and mean particle diameter (67/,)3- with time calcu-lated from the observed variation of V.'" with time shown in fig.4 and 5. S. C. GRAHAM AND J. B. HOMER 95 PARTICLE SIZES The knowledge of kcalib allows the determination of the mean particle volume at any instant from VFb and an illustration of the change in mean particle volume during the shock flow time is shown in fig. 7 for a typical shock recorded under near-ideal conditions. The results of fig. 7 are taken specifically from the experi- mental record of fig. 3 where the lower limit of detectibility by light scattering corresponds to a mean particle diameter of 1.2 nm and in which the conditions correspond closely to a similar experiment recorded and analyzed in depth in previous work.22 The particle size deduced in the present work is commensurate not only with the size of particles (diameter 10-20nm) removed from the shock tube after the experiment but also with that predicted by the condensation COAGULATION RATES As shown earlier in eqn (IS) the rate constant kcoag,satisfying the equation 6 = kcoag t6/’ has the form 6kT -5( 47L /kong = [12 -3) (p)i’2G‘ayilb’5.(23) Experimental values of kcoagwere obtained in the following manner. For each plot of log, VsPb against log, t (fig. 5 for example) the best straight line of slope 6/5 was drawn through the experimental points and the value of the intercept log, kgraph satisfying the equation log, V!b = log, kg,,pl,+(6/5) log, t was obtained graphically. The required experimental value of k,,, is thus given by the product (kcalib kgraph).The results for five shocks recorded under near-ideal conditions are compared in table 1 where a Hamaker constant for lead of 4 x 10-l2 erg has been assumed and where it is seen that the experimental values of (kcalib kgrap,,) exceed the values of kcoagcalculated from eqn. (15) by a factor of -2. TABLE 1 .-RESULTSOF FIVE SHOCKS RECORDED UNDER NEAR-IDEAL CONDITIONS WHERE [Pb] = 7x 1015atom/cm3 AND [Ar] = 1.4~ 10’’ atom/cm3 The mean value of kcal,b kgraphlkcoag for these records is 2.192 0.22 1018kolibl 1o3kgragh/ 1OISkcalib!igrsph/ 1015kcoag / kc adgraph T/K (cm3/\’) (V/S6/5) (cm3/s6/5) (cm3/s6/5) kcoa 960 2.29 1.01 2.31 1.04 2.22 920 2.41 1.20 2.89 0.99 2.91 930 2.22 0.90 2.00 1.oo 2.00 920 1.70 1.22 2.06 0.99 2.09 940 5.22 0.33 1.74 1.02 1.71 This unexpected result cannot be attributed solely to experimental error and an explanation must be found in either an overestimation of kcalib or an underestimation of k,,,,.Of the constants required in the analysis those with the greatest uncertainty are perhaps I(G2-1)/(fi2+2)12and A the Hamaker constant. Optical properties are sensitive to the presence of impurities and it is possible that the optical properties of the coagulating lead aerosols are different from those reported by Hodgson 23 for pure lead at 1059 K namely E = -10.87 c2 = 14.10 where -k2 = G2. The magnitude of both E and E~ are large and as a result the value of [(&I -I)(& +2)+&;12+9& [(El +2)2 +&$I2 = 1.22 COAGULATION OF MOLTEN LEAD AEROSOLS is also large and is insensitive to small changes in either c1 or c2.However the possibility that small quantities of impurities (e.g. of oxygen or carbon derived from TML) are present in the particulate lead phase and have modified substantially the values of c1 and c2 cannot be dismissed. Indeed a similar implication arose from our results of the light absorption of those aerosols from which the absorbance can be calculated to be a factor of 1.34 greater than would be predicted from Hodgson's values. As to the uncertainty in the Hamaker constant there is no reliable value for lead and the value of 4 x erg used to determine k,,, in table 1 is based on the known values for A of several metals.I5 This value gives a ratio A/T of 4.2 x lo-" erg/"C and Fuchs and Sutugin have shown l3 that for A/T>3.3 x lo-" erg/"C further enhancement of free-molecule collision cross-sections is insensitive to increases in A/T and this is certainly borne out in fig.2. CONCLUSIONS The experiments have been successful in measuring the rate of coagulation of an aerosol at high temperature and in yielding a time-resolved absolute measure of the mean particle size. The particle size deduced for the lead aerosol is commensurate with the previous interpretation of the system. The rates of coagulation display the t 6/5 dependence of a free-molecule aerosol but the absolute rates apparently exceed those calculated by a factor of two. This difference is not large. It may be due either to a deficiency in the collision model used to calculate the theoretical coagulation rate or quite conceivably to an over-estimation of the calibration constant which relates the recorded light intensity to the mean particle volume.We gratefully acknowledge the assistance of Mr M. A. McLeod in the experi- mental work and of Dr A. Robinson in the computational analysis. F. S. Lai S. K. Friedlander,J. Pich and C. M. Hidy J. Colloid Interface Sci. 1972,39 395. G. D. Ulrich Combustion Sci. Techn. 1971 4 47. G. M. Hidy and J. R. Brock The Dynamics of Aerocolloidal Systems (Pergamon Press New York 1970). N. A. Fuchs and A. Sutugin in Topics in Current Aerosol Research ed. G. M. Hidy and J. R. Brock (Pergamon Press New York 1971). D. L. Swift and S. K.Friedlander J. Colloid Sci. 1964 19 621. 'J. B. Homer and I. R. Hurle Proc. Roy. SOC.A 1972,327 61. 'N. A. Fuchs The Mechanics of Aerosols (Pergamon Press New York 1964). * J. R. Brock and G. M. Hidy J. Appf. Phys. 1965,36,1857. G. M. Hidy J. Colloid Sci. 1965 20 123. lo G. M. Hidy and D. K. Lilly J. Colloid Sci. 1965 20 867. S. C. Graham and A. Robinson to be published. l2 H. Hamaker Plzysica 1937 4 1058. l3 N. A. Fuchs and A. Sutugin J. Colloid Sci. 1965 20 442. l4 J. Gregory Adv. Colloid Interface Sci. 1970 2 396. J. Visser Adv. Interface Sci. to be published. G. Bohme H. Krupp and W. Schnabel in Molecular Processes on Solid Surfaces ed. Drauglis (McGraw-Hill New York 1969) p. 61 1. l7 H. C. van de Hulst Light Scattering by Small Particles (John Wiley and Sons Inc.New York 1957). M. Kerker The Scattering oj Light and Other Electromagnetic Radiation (Academic Press New York 1969). l9 B. Linder J. Gem. Phys. 1960 33 668. 2o R. R. Rudder and D. R. Back J. Opt. Soc. Amer. 1968,58 1260. 21 A. D. Buckingham and N. J. Bridge J. Chem. Phys. 1964,40,2733. 22 J. P. Homer and A. Prothero submitted to J. Chem. SOC. 23 J. N. Hodgson Phil. Mug. 1961 6 509.

ISSN:0301-5696    

DOI:10.1039/FS9730700085

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

GENERAL DISCUSSION Mr. K. C. Pointon (Shefield University) said Our method is likely to produce pure particles because if the background temperature is sufficiently low they will have crystallized before touching any foreign surface. The shapes and sizes of fall-out particles were examined by scanning electron microscopy. Particles in the clouds are allowed to settle on to a flat tip of highly polished silica held by the substrate probe. The probe is then withdrawn from the generating chamber into the glass manipulation section where a layer of 60 :40 Au-Pd approximately 1008 thick is deposited on the silica surface by vacuum evaporation. This is to protect the fall- out from reaction with the atmosphere during transfer to the electron microscope. Fig. I and 2 are micrographs of fall-out from Zn aerosols produced at a background temperature of 0.74 Tf.The Au-Pd film deposited on the substrate shown in fig.la and Ib was thick and has exfoliated ; most of the Zn particles have adhered to the Au-Pd layer but where particles have remained on the silica surface holes have been plucked in the exfoliated film. The Zn particles are typically 1-5pm diam. and have well-developed crystal faces although the particle shape is sometimes complex. A polyhedral crystat with a hexagonal profile would appear to be typical of the crop of particles formed by condensation in the cloud chamber. Kimoto et a2.l. have observed the same well-defined crystal habit for Zn particles prepared by evaporation in purified argon at low pressure.Their crystallites were equiaxed and the morphology was consistent with the normal c.p.h. lattice of Zn. Kimoto reports that a small amount of oxygen in the argon caused a remarkable deterioration in the crystal habit of the particles; they became very irregular and rough. Most of the particles shown in fig. 1 and 2 are well formed crystallographic- ally which suggests they are pure. If twinkling results from the scattering of light by reflection at crystal faces a spheroidal particle with a large number of flat faces would be expected to twinkle rapidly and rather weakly. This may explain the indistinct flickering observed. It would be difficult to understand however why the Zn particles in the form of hex-agonal prisms clearly visible in fig. 2b did not show a distinct twinkling effect.From the telescopic observation that the Airy images of the particles in a Pb smoke became brighter as the smoke thinned out we believe Pb aerosols must agglomerate considerably at high particle densities. We have yet to test this inter- pretation by examination of Pb fall-out. Fall-out from clouds of Zn aerosols shows that agglomeration was a rare event (fig. 2a 21). This is in keeping with the absence of a brightening effect in this case. Dr. S. C. Graham (Shell Res. Ltd. Chester)said 1do not consider that small metal particles with x<O.1 where x = nd/A would give preferential back scattering at visible wavelengths. As indicated in my reply to Kerker’s question following my paper with Homer the critical terms in the expansion of Qsca as a power series in x are the lowest order contributions to the expressions for the electric and magnetic dipole terms a and bl respectively.Tn the limit as x -+ 0 (munspecified) QbCd = (6/.~2>(1a,12-I-lbll’) where la1I2 = IsI2x6and lbl12 = Is12u2x10. ‘ K. Kimoto Y. Karniya M. Nonoyama and R. Uyeda Jup. J. Appl. Phys. 1963,2,702. K. Kimoto and I. Nihida Jag. J. Appl. Phys. 1967 6 1047. 97 s7-4 GENERAL DISCUSSION Thus the importance of lb112which causes the high back scattering is determined by the ratio For the simple Rayleigh Q,J= 6/x21p12x6)to be accurate to 1 % one must have at least an approximate upper limit on x,viz. xG0.1. But for x = 0.1 the ratio lb112/1a112reaches 1 % when luI2 = i.e.luI2 = 100 so that = 100 or lrn2+2I2 = 9x lo4. 1 1 Assuming that m has the approximate form m = (1/~2)Iml(l-i) which is a good approximation for metals at infra-red and longer wavelengths where such high m values are found (ref. (17)) chap. 14) then Jm2+2I2= lml4+4 = 9 x lo4 so that Iml = 17.3 and m = 12.3-12.3i. If one takes xGO.31 as the limit of the Rayleigh scattering domain for real m then lb112/1a112 reaches for lm2 +212 = 9 x lo2 or m2x30. There are few if any metals with such high values of m2 at visible wavelengths and at x = 0.3 the simple Rayleigh expression will certainly not be accurate to within 1 % even for real m values. Though metals do not have such high values of m at visible wavelengths much higher values are found at longer wavelengths.For example van der Hulst (ref. (17) pp. 268 and 288) quotes an m value of 37 -41i for platinum at A = 10 pm and 236-2361' for silver at A = 30 pm. For larger values of x,particularly 0.5 <x,< 5 different considerations apply and the back scattering efficiencies of metals at visible wavelengths vary in a manner similar to that found for a perfectly reflecting sphere and I am grateful to Kerker for drawing my attention to this possibility. Van der Hulst (ref. (17) chap. 14 especially pp. 284-287) has shown for spheres with m = 3.41 -1.94i (not untypical of the m values of metals at visible wavelengths) that the scattering efficiencylsteradian in the backward direction rises monotonically from x = 0 to a large maximum near x = 1 with a deep minimum at x = 1.65 followed by further less extreme maxima and minima.For m = 00 (and for m = 00 -ico) a similar series of maxima and minima are found at similar x values. How-ever at any given x,the magnitude of the back scattering efficiency is invariably greater for m = 00 than for m = 3.41-1.94i and presumably for any other finite value of m also. Because these maxima and minima which are very unlike the resonances observed for particles with real m are well spread out with respect to the x co-ordinate and because the xvalues at which they occur are insensitive to the value of m it is possible that the variation in back scattering efficiency as a function of x could be used to determine the size of particles in an aerosol. In principle measurements could be made on individual particles or on a number of particles provided that the aerosol was not too polydisperse.For a particle or particles with rapidly changing sizes (co- agulation or condensational growth) one would make observations at a fixed wave- length. For particles of a constant size one would vary x by varying the frequency of the incident radiation. Are such measurements of back scattering efficiencies possible and if so valuable in Pointon's experimental system? Prof. M. Kerker (Clarkson Coll. Techn.,Potsdam) said Has Pointon looked at the small metallic particles with white light and if so what is the colour? It would be interesting to observe whether these particles behave as Rayleigh scatterers or whether (a) magnification 2300 x (b) magnification 5700 x FIG.1.-Fall-out from Zn aerosols at a background temperature of 0.74 Tf.[Tofacepage 98 (n)magnification 2300 x (11) magnification 5700 x FIG.2.-Fall-out from Zn aerosols at a background temperature of 0.74 Tf. GENERAL DISCUSSION as for small perfectly reflecting particles they scatter preferentially in the backward direction. Mr. K. C. Pointon (Shefield University) said In reply to Kerker we have not used white light only green light. Particles that are easily visible with the telescope are 1 pm or larger in diameter. The size of the Airy disc however is not determined by the size of the particle but by the telescopic aperture. Therefore the brightness of the particle determines whether it is visible.The angle between the light incident on the particles and the light received by the telescope has been varied over a sub- stantial range by introducing vitreosil light pipes and angled metallic reflectors into the generating chamber. There is a great improvement in the brightness of particles when the viewing direction is nearly in line with the incident beam. We normally observe the particles against a dark background so that they appear self-luminous. By chance we observed an interesting effect which might relate to Kerker’s question about colour. When Ca vapour falling from the supersaturator crossed the path of green light entering the eye after reflection from the wall of the viewing pipe it extinguished the light. The vapour looked like a stream of black treacle.We do not know whether this effect was the result of atomic absorption or multiple scattering from particles in the very earliest stages of growth. Dr. S. C. Graham (She12 Res. Ltd. Chester) said With regard to the extinction of the stray green light (A = 5461 A) by the Ca vapour or calcium particles surely such extinction is due to absorption rather than scattering as the former is relatively so much greater for small particles than for large ones. Because Pointon’s observations are normally made against a dark background he would not normally observe such absorption. Dr. E. R. BuckIe and Mr. K. C. Pointon (Shefield University) (communicated) In reply to Graham the extinction could still be due to back-scattering.How could light of this wavelength be absorbed by Ca vapour ? The effect is interesting because it may indicate that ultra-fine particles are formed in the vapour immediately after it leaves the supersaturator. Using the telescope we do not see any particles against a dark background at this stage so that they could either be very small strongly back- scattering or both. Dr. S. C. Graham (Shell Research Ltd. Chester) (communicated) In reply to Buckle and Pointon I do indeed think that the “ stream of black treacle ” observed by Pointon was extinction caused by particles and not by calcium vapour. If the particles were sufficiently small (particle circumference/wavelength 50.2) which seems probable as simultaneous scattering was not observed then this extinction would be due to the true absorption of light within the particles rather than to scattering of light away from the forward direction (see Van der Hulst Light Scattering by Small Particles chap.14). I do not agree that the scattering of 5461 8 radiation by calcium particles into the backward hemisphere will ever be substantially greater than scattering into the forward hemisphere. Dr. E. R. Buckle (Shefield University) said I would ask Graham two questions about his paper with Homer. First his analysis of the light scattering data in terms of coagulation kinetics relies as he states on the attainment of a self-preserving size distribution. The mathematical analysis depends on the assumptior? that the size distribution function can be put into a form in which the time and the particulate 100 GENERAL DISCUSSION volume are separable (see eqn (18) of Dunning’s paper).Is there any independent evidence that this is a reasonable assumption on which to base the interpretation of your experiments? The second question is about the slope of the plot in fig. 5. I think it correct to conclude only that this is in keeping with the form of the expression for the classical free-particle collision parameter (eqn (l)) since one obtains fic~t~/~ from eqn (3) without making the assumptions that lead to eqn (1 5). When he tested the experimental value of the coefficient k of t6l5 against the one in eqn (15) there was a discrepancy. A feature of this comparison worries me. The theoretical coefficient kcoag from eqn (15) depends on the hypothesis of a self-preserving distribution but so does the “ experimental ” one k,, = kcalibkgraph because kcalib(eqn (22)) is derived from eqn (16).Therefore the quantities compared both depend on this hypothesis. Is this connected with his difficulty in getting an exact match of the theory with the experimental results ? Dr. S. C. Graham (Shell Res. Ltd. Chester) said With regard to Buckle’s first question when free-molecule or diffusion-controlled (Smoluchowski) coagulation is simulated on a computer by feeding in an initial distribution and then following the 1.75-1.50 -1.25 --1.00 -0.75 2 0.5c 0.25 -0.25 I -o*ml -0.7 5 -~.&--+-210 2f5 20 315 410 415 5fo 515 652 1 FIG.1.-The error function E($(q)) plotted against q.change in number concentration of each particle size using the known expressions for the collision rate density for particles of different sizes it is found that after sufficiently long “ coagulation ” times the computed distributions (expressed in dimensionless form) tend towards the solution of the corresponding integro-differential equation which was derived (unlike the computed distributions) using the sex-preserving hypothesis. To my knowledge no-one has yet proved that the limiting asymptotic form of the computed distributions has to be the corresponding self-preserving size distribution but there exists considerable verification that this is the case particularly for diffusion-controlled coagulation.The closeness of our computed distribution to the self-preserving distribution can be examined by feeding the computed value of t+h designated t,bcomp for each q into GENERAL DISCUSSION eqn (6) of our paper and plotting the resultant error function E($,omp),(Le. the 1.h.s. of eqn (1 6)) as a fupction of q. If $camp is identical to the self-preserving distribution then the error function is the straight line E($comp(q))= 0. The following figure illustrates E($comp(q)) for our own computed distribution as well as for those of Ulrich and of Lai Friedlander et al.,and shows how close our computed distribution is to the self-preserving distribution. With regard to the second question Buckle is correct that the t6/5-dependen~e of the particle volume is a basic feature of free-molecule coagulation and is not special to the self-preserving hypothesis.However we do not observe V(mean volume) directly but rather a scattered light intensity I where This last equation is true for any arbitrary dimensionless size distribution $arb where $arb is defined by Nv t) = (N&/$)$ardq)* Now if $arb were not the self-preserving distribution one would expect s@(q)g2 dq to be time-dependent and thus a graph of log I against log t would not give a linear plot of slope 6/5 even if a graph of log vagainst log t were to give such a plot. There-fore the fact that we do observe experimentally a linear plot of slope 6/5 for log I against log t strongly suggests (a) that l$(q)g2 dg is a constant independent of time and (b)that V,the mean volume varies as t6l5.Incidentally the “ classical ” approximation that every particle has the same volume (which is clearly impossible for a coagulating aerosol) is equivalent to defining ~, a “classical ” size distribution where i+hclass(q)= ~ 3 where 6~is the Dirac delta function. Because at any instant q = 1 it follows that every function of t,hclass is time-independent and thus $class is in a sense selfpreserving. However $class has no special significance and it is not the solution of any physically significant equation. From the above in order to relate I to Vat any instant we have to make an assumption about the particle size distribution given that we have experimental evidence as well as theoretical grounds for believing i$(q)g2 dq to be a constant independent of time.There are no good reasons for assuming that $ = J1, but there are good grounds for believing @ to be the self-preserving size distribution (i.e. the solution to eqn (6)of our paper). In particular the lead particles are formed at extremely high supersaturations so that homogeneous riucleation is rapid and gives a large number of very small particles. These are precisely the conditions that are required to allow the self-preserving size distribution to develop early in the coagula- tion process. We therefore assume that we have the self-preserving size distribution and examine the consistancy of this assumption in particular by comparing the “ experimental ” coagulation rate Constant with the theoretical one and we find that the ratio of the two kcalibkgraphlktheor kc‘cxperimental” lktheor 2.If we made the classical approximation t,hclass(g)= Jl,, this ratio would have the approximate value 2 x I .84 x (1.1 3)6/s x (2.294/2.327)6/5z4. In this last equation we have GENERAL DISCUSSION and finally 2.327 Prof. M. Kerker (Clarkson Coll. Tech. Potsdam) said Has Graham given consideration to the possibility because of the high complex refractive index that these particles might not scatter according to Rayleigh’s limiting equation for a small dielectric particle? It might be useful to carry out a “ Mie ” calculation for comparison with the Rayleigh theory. This might be the source of the discrepancy between the observed and calculated coagulation rates.Dr. S. C. Graham (Shell Research Ltd. Chester) said In reply to Kerker the scattering efficiency of a sphere (Mie theory) is given by Expanding the Mie coefficients a and b in powers of x the first few terms (ref. (17) of our paper pp. 143-4) are al = isx3(1-tx2 +isx3) +- .; bl = ism5+ ...; (2) a2 = isox5+ . . . ; b2 = ...; where The Rayleigh scattering formula refers to the limiting value of Qsca as x+O and mx-d where (2n+l){la,)2+lb,12) + 31a,I2 3 31s12x6. Whilst s t and w assume small limiting values as m-,00 u increases rapidly and without limit so that the expansion of the b as a power series in x cannot be used even as x-0. However for lead at 3 = 488 nm m2 = -10.9-I4li so that lbl12,which has the value 1-8.9-14.1i12x10/(30)2= (0.31)2x10 is still small.For xG0.1 which corresponds to the upper size limit of the lead particles at the end of the shock flow the contribution of this term to Qsca is <1 % and is quite negligible. However the use of the Rayleigh formula does introduce errors >1 % for lead particles with greater than 0.1. Thus la I2 w ls12x6(1-tx2-isx3)(1-t*x2+is*x3) z ls12x6(1-2 Re(t)x2) and for m2 = -10.9-4i 2 Re(t) = 1.35. GENERAL DISCUSSION The term lbi12gives the contribution from the oscillating magnetic dipole and as van der Hulst has shown (ref. (17) p. 160) it is the interference between the induced oscillating electric and magnetic dipoles which gives a very small particle with m = 00 its characteristically high back-scattering efficiency.For light scattered perpendicular to an incident linearly polarized beam and scattered perpendicular to the polarization of the incident beam the relationship between the (differential) scattering cross-sections of a Rayleigh particle and a perfectly reflecting particle (m= 00) of the same size is particularly simple. For a Rayleigh particle this cross-section is given by and for the latter Cdiff sca(B= 4= x/2) = a2x4 (ref. (17) pp. 12 127 and 159). In conclusion the value of m for lead at 488 nm is not large enough to invalidate the use of simple Rayleigh formulae to calculate total and differential scattering cross- sections of particles with sizes satisfying the condition x = nd/;l<O.l.

ISSN:0301-5696    

DOI:10.1039/FS9730700097

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Formation of Soot Particles BY P.A. TESNER All-Union Research Institute for Natural Gas Moscow obl. Razvilka VNIIGAS U.S.S.R. Received 1st January 1973 Probable mechanisms are discussed of the formation processesof pyrolytic carbon films and soot particles based on experimental investigations of their formation rates. Both are two-stage processes including nucleation and growth of nuclei. The formation of pyrolytic carbon from methane at temperatures below 1300 K is a molecular process. The activation energy of the formation of a plane nuclei is about 80 and of their growth about 50 kcal/mol. The formation of sqot particles may take place in two ways differing in the nature of the nuclei as well as in the structure of the soot particles obtained. The formation of soot particles during the burning and thermal decomposition of hydrocarbons is of a dual nature the strictly physical laws of the creation of a new dispersed solid phase being complicated by a chemical process.The process as a whole is difficult to investigate and has not yet been adequately studied. Discussed below are recent experimental results on the kinetics of both formation and growth of soot particles as well as some ensuing conceptions about the mechanism of such processes. STRUCTURE OF SOOT PARTICLES The soot particles have a very compact structure. The density of their material equals 2.0g/cm3 which is only 10 % less than that of three-dimensionally-ordered graphite (2.26 g/cm3). Following Biscoe and Warren and on the basis of the results of X-ray investigations it has been assumed until recently that the soot particles comprised separate irregularly located crystallites consisting of several approximately parallel graphite layers.Such a structure was termed " turbostratical ". The application of high-resolution electron microscopes 3* provided proof but graphite layers and not crystallites serve as building blocks for soot particles. These layers are bent to conform to the shape of the particles and have the form of shells replicating the outer surface of the particle. Thermal soot particles consist of concentric spherical shells. In particles of other types of soot only the external shells repeat the shape of the outer surface the internal structure of such particles containing obviously several centres of growth.The distance between the layers has a spread conforming to the general distribution law. The compact and largely regular structure of the soot particles should be taken into account when considering the growth mechanism. It is evident for instance that one cannot logically imagine the creation of such a structure by consecutive association of more or less large blocks. Most probably such a structure is the result of a molecular growth process for which the term "chemical crystallization " would perhaps be the most exact one. Experimental results have actually proved this. 104 P. A. TESNER 105 GROWTH OF SOOT PARTICLES The growth process of a soot particle is similar to that of a pyrolytic carbon film on a wall.It can be experimentally investigated in the absence of soot particle formation within a wide range of temperatures. The growth stage of soot particles has therefore been better investigated than the formation stage. Nevertheless reliable data about the kinetics of pyrolitic carbon growth during the thermal decomp- osition of methane are available up to 1300 K only.5 The growth rate of pyrolytic carbon is of the first order and is considerably inhibited by hydrogen. This inhibition effect can be well described by the Langmuir equation and can be attributed to a chemisorption of hydrogen. The growth rate of soot particles (in g cm-2 s-l) can be expressed as follows W = 260 pc~,[1- Bmt/(1 +BpH,)]exp (-66 OOO/RT) (1) where pCH4 and pH2are the partial pressures of methane and hydrogen respectively and R has units of cal mol-1 K-'.The inhibiting effect of hydrogen decreases when the temperature rises. The constant B in the Langmuir equation equals 40 at 1073 K and 25 at 1173 K. The activation energy of the process equals 66+2 kcal/inol within a temperature range 1000- 1300 K. The growth rate of a pyrolytic carbon on a plane surface is governed by the same laws as that of the growth on the surface of soot particles and possesses the same activation energy but the rate constant is about 5 times higher. Possible causes of such a discrepancy are discussed below. The growth rate of a pyrolytic carbon film is closely associated with the size of the crystallites being formed. Any individual hydrocarbon has at every temperature some constant average crystallite size for a stationary growth rate.It is reasonable to believe that the microcrystalline structure of the pyrolytic carbon film will reflect the molecular mechanism of its formation from molecules of the gaseous phase. Let us assume that each of the crystallites is being formed as a result of the growth of a nucleus in a basic plane and that this growth continues until the crystallites which expand towards each other meet. Thus the size of the crystallites depends on the rate of two processes namely the formation of nuclei and their growth. Conse-quently if the growth rate and the average crystallite size are known from experiments the formation rate of nuclei as well as the growth rate of crystallites can be determined by calculation.So for instance the growth rate of a film obtained from methane on a plane surface at 1273 K in absence of hydrogen equals 250A/s the average size of the crystallites La being 600k These values correspond to a nuclei formation rate of C = 2.6 x lo9 nuclei cm-2 s-* and to a crystallite growth rate of W = 22 A/s. The elementary collision theory permits one to determine from these data the activation energy of the nuclei formation as well as that of the crystallite growth. Assuming that a planar nucIeus consists of a single atom of carbon the activation energies of the nuclei formation Enand crystallite growth Eg can be found from the equations En = 2.3 RTlog (NfIC) (2) Eg = 2.3 RTlog (NfIN& (3) where No = rate of film growth (atoms ctr2 s-~)and Nf= number of collisions of methane molecules upon the surface (molecules cm-2 s-l).Substituting the values cited above for methane at 1073 K gives En = 81 and E = 52 kcal/mol. Consequently the experimentally activation energy of the film growth FORMATION OF SOOT PARTICLES process (E = 66 kcal/mol) represents the gross activation energy of both elementary processes. According to these concepts the formation of pyrocarbon is a peculiar branched- chain molecular process taking place on surfaces. The carbon atoms are built-in into a planar graphite lattice as a result of the interaction of methane molecules with surface carbon atoms which have free-valence electrons. The hydrocarbon radicals of the gaseous phase do not participate in this process.On the contrary some of the methane molecules decompose on the growing carbon surface and produce new radicals while others break down directly into carbon and hydrogen. Thus the solid surface generates either CH3or CH2 radical^.^ This mechanism considered explains the difference of the pyrocarbon formation rates on the surface of soot particles and on a plane surface as being due to different sizes of the crystallites. Owing to the small dimensions of the soot particles the crystallites cannot reach their stable size corresponding to the given temperature and this slows down the total growth rate. It is also possible that the growth rate of a curved graphite layer is less than that of a planar one.This molecular growth mechanism of pyrocarbon during the thermal decomposition of methane is common for other hydrocarbons. This can however be regarded as true only for temperatures below 1300 K. There are not enough reliable data on the kinetics of the growth at higher temper- atures,6 largely resulting from the undetermined composition of the gas interacting with the wall. Existing data on the formation kinetics and structure of the pyro- carbon nevertheless allows one to state that the chain process of its growth takes place at temperatures up to about 2500 K. Actually pyrocarbon films obtained at high temperatures show a pronounced texture and an anisotropic microcrystalline structure 'not differing substantially from those produced at lower temperatures.And kinetic data for the rate of pyrocarbon growth for methane and acetylene at 1800 to 2100 K allows one to conclude that for films growing at such temperatures one active collision of a molecule upon the surface takes place per lo3to lo4 molecular collisions. There is no reason definitely to claim that the growth of the film at higher temper- atures is such a strictly molecular process as that below 1300 K. On the contrary one may believe that radicals contained in the gaseous phase can play a more or less important role under such conditions. FORMATION OF SOOT PARTICLES The classical scheme of aerosol formation including nucleation and growth is fully applicable to soot formation processes. But unlike condensation nuclei of soot particles are products of a chemical reaction.And since the number of molecules required to form a nucleus cannot enter the reaction simultaneously there is no doubt that the nucleation of a soot particle is of a complex nature and comprises a number of consecutive elementary acts. The understanding of the soot particle generation mechanism requires measurements of the process rate under various conditions. The obtaining of such data involves considerable difficulties due to the high rates of the process. Nevertheless available results of such measurements although far from complete can be considered important. They are briefly summarized (i) the formation rate of soot particles has a sharp maximum corresponding to a small degree of total decomposition of the hydro- carbon.g*lo (ii) The soot particle formation process is characterized by the presence of concentration thresholds and an induction period.6 (iii) The initial growth rate P.A. TESNER of soot particles is considerably (in some instance by two orders) higher than the stabilized growth rate of a pyrocarbon surface. l1 (iv) During the thermal decomposition of diluted acetylene soot particles may form by two substantially different processes. The activation energy of one of them is 33 and of the other 175 kcal/mol.l (v) For self-combustion of acetylene the dispersity of the soot formed will be the greater the higher the temperature in the front of the flame. A maximum dispersity will be reached in detonation of acetylene when-due to minimum losses of heat from the front by radiation-the temperature reaches its highest value.The specific surface of soot obtained from detonation of acetylene attains 180 m2/g (average particle size 170A). The specific surface of detonation soot does not depend on the initial pressure. (vi) The absolute rate of soot particle formation in the diffusion-type burning of an acetylene +hydrogen mixture equals IOl5 particles ~m-~ When acetylene detonates at an initial pressure of 10 kg/ s-l. cm2 this rate exceeds lOI9 particles ~m-~ s-l. All the experimental facts and theoretical considerations suggest the following model. The formation of soot particles is like any process of the initiation of a new dispersed phase limited by the nucleation. Nuclei may be of two types namely either complex unsaturated polymer molecules or simple radicals.The properties of the primary nucleus define the process of its further growth and the properties of the soot particles produced. A rough analogy may here be drawn between a nucleus and a DNA molecule in which a genetical code is incorporated. The "molecular nucleus " obtained as a result of reactions including condensation aromatisation and dehydrogenation continues to grow by virtue of the same reactions. The product will be a soot particle having an indefinite structure being X-ray amor- phous and containing a considerable amount of volatiles. Such a process was investigated by Homann et all3*l4 in rich premixed flames of acetylene and was observed by Johnson and Andersen lS as well as by Tesner and Altshuler during the thermal decomposition af acetylene.It seems that the growth rate of these soot particles considerably exceeds that of the pyrocarbon. A "radical nucleus " initiates a quite different chain of transformations which finally produce soot particles with a compact regular and well-investigated structure. The first step of these transformations should be the conversion of the radical nucleus into a nucleus having a physical surface i.e. into one which is similar to the nucleus of an aerosol particle produced by condensation. Such a nucleus is a soot particle of a minimum size and its further growth process is similar to the pyrocarbon growth described above. The formation process of a nucleus from a radical-nucleus has not yet been investi- gated and is most difficult to investigate.Taking into account all that is known about radical processes this stage may be conceived as follows. The initial interactions between the radical nucleus and the original hydrocarbon molecules are radical reactions resulting in the formation of new radicals. It is quite clear that the activity of the radicals falls in the course of this process by formation of carbon-carbon bonds. Hence the rate of their interaction with the original molecules will decrease too. At a certain moment the radical nucleus will lose its radical properties attain the pro- perties of a physical surface and become a soot particle of minimum size thereby representing a nucleus. Consequently in contrast to the usual radical chain in the chain under consider ation more and more heavy and less active radicals will be formed and its propagation rate will gradually slow down.So,for instance for acetylene the elementary reaction act and the chain leading to the formation of a nucleus are as follows 108 FORMATION OF SOOT PARTICLES elementary act chain cn+ CtH2-Cn+2 + H2 c2-c4-c6- . .-c" /radical nucleus \ nucleus The formation of a great number of soot particles from radical nuclei may be described by equations similar to those of a branched chain process with mutual termination of chain^.^ The termination represents in this process the destruction of radical nuclei on the surface of the particles formed. Concerning the branching which was postulated in order to explain the experimentally observed increase of the particle formation rate its mechanism is not understood.A comparison of calculations and experimental data permits the determination of the activation energy of the formation of radical nuclei. For the formation of soot from acetylene its value is around 170 kcal/mol. Obviously the C2 radical is the only one requiring such an activation energy for its formation from acetylene. The chain-type scheme of the nucleation and growth described above cannot be regarded as strictly proved but it explains satisfactorily the experimentally observed regularities. This scheme does not take into account the coagulation of the growing particles which actually takes place and results at late stages of particle growth in the formation of a chain-like structure.The regions of existence of both soot formation processes described above are still indefinite. Probably the first process initiated by a molecular nucleus takes place at lower temperatures and at small concentrations of hydrocarbons. It seems that industrial soot production technology is probably based on an application of the second process since the structure of all industrial soots is practically identical and they do not contain any considerable amounts of volatiles. Finally a great resemblance must be noted between the formation mechanisms of pyrocarbon and soot. Both are two-stage processes limited by nucleation. And both are branched chain processes. The growth process of a carbon surface is similar to a planar model of the three-dimensional soot formation process.The difference consists in that the growth of crystallites on a surface is limited by their coming into contact. The formation rate of pfanar nuclei and their growth rate at a constant hydrocarbon concentration in the gaseous phase is constant But the growth of nuclei in volume is not limited although the generated surface of the particles results in the destruction of radical nuclei and in the slowing down of the particle formation rate. A. Voet Rubber Chem. Techl. 196437,630. J. Biscoe and B. E. Warren J. Appl. Phys. 1942 13,364. R. D. Heidenreich W. M. Hess and L. L. Ban J. Appl. Cryst. 1968 1 1. P. A. Marsh A. Voet,T. 3. Mullens and L.D. Prb Carbon 1971,9 797.P. A. Tesner M. M. Polyakova and S S.Mikheeva DAN S.S.S.R. 1972,203,402. P. A. Tesner Formation of Carbonfrom GasPhase Hydrocarbons (Chimia Moscow 1972). 'IJ. C. Bokros Deposition Structure Properties of Pyrolytic Carbon. Chemistry and Physics of' Carbon ed. P. L. Walker (Marcel Dekker New York) vol. 5 p. 27. * B. N. Altshuler and P. A. Tesner GasovayaBornisltl. 1969,6,41. P. A. Tesner T. D. Snegiryova and V. G. Knorre Combustion Flame 1971 17 253. lo P. A. Tesner et d.,Cornbustion Flame 1971,17,279. l1 P. A. Tesner apd B. N. Altshuler DANS.S.S.R. 1969 187 1100. l2 P. A. Tesner et al. Combustion and Explosion. (Proc. 3rd All-Union Symp. Combustion and Explosion). (Nauka Moscow 1972) p. 725. ' K. H. Homann CombustionFlame 1967. 11,265. l4 K. H. Homann and H. G. Wagner Proc. Roy. SOC.A 1968,307,141. G. L. Johnson and R. C. Anderson,Proc. 5th Con$ Carbon 1962,1 395.

ISSN:0301-5696    

DOI:10.1039/FS9730700104

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Coagulation of Carbon Particles in Premixed Flames BY J. B. HOWARD AND G. C. WILLIAMS B. L. WERSBORG Fuels Research Laboratory Dept. of Chemical Engineering Massachusetts Institute of Technology Cambridge Massachusetts Received 4th December 1972 The size distribution number concentration and fraction charged of carbon particles at successive stages of formation in a low pressure flat flame were measured using molecular beam sampling involving electrical beam deflection and electron microscopy of beam deposits and an optical absorp- tion technique. Observed cluster-type structure within roughly spherical particles and decreasing particle number concentration following rapid nucleation indicate the particles do indeed coagulate during growth. Particle size and number concentration data confirm this conclusion although the experimental coagulation rate exceeds by a factor of about 10the kinetic theory collision rate approxi- mately adjusted for electrostatic forces based upon the measured extent ofparticle charging and Van der Waals attraction.Calculations based upon extrapolation of the experimental coagulation rate constant into the flame region of significant particle nucleation and surface reaction indicate that the particles nucleated first can grow predominantly by surface growth to a volume mean diameter of about 100 8,and that the number of primary particles per spherical unit within the final chainlike clusters is of order 10. Thus crystallites the number of which is of order lo3per spherical unit do not represent former particles.Although the chemistry of dispersed carbon formation in flames has been the object of many investigations coagulation of the particles has received little attention. Coagulation is known to occur in the final stages of carbon formation but its role during particle nucleation and growth by surface reaction has remained obscure. The nucleation step would involve coagulation if nucleation amounts to a continuous transition from large hydrocarbon molecules to small soot particles of continuously decreasing number concentration as advocated by Homann.' BartholomC and Sachsse and Fenimore and Jones assume that carbon particles can grow by coagula-tion to a size too large to permit their burnout. If at least some of the carbon particles are charged coagulation may be influenced by interparticle electrostatic forces.This influence and the importance of ionic nucleation have been discussed previo~sly.~-~ Recently,' the following quantitative connection between particle growth by surface reaction and coagulation was derived by relating the rate of change of the volume mean particle radius a3 to particle number concentration n,rate of appearance Nu of the smallest particles of radius ao and surface growth rate Si of particles in the ith class having area mean radius af The surface growth rate at a given flame position may be assumed to be independent of particle size. Also and coagulation rate fiC are related by Nu = dn/dt+N,. (2) 109 COAGULATION OF CARBON PARTICLES Denoting the area mean radius as a, eqn (1) then becomes These equations show that the rate of change in particle radius is in general different from the surface growth rate and they provide a means for distinguishing between the contributions of coagulation surface growth and nucleation.The objective of the present investigation was to measure the rate of carbon particle coagulation under well known flame conditions and to assess quantitatively the role of coagulation during particle nucleation and growth. To these ends particle size distribution number concentration and fraction of particles charged were measured at different stages of carbon formation in a unidimensional low pressure flame using molecular beam sampling electron microscopy and optical absorption.These and other experimental results are compared with the theoretical coagulation rate based upon kinetic gas theory and a simple account of interparticle Van der Waals and electrostatic forces. The sampling and analysis of carbon particles from flames using multistage molecular beam sampling and electron microscopy were improved until 15A diameter particles could be included in the measurements. Details of the apparatus and experi- mental techniques were described earlier.' In general a flat premixed acetylene- oxygen flame maintained at 20Torr equivalence ratio 3 and cold gas velocity of 50cm/s on a 7cmdiameter burner was probed along its centre line at different heights above the burner using a quartz nozzle expanding into the beam system.By opening a shutter for an adjusted length of time the sample beam was admitted to the detection stage operated at 8 x Torr in which particles were deposited directly onto electron microscope grids. A second sample was taken under identical conditions except that an appropriate electric field was applied across the beam to deflect all charged particles. The difference between the deposit intensities in the two cases permitted calculation of the fraction of particles charged. The intensity was obtained together with particles size and size distribution by a particle count and diameter measurement on electron micrographs. The intensity measurements gave relative particle number concentrations from which approximate absolute values were obtained by calculating a calibration factor from the beam geometry traced by soot deposits.The absolute value of particle number concentration was also determined by optical absorption measurements * in a second flame produced under identical conditions on a 10 cm diameter burner. The attenuation signal was obtained using a laser source (A = 6328A) and two photomultiplier detectors. Temperature profiles were obtained using Si0,-coated thermocouples. The absorption technique requires knowledge of the extinction cross section of young carbon particles which because of their substantial hydrogen content differ optically from the older carbon particles for which optical properties are available. This information was obtained using the molecular beam system to collect particle samples on glass slides and adjacent electron microscope grids.Subsequent measurement of the attenuation of the laser beam by the slide deposits and of particle size distribution and number per unit area in the deposits using the electron microscope grids permitted calculation of the extinction cross section. Under the flame conditions here studied visual observation of flame luminosity indicates that carbon formation starts at 1.5 cm height above the burner. Electron micrographs of representative carbon particles collected at different heights above PLATE1.-Carbon particles at different growth stages (a,b and c at 4cm 6 cm and 7 cm height above the burner of a 20 Torr C2H2-02 flame magnification 90 000 x ;d at onset of chaining in a 1 atm C3Hs-02 flame magnification 158 000 x ).To face page 1111 J. B. HOWARD B. L. WERSBORG AND G. C. WILLIAMS the burner are shown in plate 1. Up to 4 cm the particles are mainly spherical (a) whereas chainlike clusters become noticeable at 6 cm (b) and predominant at 7 cm (c). In (d) are shown enlarged particles from a propane-oxygen flame at 1 atm. height above burner /cm FIG.1.-Mean particle diameter [volume mean diameter (a),number mean diameter (a)]. 1o.c m I g o\ 2 \ 7.5 .-+I *E 8 0 8 5.c B E CI .-U 2.5 a a 01234567 height above burnerlcm FIG.2.-Particle number concentration [all particles (A),uncharged particles ( a)]. Their shape which is representative of that which prevails just before chaining becomes predominant may be interpreted as evidence for the fact that carbon particles will collide at all stages of formation but the earliest collisions are hidden by large simultaneous surface growth which tends to fill in the boundaries between particles.COAGULATION OF CARBON PARTICLES This behaviour leads to a gradual transition from roughly spherical clusters to the familar chainlike clusters. Thus the spherically appearing units within the chains may not be used to calculate surface growth rates or the number of nuclei as these units themselves are generally composed of several primary units. This interpreta- tion is supported by ultrahigh resolution electron micrographs on which may be recognized particle domains commonly known as crystallites arranged around different growth centres within one " spherical " unit.The growth centres appear to have nucleated independently and grown for some time as separate particles and to have coagulated while surface growth possibly accompanied by some migration was sufficiently rapid approximately to even out the cluster surface. In the determination of particle size distribution and number concentration from electron micrographs clusters were counted as single particles and non-spherical clusters were assigned the diameter of the volume equivalent sphere. By analyzing about 100 particles per micrograph measurement error was kept below 10 % for diameter and 20 % for relative number concentration. Owing to the difficulty of seeing the smallest particles under the electron microscope error in the case of absolute number concentration undoubtedly exceeds 20 %.The size distributions thus measured progress from approximately Gaussian at 2 cm height above the burner to approximately lognormal at 7 cm. The relative standard deviation is about 0.2 and independent of mean particle size so long as the particles are spherical but it rapidly approaches about 0.5 with the appearance of chainlike clusters. Mean particle size and number concentration at different heights above the burner are shown in fig. 1 and 2. From a small concentration at 2 cm particle number increases rapidly at first peaks shortly after 3 cm and then decreases. This behaviour is assumed to reflect the opposing effects of nucleation and coagulation the number increasing effect of nucleation being dominant at first but subsequently negligible in comparison with the decreasing effect of coagulation.In view of the error in these data the exact position of the particle number peak should be located by more accurate measurements. The absolute number concentrations measured by absorption (not shown) at 4 and 5 cm height above the burner differ by less than 20 % from those determined by electron microscopy which is within the error limit of the latter technique. The absorption values at 3cm height above the burner are however twice as large. The difference could be due to absorption by large gas phase hydrocarbons or to incomplete detection of small particles on the micrographs.A similar decrease in particle number with increasing height above the burner was observed before by Bonne Homann and Wagner.lo Their remarkable study does not use the concept of a volume equivalent particle diameter for chainlike clusters. Thus their number concentration measurements describe the number of approximately spherical units within a chainlike cluster which stays nearly constant in the tail of the flame. The measured concentration of neutral particles is given by the dashed line in fig. 2. The difference between these results and the corresponding total concentra- tion values is the concentration of positively and negatively charged particles. The polarity of the charge and charge per particle where studied by reducing the deflecting field strength in a stepwise manner and collecting the particles on grids adjacent to the deposition area of neutral particles.This measurement gave intensity problems which prohibited a reliable count of particle density on the grids due to the difficulty of identification. Only chainlike clusters could reliably be distinguished from back- ground grain and contamination ; these particles were exclusively positively charged. The results do indicate however that a1 charged particles under the flame conditions J. B. HOWARb B. L. WERSBORG AND G. C. WILLIAMS studied are predominantly of positive polarity with one charge per particle but a few negative particles and a few particles with two charges cannot be exchded. Our present charge measurements which use a Faraday cup instead of the electron microscope grids indicate that carbon particles under different flame conditions can be predominantly neutral positively charged or negatively charged.The charging state is a strong function of flame temperature which in turn is influenced by the cold gas velocity and gas composition. Experimental coagulation rate constants were obtained by assuming a mono- disperse system and expressing the coagulation rate in the form of the Smoluchowski l1 equation N = $Kn2 (4) where K is the coagulation rate constant. Combining eqn (2) and (4) gives d(l/n)/dt = K/2-N,/n2 (5) which shows there exists a linear relationship between n-l and t when the rate of nucleation is sufficiently small the slope of the line being K/2.Inverse particle ~ A' <,.a&' ' __.--..I/__i !23456789 height above burner/cm FIG.3.-Gas volume per particle at different growth stages [electron microscope data of this study ( x ) ; calculation from electron microscope data of Homann and Wagner (A); calculation from absorption data of Bonne and Wagner (e)]. number plots are shown in fig. 3 for the electron microscopy data of both this study and that of Homann and Wagner l2 and absorption data of Bonne and Wagner.13 Particle number concentrations of Bonne Homann and Wagner were calculated from their values of soot mass fraction and particle diameter. Differences between the present data and those of the previous studies are due in part to the facts that the previous workers used an equivalence ratio of 3.5 and Bonne and Wagner in the calibration of their absorption measurements did not allow for change in the extinc- tion cross section of young carbon particles with change in particle composition.COAGULATION OF CARBON PARTICLES The approximately straight part of the curves downstream of about 4cm height above the burner indicates a predominant coagulation of carbon particles to larger clusters; twice the slope of each line is the experimental coagulation rate constant for the flame conditions and zones represented. Additional information is derived from eqn (3) which in the region where surface growth and nucleation are negligible compared with coagulation reduces to d[ln(n)]/3d[ln(a3)] = -1. (6) Values of the characteristic ratio identified by eqn (6) at different heights above the burner are shown in fig.4. The numerical evaluation of particle number concentra-tion extrapoIates the values of this study to 8 cm height above the burner and shows that the characteristic ratio is scattered due to measuring errors. Its average is almost exactly -1 indicative of predominant particle coagulation downstream of 4.5 cm height above the burner. The characteristic ratio calculated from the absorp-tion measurements of Bonne and Wagner l3 is -1 from 4 to 6 cm height above the burner. In this region the particles are approximately spherical and their size and number concentration change predominantly by coagulation. Although coagulation dominates also between 7 and 9 cm the characteristic ratio nevertheless increases in this region due to the use of the diameter of the spherical units within chains - 1.4 -"-2 -!.L3%5b7.33 height above burnerlcm FIG.4.-Characteristic ratio for particle coagulation [electron microscope data of this study ( x ) ; calculation from electron microscopedata of Homann and Wagner (A);calculationfrom absorption data of Bonne and Wagner (O)].which remained nearly constant instead of the volume equivalent diameter of the cluster. Similar to the values obtained by electron microscopy in the present study the deviations from -1 in the region from 2 to 3 cm are due to surface growth and nucleation influences. The values obtained for the study of Homann and Wagner l2 are rather scattered which may be due to the fact that particles less than 40 diameter J.B. HOWARD B. L. WERSBORG AND G. C. WILLIAMS were not included in the electron microscope analysis. Thus experimental coagula-tion rate constants are only obtained from the measurements of Bonne and Wagner between about 4 and 7 cm height above the burner and from the present data down-stream of the 4.5 cm position. The values found are given below in terms of the kinetic theory collision model. Carbon particles in low pressure flames are under free molecular flow conditions and therefore constitute a highly dispersed aeros01.l~ If the size distribution is approximated as monodisperse the coagulation rate constant is K = 16a2y(zkT/m)) (7) where a is the mean particle radius y is a correction factor accounting for inter-particle forces kis the Boltzmann constant T is temperature and m is particle mass here estimated by assuming particle density to be 2 g/cm3.Experimental y factors shown in fig. 5 were obtained from eqn (7) using K values calculated as described above from line slopes in fig. 3 and a gas velocity of 3 m/s at 2000 K. Values for all flame positions studied are presented for completeness but the only values sufficiently free of nucleation effects so as to reflect coagulation behaviour alone are those in the regions described above as yielding coagulation rate constants. In these regions y appears approximately constant indicating little or no net particle size and tempera-ture influences The y values from this study are approximately 29 and very similar to those of the absorption study which are around 21.n A W a, Y 20 20- C .-. /d c.’ I ‘a 1 M ---__ .-I----____ ----__A-A-8 A A 8 /.// I / 2 0 1234567a9 height above burnerlcm FIG.5.-Experimental coagulation rate factor (y) [electron microscope data of this study (x ) ; calculation from electron microscope data of Homann and Wagner (A);calculation from absorption data of Bonne and Wagner (O)]. In an attempt to explain why the observed coagulation rate is much larger than the kinetic theory collision rate the contributions of Van der Waals and electrostatic forces were examined by calculating theoretical y values for simplified cases described presently.Cloud shielding and diffusional effects are negligible under the experi-mental conditions and the particles are again assumed to be uniform in size. The effects of gas-particle collisions on the energy and monentum of two interacting COAGULATION OF CARBON PARTICLES particles are neglected. The contribution of Van der Waals forces to the potential of two spherical particles of radius a with distance r between centres is E = -(H/12)[z-'+(z-1)-'+2 In (1 -z-')] (8) where H is the Hainaker constant related to the London-Van der Waals constant OL by H = n2g2u,g being the number of atoms per unit volume in the particles and z = (r/2a)2. The electrostatic contribution to the potential using Maxwell's l6 method of electric images is Ee = (kee2/2a>[(s1I$- '-1)(Q +Q:) +2( a/r>siz$-'QiQ2I (9) where k = 9 x 109Jm C-2 e = 1.6~1O'l9C $ = S -(a/r)2S:2 a3 s, = (i-e2)c eyi-e2ni+2) m=O /J=[(1 +8)a/rI2,8=y-(y2-l)f y=r2/2az-l and eel and eQ2 are the particle charges.The equivalent equations for unequal particle radii are given elsewhereO6 If both particles are charged with the same polarity opposing electrostatic repul- sion and Van der Waals attraction lead to a positive maximum in the potential E(r,) = E +E at r = rm where rm> 2a. Since collision is then limited to particles whose initial kinetic energy re€ative to axes moving with the mass centre exceeds E(r,) it is reasonable to assume that y = exp [-E(r,)/kT]. (10) In all other cases including both particles charged but with opposite polarity only one particle charged and both particles neutral the interparticle forces are attractive and from classical analysis of the two particle encounter,17 the collision cross section is increased by the factor y = (1 +&/a)2[1-2E(&)/pv;] (11) where 2~ is the minimum separation distance to within which the particles' surfaces may approach without resulting in collision E(E)is the value of E,+& when r = 2a+2~, p is the reduced mass here given by m/2,and u is the relative velocity of the particles.Since the average initial kinetic energy of the pair relative to axes moving with their mass centre is 2kT,'* u is taken as 4kT/m and pu; becomes 2kT. Therefore y = (1 +&/a)2[1-E(&)/AT]. (12) The proper value of E is that value for which y is rninim~rn.'~ If neither particle is charged eqn (8) and (1 2) give y = z,C1+(~/12k~){z,' +(zm-l)-' +21n (I-Z;'))] (13) where z, which is the value of z at r = 2a+2~,is the root of the equation (3-22,)/(2,-1)'-2 In (1-2;') = 12kT/H.(14) If one particle is charged or if both particles are charged but of opposite polarity E is found by numerical or graphical minimization of y in eqn (12) using eqn (8) and (9). J. B. HOWARD B. L. WERSBORG AND G. C.'WILLIAMS Values of y calculated as described above for different particle sizes states of charging and H values are shown in fig. 6. The value of N for carbon particles in flames is not known but it should be within the range 10-20-10-L8 If neither J. particle is charged y is independent of particle size and equal to 2.75 for the largest H here considered.If one particle carries one charge y is increased by image forces particle diameter 2a/A FIG.6.4ncrease in collision cross section of two equal sized particles by Van der Waals and electro- static attraction [Ql = -Q2 = 1 (solid); Ql = 0,Q2 = k1 (broken) ; Q1= Q2= 0 (dashed) ; Hamaker constant = lO-'O(a) 10-19(b),10-18(c) J; T = 1800 K). but this effect compared with that of Van der Waals forces alone is substantial only for small particles and small values of H. It appears that the y resulting from image forces cannot be substantially larger than 3 if the particles have predominantly only one charge. If both particles carry one charge of opposite polarity y is of order 10 for small particles.However if ambipolar charging predominates repulsion between particles of the same polarity must also be considered and the net effect on coagulation rate may be small. In view of the above calculations and the observed condition of 0 or 1 positive charge per particle it appears that Van der Waals and electrostatic forces together may account for a factor of only 2 or 3 increase in the coagulation rate constant under the conditions studied. The situation may however be quite different for other flame conditions in which particle ionization is more pronounced and even under the present conditions the detected charge must be regarded as one cause for the chained appearance of the final carbon particles. Nevertheless a factor of order 10 increase in y remains to be explained.Other possible causes meriting study include polydispersity and deviations from the assumed sphericat shape. 2o Our calculations not reported here show that polydispersity exerts less than a 20 % increase if the particles are assumed to be neutral hut the actual effect undoubtedly COAGULATION OF CARBON PARTICLES exceeds this prediction since y for small charged particles colliding with large neutral particles can be significant. The possibility that substantial numbers of particles could be decomposed or burnt out seems unlikely for the fuel rich conditions employed. The inability to predict the coagulation rate constant in the flame region in which it can be measured i.e. in the region where nucleation has practically ceased prevents confident prediction of y values in the region of significant nucleation.In spite of this shortcoming the cumulative number concentration of carbon particles may be calculated by integrating eqn (2) numerically using the experimentally determined value of y. This calculation is quite insensitive to the extrapolation of y since the coagulation rate constant is most important in the zone of carbon formation where it can be determined experimentally or just upstream of this zone in a region where the extrapolation will not be far from the experimentally determined value. In the early stages of carbon formation particle coagulation seems to be unimportant due to the small particle number concentration.In this range the change in particle number is approximately equal to the nucleation rate.’ The cumulative number concentration calculated with a constant y = 28.7 is shown in fig. 7 as a function of height above burner and there compared with the experimental particle number concentration. It is apparent that the contribution of coagulation to particle growth is small up to about 3 cm height above the burner. This approximation implies that the particles nucleated first grow predominantly by surface growth to a volume mean diameter of around loOA. The ratio of cumulative number concentration to the prevailing number concentration gives the cumulative number of particles appearing under the electron microscope per prevailing particle. This ratio (fig. 7) is believed to be a good approximation to the average number of nuclei or original 01234567 height above burner/cm FIG.7.-Instantaneous and accumulative particle number concentration and average number of nuclei per particle at different growth stages [accumulative particle number concentration ( x ) ; instantaneous particle number concentration (A);ratio of accumulative to instantaneous particle number concentration (011.J. B. HOWARD B. L. WERSBORG AND G. C. WILLIAMS particles in each prevailing particle because the concentration of unobservable particles should be small owing to the good lower limit of visibility (15 A) and the rapid growth of young particles by surface reaction. Surface growth of carbon particles becomes quite small after 4 cm height above the burner which position coincides with the onset of predominant chain formation.' Thus the number of nuclei per spherical unit in a chainlike particle is about equal to that calculated between 4 and 5 cm height above the burner.This ratio is of order 10 and is substantially smaller than the number of crystallites per spherical unit which is of order lo3. According to this result crystallites in carbon particles do not represent former particles. Thus the structure of these particle domains may be used to locate zones of predominant surface growth which in turn identify nuclei within spherical units. We are grateful to Project SQUID whose support under contract N00014-67-A- 0226-0005 NR-098-039 made this work possible. K. H.Homann Angew. Chem. Int. Ed. 1968 7,414. E. BartholomC and H. Sachsse 2. Elektrochem. 1949 53 326. C. P. Fenimore and G. W. Jones Combustion Flame 1969 13 303. E. R. Place and F. J. Weinberg Eleoenth Symp. (Znt.) on Combustion,(The Combustion Inst. Pittsburgh 1967) p. 245. J. B. Howard Twerfth Symp. (Int.) on Combustion (The Combustion Inst. Pittsburgh 1969) p. 877. R. T. Ball and J. B. Howard Thirteenth Symp. (Int.) on Combustion (The Combustion Inst. 'B.Pittsburgh 1971) p. 353. L. Wersborg J. B. Howard and G. C. Williams Fourteenth Symp. (Znt.) on Combustion (The Combustion Inst. Pittsburgh 1973 p. 929). L. Fox S.M. thesis (1972 Massachusetts Inst. Tech. Cambridge Massachusetts). F. A. Heckman personal communication 1971 Cabot Corp.Billerica Massachusetts. lo U.Bonne K.H. Homann and H. Gg. Wagner Tenth Symp. (Int.) on Combustion (The Com- bustion Inst. Pittsburgh 1965) p. 503. l1 M.von Smoluchowski 2.phys. Chem. 1917,92,129. l2 K. H. Homann and H. Gg. Wagner Ber. Bunsenges. phys. Chem. 1965,69,20. l3 U. Bonne and H. Gg. Wagner Ber. Bunsenges phys. Chem. 1965 69 35. l4 B. L.Wersborg Sc.D thesis (1972 Massachusetts Inst. Tech. Cambridge Massachusetts). H. C. Hamaker Physica 1937,4 1058. l6 J. C. Maxwell A Treatise on Electricity and Magnetism (Dover Publications Inc. New York 1954 republication of 3rd ed. of 1891) vol. 1 chap. 11 pp. 244-283. l7 J. 0. Hirschfelder C. F. Curtiss and R. B. Bird Molecular Theory of Gases and Liquids (John Wiley and Sons,Inc. New York 1954) chap. 1 pp.45-51. S. Chapman and T. G. Cowling 77ze Mathematical Theory of Non-Uniform Gases (Cambridge University Press Cambridge 2nd ed. 1962) chap. 5,p. 93. l9 N. A. Fuchs and A. G. Sutugin J. Colloid Sci. 1965,20,492. 'O G. Zebel Aerosol Science ed. C. N. Davis (Academic Press New York 1966) chap. 2 p. 31.

ISSN:0301-5696    

DOI:10.1039/FS9730700109

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Smokes Droplets Flames and Electric Fields BY F. J. WEINBERG Imperial College London S.W.7 Received 23rd Nouember 1972 The paper summarises recent results on the influence of electric fields on carbon silica and lead oxide smokes,as well as on suspensions of fuel droplets in flame systems. The object in each case is to cause the particles to acquire charge for their subsequent manipulation by fields. Examples of using this as a method of controlling the trajectories of particles-either to remove them or to affect the process of their growth or consumption in the reaction zone-are discussed. The latter includes a measure of control over the reaction by varying particle sizes and concentrations and by transposing charged nuclei. Mechanisms of charge acquisition are considered theoretically and it is shown that in the absence of other charging mechanisms (such as thermionic emission ur electrical breakdown of the gas) chemi-ionization in the flame may be used for this purpose.On the supposition that diminishing resources of fossil fuels and increasing concern about pollution will allow consideration of more complex combustion systems in future a theoretical assessment of the maximum effects attainable in practice is carried out for the variety of effects observable in the laboratory. A great variety of smokes-e.g. of soot ash metal oxides from additives-are produced in flames. On the input side suspensions or sprays of fuel droplets are frequently involved. Particulate suspensions associated with flames acquire charge if for no other reason than because flames produce a plentiful supply of ions and in the presence of electric fields these attach to particles.Charged particulates can be manipulated by electric fields not only when they are already fully grown but also during the process of their formation or burning up It is for this reason that the association of electric fields with flames involving smokes or droplets is of practical as well as of fundamental interest. A series of studies 1-6 of these phenomena has been carried out yielding many interesting results showing the large effects which can be exercised by applied fields but perhaps not enough by way of clear distinction between what is of purely academic interest and what methods of electrical control may have practical potential.It is to be expected as one consequence of diminishing resources of fossil fuels and increasing concern about pollution that the use of more elaborate combustion systems- including perhaps the application of electric fields-will come to seem less far-fetched and become more generally accepted. The object of this paper is to bring together the theoretical mechanisms and practical consequences of these effects in order to make suggestions as to the practicability of the various possible schemes. EFFECTS OF MOVING CHARGED PARTICLES BY FIELDS A charged particle will respond to a local field intensity E by acquiring a local velocity v = kE (1) in the direction of E where k is its mobility. The manner in which k depends on particle size and on the charge acquired will be considered in the next section.This 120 F. J. WEINBERG drift velocity of the particle is superimposed upon any flow-induced velocity and may be used to produce a variety of different effects. The first and mat obvious application is to modify the trajectories of fully-formed particles or of non-reacting droplets. They can be induced to deposit in specified places (the electrodes) prevented from depositing on other surfaces caused to deviate from their normal trajectories along flow lines even made to proceed in sine-waves by the application of an alternating field As regards control of deposition the best known example is probably that of " electrostatic " precipitators. In these devices however much energy is expended in maintaining a corona discharge for generating the charges which will attach to particles.In the applications discussed in this paper the charges used are in the main formed spontaneously-for example by chemi- ionization in the reaction zone. In the absence of the field they would merely recombine uselessly. Accordingly the power dissipation is entirely due to the drift of charge and is exceedingly small (see later). An example of using the principle of guiding fully-formed particles is the preven- tion of deposition on a particular surface. In the case illustrated by fig. 1 positively C 5 t imelmin FIG.1 .-Weight of soot deposited on collector plate against time. Curve 1 no field ; curve 2 plate positive with respect to burner.charged soot particles from a flame are prevented from collecting on a cooled plate immediately above it. The upper curve shows the continuously growing mass deposition in the absence of a field the lower that when the collector plate is charged positively with respect to a matrix-electrode in the burner mouth. Under the latter conditions carbon deposits copiously on the matrix and all around the burner mouth although it has to travel downward to reach these sites. It has been shown that all the carbon particles become charged at least when a suitabIe field is applied and can be made to drift to an electrode even against the direction of the gas flow. Incidentally in addition to its site the form of the deposit is altered when deposi- tion is influenced by an electric field.Since field lines converge on the protuberances formed by deposits the growth on electrodes tends to occur in treelike structures and at a much reduced density. This principle can be applied to precipitate any particulate pollutant.6 A some-what modified procedure must be used for substances whose boiling point lies below SMOKES DROPI,ETS FLAMES AND ELECTRIC FIELDS the final flame temperature and which are at the same time not sufficiently active thermionically to emit electrons at temperatures below which they condense from their vapour phase. Lead oxide falls into this category. In that case we should have to depend on charging by flame ions over fairly large distances determined by the condensation process (unless the species happens to have a low ionization potential in the vapour phase).However because of limitations due to space charge (see later) it is unprofitable to maintain fields over large distances and it has been shown that very effective precipitators can be constructed based on small secondary flames used purely as ion sources or even just on special surfaces maintained hot by flame products. An entirely different example is provided by using a field to produce charged fuel droplets and guide them into a flame.5 Fig. 2 shows a burner operated entirely by ion pumps IkHTatomizer t t --FIG.2.-Burner operated entirely by electric fields which inducts air atomizes and charges liquid fuel and guides droplets to mixing vaporization and combustion sections.electric fields in which kerosene is mixed with and burned in air. The burner “breathes in ” its own air using ion pumps based on the Chattock l2 effect. The fuel (to which a small amount of antistatic additive is added to make it more conduct- ing) is dispersed by an electric field which produces a fine spray of charged droplets. The trajectories of these charged droplets are determined by two orthogonal compon- ents of the electric field that between the jet and the matrix which guides them into the flame and that applied by the circumferential ring electrode which serves to vary the cross-sectional area of the spray and to focus it on a part of the matrix. In this manner a highly controllable high-intensity flame has been produced without the use of any fuel pump or air compressor the process being controlled entirely by the potentials applied to the various electrodes.Alternating fields may be used for example to cause droplets to evaporate in shorter distances by lengthening their trajectories in a given distance downstream. Thus trajectories in the form of sine waves with excursion amplitudes of the order of centimetres have been recorded for electrically sprayed liquids subjected to trans- verse a.c. fields. A second group of applications arises when charged particles or droplets are manipulated by fields during the process in which they are formed or burned up. This makes it possible to vary their residence time in the reaction zone and for example exercise control over the size of particles which are formed in flames.Fig. 3 shows an example taken from two different studies.4* The carbon particles derive from a F. J. WEINBERG 3 4 5 0' I I 1 I I 5 applied potential/kV FIG.3.-Particles grown in applied fields ; variation of radius with applied potential. Curves 1 and 2 carbon particles in positive and negative charge flux ; curves 3 4and 5 silica particles in positive flux at electrode separations of 0.35,0.09 and 0.02 m. -I I I I I Ill1 I I I I t Ill. applied potential/kV FIG.4.-Collection rate of carbon from counter-flow diffusion flame as a function of applied potential in flux of positive charge. Curves 1 2 3 and 4respectively on negative electrode exhaust system burner flange and total ; curve 5 current.SMOKES DROPLETS FLAMES AND ELECTRIC FIELDS flat counterflow diffusion flame in which the field is applied between the two burner mouths. The particles of silica smoke were produced in a study of oxide particles generated in premixed flames in this instance by injecting traces of hexamethyl disiloxane. The soot particles could in principle burn up in the flame zone; the silica particles could not. Nevertheless the pattern which here depends upon residence time is very similar. Note that the particles’ volume is reduced by a factor of about 200 in going from zero to 1 kV for e.g. carbon It is also possible to produce the converse effect i.e. to grow giant particles by the application of a suitable field. In the absence of other effects the size to which a particle grows in the reaction zone is due to a residence time determined by the zone’s thickness and the flow velocity through it.By applying a small retarding field so as to hold the particlesstat-ionary ( or as nearly so as possible) aginst the flow in the zone in which they -grow,macroscopic growths ofcarbon have been produced simul- taneously all over the flame frant..* The control of residence time in reaction zones merges into direct interaction with the reaction process by modifying the concentration of one of the participating species. Depending on the type of reaction the relevant concentration may be in the form of total surface area of the cloud of particles (if reaction proceeds on the surface) or of the number density of particles in the smoke (where coalescence is the important process).Again an example from studies on flame carbon is taken. Fig. 4 shows rates of mass deposition OII various parts of a counterflow diffusion flame system when the ion flux through the pyrolysis zone is positive (so that attachment charging reinforces thermionic emission and all particles are charged positively-as evidenced by the confinement of the deposit to the negative electrodes). The total mass de- posited decreases by about 98 % by the time the applied potential reaches 1 kV. Thus the decrease in particle size is not due to any large increase in the number of particles formed as the surface on which growth normally occurs is being rapidly removed. (Note the contrast with pollutants such as metal oxides which cannot burn up in the flame so that decreased particle size brought about by decreased residence time must be accompanied by an increased number of particles.) A fourth distinct means of interaction by fields is the removal of charged nuclei.Growth on charged nuclei can occur by chemical reaction or by purely physical condensation-as happens for example in the Wilson cloud chamber.’-’ This occurs because in an atmosphere of saturated,vapour droplets below a certain size cannot exist in equilibrium when the surface energy made available by their contraction is sufficient to supply all the latent heat of vaporization. The effectiveness of a nucleus in overcoming this threshold is greatly enhanced when it is charged for then the surface charge on the incipient droplets opposes the surface tension and diminishes the surface energy.Charged nuclei being very small tend to have a much larger mobility than the fully-formed particles. Whereas a small field may be used to transport them to a zone in which they are required (e.g. a pyrolysis zone) a large field will very greatly diminish their number. It has been shown that in the presence of large fields the mass rate of deposition of soot from flames is almost entirely made up of particles which do not have a charged precursor (even though they all acquire charge later in their existence and even though they might all have originated on charged nuclei in the absence of a field). For smalter fields local intensity can be used to control the local concentration of charged nuclei Whenever ions and charged particles of mobility k drift in a field a body force F per unit volume acts on the gas i.e.F = jlk (2) F. J. WEINBERG where j is the local current density. This induces a gas flow (the " Chattock wind effect "l 2 the precise nature and magnitude of which 3* depends on the geometry of the field and the surrounding surfaces. Although this is incidental to the subject of controlling particulate suspensions by fields it is inevitably present and usually quite large because of the low k values. It also has severaf uses in its own right. These range from modifying heat transfer from flame gases to mixing flame stabilisation and other situations where control over the fluid mechanics without the use of solid walls is beneficial 14* l5 to combustion.Two such processes are particularly relevant here. One is the impingement due to fluid mechanical forces which contributes to causing particulates to deposit on electrodes in any kind of electrical precipitator. The other is the application of ionic winds to gas pumping as in the air induction states uf fig. 2. The velocity obtainable per ion pump stage is of the order of several I00 cm/s,13p l4 so that for fuels burning in air one or two stages are generally adequate. SIZE CHARGE AND MOBILITY The manner in which the field modifies the trajectory of ii charged particle is defined in terms of the particle mobility k by eqn (1). The mobility in turn depends on the particle radius r and its charge Ne (e being the electronic charge positive or negative).These quantities vary with time according to the history of the particle's growth or burning up the rate of charge acquisition being itself a function of r. These histories become modified by the application of a field from the moment the first charge has been acquired. The mobility is calculable at any instant depending on the regime which is determined largely by the particle radius r. Starting from the very smallest at molecular diameters the theory of small ions (see e.g. ref. (16)) applies. Here the mobilitv is 0.235[(M + Mi)/Mi]o*Spi k=-9 w-1)OMl0% (3) where p is density M is the molecular weight and D is the dielectric constant; the suffixes i and 0 denote ion and carrier gas respectively.For larger ions the effects of divergence of the field induced around them by their own charge becomes negligible and the classical Langevin equation k = 0.815 (e;li/Mc)[(Mi+ M)/MJ0s5 (4) becomes relevant. When particles become large in comparison with the mean free path I. and no longer " sense the gas as individual collisions ",the viscosity q and density p become the relevant gas properties. In the Stokes regime the mobility then is k = eN/6nqr (5) and in the Newton regime at a field strength E k = (eN/0.22rrpE)o.5/r. (6) Which of these is applicable depends on the Reynolds number attained. Using eqn (5) for Re< 3 and (6) for Re> 700 keeps error to below 20 %. The equation k = 0.12(Ne)'e7 ' /r(Ep)0*299r10.43 (7) has been proposed for the intermediate region.I8 The case of particles continuously acquiring charge along their trajectories has also been considered.For bombardment charging (see later) the equations become k = Er/2nb/ (8) SMOKES DROPLETS FLAMES AND ELECTRIC FIELDS in the Stokes regime and k = 2.08/p0*5 (9) in that covered by Newton's law. These values are too large by about 20 % because the particles never quite attain their equilibrium charge under bombardment.18 The numerical values are in fact very high exceeding I /20th of the mobility of a molecular ion in some cases. As regards the mechanisms by which particles or droplets acquire charge there is much variety ranging from the spontaneous processes of thermionic emission to those which are entirely contrived by the application of a field.When the object is to produce a charged dispersion of liquid or solid fuel,5 dispersion in a field (but in the absence of breakdown) is ideally efficient in terms of minimizing the wastage of charge deliberately provided. In this the particulate phase may be treated as the fragments of an initially continuous charged capacitor,' resulting in high levels of specific charge and of mobility. Fig. 5 shows results for droplets of kerosene with some I 1 1 1 1 I I f I 50 I00 drop diameterlpm FIG. 5.-Electrically sprayed droplets ; charge against diameter. Circles horizontal ; triangles, vertical sprays. Curve from theory see eqn (10). anti-static additive dispersed by an electric field the solid line being calculated on the theory of a disintegrating charged condenser which yields Ne = 9,/%nr2E.(10) In this way many millions of electronic charges can be impressed upon a small droplet; the experimental points obtained for a range of horizontal and vertical sprays conform well to the theory. For solid fuel dusts the dispersing field is applied to a fluidized bed of the p~wder.~ These methods give rise to suspensions which are highly controllable by fields right up to the point of burning. In flame zones other methods of charging become useful particularly thermionic emission and the attachment of chemi-ions produced in the reaction zone. Ther-midnic emission is specific to materials of low work function and depends on local temperature as well as on the nature of the material.Since it always leaves the particles with a positive charge it is important to apply fields in such a way as to F. J. WEINBERG subject the smoke to a flux of positive ions so as to reinforce rather than to oppose thermionic charging. In the absence of an applied field the thermionic emission current density is j = BT2exp (-e4/kT) (11) where B like 4,the work function is characteristic of the material ; e is the electronic charge k the Boltzmann constant and T the temperature which determines the number of electrons with sufficient energy to escape. When the emitter is a positively charged particle of small radius r two additional terms arise in the work function 2o ; (Ne/r)due to the surface charge (Ne) and (e/2r)due to the dipole induced by the departing electron The current then becomes j = BT2exp {( -e/kT)[4+ (N+ +)(e/r)]).If an electric field E is applied so as to assist the removal of electrons the effective work function of the material is decreased (the Schottky effect) and the emission current density then becomes j = BT2exp [-(e/kT){$-(eE)*)]. This theory has been further elaborated for very small particles for clouds of reacting particles and for the simultaneous presence of ions in fieldsi4 The use of fields to induce chemi-ions from the reaction zone to attach to any particles generated in flames is based on two mechanisms " diffusion " charging and " bombardment " charging. The former refers to the attachment of charge as the result of ion particle collisions due to random thermal motion of the ions and occurs irrespective of the local field intensity except insofar as this determines local ion concentration.The rate of charge acquisition by this mechanism is given by d(Ne)/dt = zr2cni exp [-e2(N-+)/rkT] (14) where c and ni are the root mean square velocity and the concentration of the ions respectively. Bombardment charging is due to ions drifting along lines of field intensity which terminate on the particle due to the dipole induced on it by the applied field. The ions drift at a very much higher velocity than the particles do so much so that the velocity of the latter can generally be ignored by comparison. The rate of charging then is d(Ne)/dt = 3zr2ji[ 1-(Ne/3Er2)]2.(15) For a non-conducting particle the right-hand side is multiplied by D/(D+2) which is of the order 1. In this case there is an equilibrium charge Ne = 3Er2 (16) which is due to the formation of an electrostatic stagnation point upstream when the effect of the dipole is neutralized. However it turns out that when large fields are applied to flames the equilib- rium conditions-indeed all the retardation effects due to appreciable particle charge in bombardment diffusion and thermionic charging-are often irrelevant. This is because the field tends to remove the particle from the charging zone in a time too short for its charge to become appreciable. There are obvious exceptions to this- for example see above for the case of using a small field to hold particles stationary against the gas flow in order to produce large agglomerates-but when it applies a unified and greatly simplified theory may be used for calculating the charge acquired by particles.6 Thus in principle particle charge inability and hence trajectories in fields are SMOKES DROPLETS FLAMES AND ELECTRIC FIELDS calculable.However the physics of the subject is rather in advance of the chemical kinetics (not perhaps an unusual state of affairs at least in the field of combustion) and the kinetics of the growth of carbon particles for example is not sufficiently well understood to allow fully predictive calculations. It is much simpler to measure the mobility of particles withdrawn from flames by electric fields experimentally measure their size and deduce their charge.The values used in the next section were so obtained. PRACTICAL EFFECTS AND THEIR LIMITATIONS The largest mobilities occur for droplets (or particles) charged during their dispersion. Fig. 6 shows velocities of charged kerosene droplets (corresponding to those shown in fig. 5) in applied fields. These velocities were measured by photo- graphing tracks by interrupted illumination for the lower range and by laser Doppler C 22 43 6Q 80 103 120 140 field intensity/kV m-I FIG.6.-Electrically sprayed droplets ; velocity against applied field. Circles and crosses show results obtained by photographing particles by interrupted illumination and by laser Doppler velocimetry respectively.Curve from theory see text. velocimetry for the higher range the solid curve being based on the mobility theory discussed above. Velocities of many m/s are attainable at quite modest fields. The lowest mobilities occur when large fields are applied to flames producing smokes. The large fields may be useful for controlling the trajectories of charged particles but where they are simultaneously used for particle charging they decrease ion concentra- tion and tend to remove particles from the zone of charge acquisition as soon as the first charge has been acquired. This has been shown for carbon and silica to result in mobilities of the order of m2 s-I kV-' as compared to lo-' ni2 s-I kV-I for electrically sprayed droplet^.^ The latter is an appreciable fraction of the mobility of unattached flame It.J. WEINBERG ions owing to the many millions of electronic charges carried by sprays produced in this manner. In order to assess thepracticability of various applications we need to know not only mobilities but also field inteasities attainable in practice. Now the maximum field to which these charge-carriers can be subjected is limited for unipolar space charges between the ion source and each elebtrode by the onset of breakdown at the electrode at which the field intensity reaches a maximum. This limits the maximum current density which can be drawn in a uni-dimensionat system.to j = EEkjgnX (17) where Eb is the breakdown field at the electrode and X is the distance between the electrode and the ion source.’ This applies for an unlimited source of charge; for weak sourcesthere is the obvious limitation where j represents th3,saturation current density for which charges are removed as fast as they are generated there being no time for recombination.For flames of hydrocarbons burning in air however the former restriction (eqn (17)) is generally limiting. This is because jsis relatively large at least for near stoichiometric mixtures and because the strength of an ion source can always be made greater the simplest method being by increasing the area of flame surface per unit area of electrode. Using these theoretical concepts l4 the absolute maximum effects obtainable by fields have been predicted. Thus for a system of minimum separation between cold electrodes (taken as I cm) in which only flame ions (taken as mostly H30+and negative ions of about the same mobility produced by attachment of electrons in the cold electrode space) drift along the maximum current density is 2.5 A rnU2providing at the absolute maximum one charge for each of 1.6 x 10l9 particles.The corres- ponding expenditure of power is W = kEi/6n (19) which predicts 920 W m-2 (the S1 system of units tends to disguise the fact that this is a negligible quantity ; the value is for hot gas and should be compared with the power generated per square metre of flame!) In the presence of particles or droplets two cases arise; that in which particles drift in the presence of ions and acquire charge from them and that in which the par-ticulate phase is the sole charge carrier (e.g.the electrically dispersed fuel droplets discussed above). In the former case the current density is almost entirely due to the ions alone and the space charge and consequent field distribution may be treated on this basis.I8 In the latter case taking electrical dispersion of droplets as an example the relevant mobility is that of the droplets which as mentioned above is exceedingly high. Although it is at the bottom of the droplet size range (fig. 5) that mobilities of the same order as that of ions arise it is the large droplets that transport most mass. Thus it follows from eqn (17) that the volume of liquid that can be conveyed in this manner per unit area per unit time is V = (E,2kjgnXNe)(4nr3/3).(20) Substituting the Stokes mobility for this case (eqn 5) gives V = Ezr2/36nXq. (21) This is of the order of hundreds of litres m-2 s-I for electrode separations of the order of centimet res. Keeping electrode separations sinall is indeed the main problem in introducing s7-s SMOKES DROPLETS FLAMES AND ELECTRIC FIELDS large field intensities into flames. Here it is important to note that the zone of ion generation (the exceedingly thin chemi-ionization region which accounts for well over 99 % of the free charges) generally does not coincide with the region in which particu- lates are formed. Even though the pyrolysis zone in carbon formation or the region in which metal oxide smokes condense may be quite a small distance from the chemi- ionization zone even a fraction of a millimetre makes an important difference to the field intensity as shown later.As regards the zone of ion generation the field intensity in this region of virtually infinitesimal thickness does not become appreciable until the applied potential exceeds that at which a saturation current is drawn. The field distribution is given by E2= Ei +8njx/k (22) where E, the field in the ion source remains small so long as the ion source can respond to increased potential by yielding more charge. Once saturation is reached further increases in potential result in a rapid rise of E,. However for strong ion sources and large electrode separations the breakdown condition (eqn (17)) is likely to be exceeded first. Fig.7 shows the maximum distance between cold electrodes 0.5-E 4 a 0 Y a I I I I 0.7 0.8 0.9 I.o fuel air ratio/fraction of stoichiometric FIG.7.-Maximum electrode separation for attainment of supersaturation field intensities in ion source as a function of fuellair ratio. 1 methane ; 2 propane ; 3 ethylene. (assumed symmetrical about the flame surface) for achieving appreciable fields in the chemi-ionization zone itself as a function of fuel/air ratio. However even when the field in the ion source is insignificant-perhaps because the electrode spacing has to be considerably larger than the values of fig. 7 so that the saturation condition is unattainable-the field intensity in a closely adjacent zone in F. J. WEINBERG which particulates axe formed can be appreciable.This is illustrated in fig. 8 which shows the growth of field intensity with distance from an unsaturated ion source. For example for an electrode spacing of 20 cm under conditions just below break- down at a cold electrode (3 x lo3 kV m-l) the field is 300 kV m-l at a distance of 1 mm from the ion source and still almost 100 kV m-1 at 1/10 mm. These correspond to velocities of metres per second even for the lowest mobilities mentioned above. 300-4 I f 200-$ x Y ..4 U 8 .--a 100--43 distance/fraction of electrode spacing FIG.8.-Field intensity as a function of (small) distance from ion source for conditions of incipient breakdown without attainment of saturation. We may conclude that this is a subject in which practical applications do not always follow directly from a scaling-up of laboratory experiments-no matter how spectac- ularly successful the latter are-and should not be attempted without a thorough understanding of the theory.Unsuccessful transposition to large-scale apparatus without taking theory into account have sometimes led to the equally erroneous conclu- sion that the methods are generally not useful. Thus there is obviously no prospect of removing all the soot generated in a jet engine flame tube by applying a field right across the duct-the ion source is much too strong in relation to the distance across which the potential is applied-this being a situation in which closely spaced plates are ruled out by the consequent pressure drop.Yet even under such conditions no great difficulty would be expected in attempting to prevent carbon deposition on some particular cold surface which is part of the device. Again as regards diminishing carbon formation by removal of the growing particles from the pyrolysis zone a local field intensity of 100V/cm will suffice to induce the least mobile of the particles mentioned above to cross a growth zone of 1 mm width in 0.1 s. For precipitation of particulate clouds the geometry of closely spaced plates as used in "electrostatic " precipitators is ideal the difference being that here no power is dissipated in producing a corona discharge. Under conditions when flame ions cannot be made to survive long enough (because distances are too large to apply a field) a small auxiliary flame or even ion emission from hot plates can provide the necessary charge.Lastly as regards droplets or particles deliberately charged during their dispersion very few of the above limitations apply. Owing to their high specific charges appreciable mass fluxes can be induced by quite modest fields linear velocities being 1-2 orders of magnitude greater than normal burning velocities. SMOKES DROPLETS FLAMES AND ELECTRIC FIELDS I am indebted to Mr. R.J Bowsex for checking the manuscript. K. G. Payne and F. J. Weinberg Proc. Roy. Soc. A 1959,250,316. E. R. Place and F. J. Weinberg Proc. Roy. Soc. A 1965 289 192. F J. Weinberg Proc. Roy Soc. A 1968,307 195. P. J. Mayo and F. J. Weinberg Proc.Roy. SOC.A 1970,319 351. K. C. Thong and F.J. Weinberg Proc. Roy. Soc. A 1971,324 201. D. R. Hardesty and F. J. Weinberg 14th Int. Symp. Combustion (The Combustion lnstitnte Pittsburgh 1972). J. Lawton and F. J. Weinberg Proc. Roy. SOC. A 1964 277,468. * T. P. Pandya and F. J. Weinberg Proc. Roy. SOC. A 1964,279 544. H. A. Wilson Phil. Trans. 1897 189 265. lo H. A. Wilson Phil. Trans. A 1899 192,403. l1 H. A. Wilson Phil. Trans. A 1899 193,289. l2 A. P. Chattock Phil. Mag. 1899,48,401. l3 J. Lawton P. J. Mayo and F. J. Weinberg Proc. Roy. SOC.A 1968 303 275. l4 J. Lawton and F. J. Weinberg Electrical Aspects of Cornbustion (Clarendon Press Oxford 1969) P. J. Mayo L. A. Watermeier and F. J. Weinberg Proc. Roy. SOC.A 1965 284 488. l6 L.B. Loeb Basic Processes of Gaseous Electronics (University of California Press Berkeley 1961.). l7 P. Langevin Ann. Chim. Phys. 1905 5 245. K. Gugan J. Lawton and F. J. Weinberg 10th Znt. Symp. Combustion (The Combustion Institute 1965) p. 709. l9 K. C. Thong and A. R.Jones J. Phys. D Appl. Phys. 1971,4 1159. 2o F. T. Smith J. Chem. Phys. 1958 28,746.

ISSN:0301-5696    

DOI:10.1039/FS9730700120

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Brownian Coagulation of Aerosols at Low Knudsen Number -f BY GILBERT AND MILTONKERKER A. NICOLAON * Dept. of Chemistry and Institute of Colloid and Surface Science Clarkson College,of Technology Potsdam New York 13676 U.S.A. Receiued 15th January 1973 Dibutyl phthalate aerosols of narrow size distribution have been prepared in a falling-film gener- ator using nitrogen rather than helium as the carrier gas. The Knudsen number in nitrogen is considerably lower so that the Cunningham correction is much less. A large number of coagulation experimentsgive average coagulation times in excellent agreement with theory. However thespread ofthe values ismuchgreater than obtained earlier in helium. The spread of the results reported here may be due to the lower thermal conductivity of nitrogen.Smoluchowski's theory of Brownian coagulation of aerosols in which the motion of the particle is controlled by the Stokes-Einstein diffusivity is valid in the hydrodynamic domain where Kn = L/a+1. (1) The Knudsen number is the ratio of the mean free path 3. of the gas molecules to the radius of the particle a. When this becomes as large as unity the empirical Cunning- ham correction must be ulilized leading to This correction is given by Davies as A = 1.257+0.4. . .exp (-1.10 a/R). (3) The first integral of eqn (2) describes the rate of formation of particles of radius ah by coagulation of particles of radius a with those of radius ah-[. The second integral gives the rate of disappearance of particles of radius ahby coagulation bith other particles.The smallest and largest classes of particles are given by a and a,. The particle concentration of class a is given by n,,' k is the Boltzmann constant Tis the Kelvin temperature and v is the viscosity of the gas. When the Knudsen number is large (Kn>10) the particles can be treated as if they were large molecules and the coagulation can then be described by the kinetic theory of gases. Lai et aL3 have discussed this case recently. There is a transition regime (10>Kn>O.l) for which the fluid mechanics of the particles have not yet t This project has been financed in part with federal funds from the National Science Foundation under grant number GP-33656X. 133 BROWNIAN COAGULATION OF AEROSOLS been reduced to theoretical analy~is.~ Indeed it is the lower end of the transition regime (1 .O> Kn> 0.1) which is treated with the aid of the Cunningham correction.For aerosols suspended in air at atmospheric pressure and 20°C the transition regime corresponds approximately to 1.5 nm <a< 150 nm and it includes in the atmosphere the important class of so-called Aitken nuclei which probably act as condensation and freezing nuclei. Although Smoluchowski's theory was published more than 50 years ago numerical solutions to his non-linear integro-differential equation have been obtained only recently with the advent of electronic digital computers. Virtually all earlier work had been restricted to the initial rate of coagulation of a monodisperse system for which the process follows second-order reaction kinetics where N is the total particle concentration.Experimental studies have lagged even further. These have mainly utilized eqn (4) and typically have attempted to demonstrate merely that the particle concentra- tion follows the second-order rate law hopefully with a rate constant close to that predicted by the theory. Frequently these aerosols were poorly-defined systems and the particle sizes shapes and concentrations were not determined accurately so that the results can hardly be considered definitive. We have recently completed an experimental study of the Brownian coagulation of an aerosol for which Kn = 0.78. The results were in agreement with Smoluchow- ski's theory of Brownian coagulation as modified by the Cunningham correction [i.e.eqn (2)] and we plan to extend this experiment throughout the entire range of Knudsen numbers viz. the free molecule the transition and the hydrodynamic regimes. This paper reports the next step in this programme. It is a study of coagulation at a lower Knudsen number (Kn = 0.20).* This lower value of the Knudsen number was obtained by preparing the dibutyl phthalate (DBP) aerosol in nitrogen rather than in helium as in the earlier work. Thus it was mainly the mean free path of the gaseous medium that was altered rather than the aerosol particle size and this permitted utilization of our previously developed light-scattering technique for monitoring the particle size distribution as well as an aerosol generator similar to the one which had proved so successful in the earlier work.A number of modifi- cations were made in the preparation of the aerosol when nitrogen was utilized as the carrier gas in place of helium. DBP AEROSOLS IN NITROGEN The aerosol generator has been described ear1ier.*-l1 A mixture of the gas and NaCl nuclei flows laminarly down a vertical tube along whose wall flows a film of DBP maintained at an elevated temperature. Aerosol is formed upon cooling to room temperature by condensation of the DBP upon the nuclei. The monodispersity of the aerosol can be significantly improved by evaporating and then recondensing the initial DBP aerosol. This will be termed a regenerated aerosol. Heat transfer and convective diffusion calculations are in agreement with measurements of the temperature distribution and the extent of saturation of the vapour respectively.* This value of the Knudsen number corresponds to the modal value in the size distribution. For the uncoagulated systems the coefficient of variation was about 0.10. However for the coagulated systems the spread of sizes becomes considerably greater. G. A. NICOLAON AND M. KERKER The influence upon the particle size distribution of parameters such as furnace temperature,' DBP boiler temperature,8 flow rate,8 number and size of nuclei,'" and cooling rate,l0 have been discussed. F1LTER.-+ rl t FIG.1.-Filter for collection of aerosol. The major procedural change in this work with nitrogen was to collect the aerosol for gravimetric analysis by filtration rather than by thermal precipitation.There was considerable leakage of aerosol through the thermal precipitator 'when nitrogen was used presumably because of the lower thermal conductivity of nitrogen compared to helium. Fig. 1 depicts the filter. It utilized millipore filters with pore diameters of either 1.2 or 3.0 pm. The results in table 1 verify that the amount of aerosol collected was independent of pore size over the range 0.8-8.0 pm. TABLE 1.-AMOUNTOF AEROSOL COLLECTED FOR DIFFERENT PORE SIZES OF THE MILLIPORE FILTER (CARRIER GAS N2; FLOW RATE 1 l/min ; BOILER TEMPERATURE 110") pore diam./ mass/(mg/l) rnass/(mg/l) /rm (expt 1) (expt 2) 0.8 0.76 0.79 1.2 0.78 0.79 3.O 0.75 0.80 8.o 0.74 0.78 We have also noted even for helium that the mass concentration of aerosol obtained when collection was by thermal precipitation was about 5 % less than that by filtration.This would give higher aerosol number concentrations in the earlier coagulation work with better agreement between theoretical and experimental coagulation times. The percentage saturation of the DBP vapour at the exit of the boiler was calculated using the earlier convective diffusion theory and this is compared in table 2 with the experimental results at two flow-rates. Also listed in this table are new results for helium based upon collection by filtration rather than thermal precipitation. The agreement is excellent particularly since there is significant uncertainty both in BROWNIAN COAGULATlON OF AEROSOLS values for the diffusion constant of DBP as well as the actual temperature of the DBP at the vapour-liquid interface.In this connection a comment on the teinperature of the DBP is in order The elevated temperature of the DBP filiii is niaintaincd by circulating oil at constant temperature through an external jacket. In effect the gas stream is always slightly cooler than the oil so that the temperature of the DBP at the vapour/liquid interfxe TABLE 2.-cOMPARISON OF THE PERCENTAGE SATURA'TION AT THE EXIT OF THE VAPORIZER OBTAINED THFORETICALLY AND F.XPEH1Mt.N'TALI.Y (DBP TEMPERATURE 108") gas flow rate,'(I min) saturation t heorct ical ";saturation u xper iment aI He 1 .o 96 95 He 2.0 84 88 N* 1 .o 74 82 N2 2.0 53 51 is also probably cooler.Thus for the above convective diffusion calculation we have assumed a DBP temperature of 108 in view of the fact that the oil temperature was 110" and the temperature withir the gas stream was 106-107". Acutally the measured concentration of DBP provides a better criterion for the effect ofthe boiler conditions upon the properties of the aerosols than the " boiler temperature " and the former quantity will be utilized henceforth. The coagulation experiments to be described in the next section were carried out (as in the earlier work) with a standard aerosol. The conditions were nitrogen flow rate 1.0l/min; furnace temperature 590°C ; DBP flow rate 25 ml/min ;concentration (by filtration) 0.78mg/l.This aerosol was regenerated in the manner described earlier. We have prepared and analyzed the particle size distribution of several hundred DBP aaosols in both helium and nitrogen over the past three years and these results are summarized in table 3. The second column pertains to the standard aerosol in helium the third column to the regenerated standard aerosol in hetium and the fourth column to the regenerated standard aerosol in nitrogen. The operating condItIons for the helium system are helium flow rate 2.0 l/min ;furnace temperatuw 590'C ; DBP flow rate 25 ml/min ; concentration (by filtration) 0.84 mg/l. The conditions for the nitrogen system have been given above. The low values of the standard deviation of the modal radius and of the coeficient of variance indicate the high degree of reproduoibility obtainabk with this aerosol generator.TABLE 3.-sUMMARY OF PARTTCLE SIZE ANALYSES FOR DBP AEKOS0I.S IN HF.1-IUM ASD IN NlTROCiEN DgP in heliurv DBP in nilrogcn DBP in helium regeocratsd regennaf ed no. of runs 210 100 125 modal radius/prn 0.235 0.236 0.314 std. deviation 0.005 0.006 0.007 coefficient of variation 0.16 0.10 0.41 std. deviation 0.01 0.oi 0.0 1 Just as in the case with helium the effect of regeneration in nitrogen was to give a npxe monodisperse aerosol wi,th the Same modal radius. Also even a narrower sizc.distribution was obtained if only the aerosol near the axis or near the wall is G. A. NICOLAON AND M. KERKER sampled. Indeed in such a case the aerosol is about as monodisperse as the well- known Dow polystyrene latexes.The effects are illustrated in fig 2 and 3. in fig. 2 the angular distribution of the polarization ratio of the scattered light is plotted against scattering angle for (A) a standard aerosol which has not been regenerated (B) for a regenerated standard aerosol and (C)for the latter aerosol which has been sampled from within the axial region. The polarization ratio is the ratio of the polarized radiance whose electric vector is parallel to the scattering plane relative to the polarized radiance whose electric vector is perpendicular. The procedure for inverting these data to obtain the logarithmic particle size distribution is described el~ewhere.~ The corresponding size distributions are plotted in fig.3. The modal value of the radius is 0.240pm for each aerosol but the breadth parameters (which correspond closely to the co- efficient of variation) are 0.16 0.10 and 0.04 respectively. Although these particular examples were selected from results with helium similar effects were obtained with nitrogen. I 1 46.1 70 I00 I30 6 Fw. 2.-PolarizatiOn ratio against scattering angle for (A) standard DBP in helium ; (B) the same which has undergone evaporation and condensation; (C) the same as (B) which has been sampled from the axial region. COAGULATION OF DBP AEROSOLS IN NITROGEN The coaguhtion experiment was similar to that described earlier The initial size distribution of the regenerated standard DBP aerosol in .nitrogen was determined BROWNIAN COAGULATION OF AEROSOLS by light scattering early in the life history of the aerosol.This must occur prior to appreciable coagulation since inversion of the light-scattering data with the aid of the Mie-Lorenz functions is accurate only if the distribution is narrow and is unimodal. 3 8 ct x radiuslpm FIG.3.-Size distribution corresponding to aerosols (A) (B) and (C). whose polarization ratio against scattering angle is plotted in fig. 2. The modal value of the radius is 0.240pm. The breadth parameters uo = 0.16 0.10 and 0.04 respectively. Light-scattering data were then also obtained at later times after passage through hold-up tubes of various volumes. The size distribution of the aerosol was calculated as a function of time using the initial size distribution and Smoluchowski’s theory of Brownian coagulation.Theoretical light-scattering results corresponding to the distribution for the coagulated systems were calculated and these were then compared with the experimental light-scattering data. The flow chart for the calculation is outlined in fig. 4. Presumably if the experimental data can be fitted to a calculated result the coagula- tion mechanism proceeds in accordance with Smoluchowski’s model. Furthermore if the experimental and calculated time scales agree there is no potential barrier to coalescence upon collision. If the experimental time is greater than the calculated time the collision efficiency is less than unity and the potential barrier can be cal- culated.12 If the experimental time is less the aerosol is coagulating faster than predicted by Brownian diffusion so that other mechanisms must be involved.One improvement in the procedure used in this work was to make 4 to 6 light- G. A. NICOLAON AND M. KERKER scattering analyses of the aerosol over an extended period of time prior to obtaining any coagulation data and using the average of the values for the size distribution. The values obtained were usually similar attesting to the stability of the aerosol generator. However on occasion there would be a small deviation and if this transient value had been used to characterize the initial aerosol the calculated size distribution of the coagulated aerosol would have been significantly different.LIGHT SCATTERING DA~A LIGHT SCATTERING DATA FOR INITIAL AEROSOL FINAL AEROSOL -FOR 1 1 I. INVERSION Of DATA 4 COMPARISON 1 t INITIAL SIZE DISTRIBUTION CALCULATED LtGHT SCATTERING RESULTS &* I q I M. I I \ / 2 BROWNIAN COAGULATION 3 LIGHT SCATTERING CALCULATION 6'\ / CALCULATION 1 FfWL SIZE DlSfRlBUtlONl FIG.4.-Flow chart for coagulation calculation. Average hold-up time is t' ; average calculated time is t". Another procedural change was to utilize for the aerosol number concentration the value based upon a gravimetric analysis of each particular run. In the earlier work an average value for many runs had been used and the concentration was not determined for each particular run. The aerosol was collected for weighing by TABLE 4.-vARIATION OF NUMBER CONCENTRATION OVER A PERIOD OF 12 DAYS modal value breadth mass of radius parameter.concentrationI number concentration no. omlm 00 (mg/l) no./(10-6 cm-3 1 0.308 0.10 0.75 5.5 2 0.309 0.11 0.79 5.6 3 0.315 0.12 0.76 5.0 4 0.311 0.11 0.72 5.0 5 0.313 0.11 0.74 5.1 6 0.317 0.12 0.77 5.0 7 0.313 0.12 0.78 5.3 8 0.314 0.11 0.80 5.4 9 0.311 0.10 0.79 5.6 10 0.320 0.12 0.79 5.O 11 0.308 0.10 0.79 5.8 12 0.311 0.11 0.75 5.2 filtration rather than by thermal precipitation. The extent of variation in the number concentration for a series of runs carried out over a period of 12 days is shown in table 4. The day-to-day variation was sufficient to introduce a significant error in the number concentration of the initial aerosol had the average value been used.On the other hand the concentration was stable over the course of a day run. BROWNIAN COAGULATION OF AEROSOLS The results are shown in table 9. The experimental timCs are average residence times obtained from the volume of the hold-up tube and the htv rate. The third column termed quasi-static time is the dlculated time with the assumption that each fluid particle spends the same amount ofi-time in the hold-up tube. Actually the aerosol is in Poiseuille flow with a pambolic.velocity profile. The aerosol near 1 the wali is moving much mote slowly than the aerosol abng the axis of the tube and is therefore undergoing coagulation for the longer time. The results in the last column were obtained by the procedure outlined earlier for transforming quasi- static to Poiseuille times The angular distribution of the polarizatioo'ratio which is used in these experimmts to monitor the coagulation goes through a sequence of states for the Poiseuille flow calculation which is similar to that for the quasi-static calculation except that the former proceeds more slowly.This permits preparation of a calibration curve. Then the calculation is carried out according to the scheme of fig. 4 assuming quasi-static flow varying tl untit the calculated fight-scattering results best fit the experimental data. Finally the corresponding Poiseuillc time is obtained from the calibration curve. The fourthscolumn in table 5 gives the standard deviation for the quasi-static times.TABLE 5.-cOMPARImN OF EXP6RIMENTAL AND CALCULATED COAGULATION TIMES (SECONDS) exptl t imc no. of runs quasi-Statictime ad Poi~uillc t imc 82 32 67 27 84 154 105 116 49 145 235 23 196 41 245 327 24 26s 61 340 The miterioa for best fit was the minimum value of tk deviation measure given by ( 130" where p(0) and p'(0) are the measured and calculated values of the polarization ratio at each of the 19 angIes obtained between 40"and 130" zt 5" intervals. Fig. 5 illustrates a typical example of the fit of the calculated results to the experimental data which are plotted as points. The curve represents the angular distribution of the polarization rates calculated for that coagulation time for the initial aerosol which minimizes the deviation measure (eqn (5)) For this cxample the experimental hold-up time is 154 as.The catculated result gives a hold-up time of 169 s with a Corresponding deviation measure' of 0.10. ' 6 * Although the average values of the coagulation time in table 5 agree well with the experimental coagulation times there is a considerdble spread in the individual values as indicated by the standard devations. In ordeb to determine whether this spread arose from the accuracy in fitting the experimental and calculated results all runs were eliminated for which the deviation measure'was greater. than 0.25.. The redts are shown in table 6. Theagreement between the experimentaland calculated coigula- tion times is not affected significantly (it is slightly poorer) nor is the spread of the results any narrower.Accordingly the light-scattering analysis does not appear to be a factor in accounting for the spread of the.coagulation time. There is another factor which; may account fgr.t,hese,resultg. We hare observed occasionally sporadic convective " storms ** in these aerosols in nitrogen particularly in the bold-up tubes in contrast to #thequiescent appearance under illumination of the helium system. Ths,tendewy,rnay be-due to the low heat conductance (and 0.A. NlGOLAON AND M. KERKER sharper temperature gradieats) of .nitragen and the randomization d the results which was not,encountered in the earlier work with helium &t be caused by this effect. The subsequent mi>cing,would tad to makc cbe system deviate from the condition of Poiseuille flow and inore resemble the well-mixed system which we have e Frc;.5.-Angular distribution of polarization ratio. Points are measured values for experimental time of 1% s. Curvc corresponds to calculated time(169 s) which best fi6 these values (D= 0.10). called the quasi-static model. One would expect then that the coagulation time calculated according to Poisetdle flow would be an upper limit and that the average values would be lower. Any barrier to coalescence corresponding to a coalescence efficiency of less than unity would lengthen the coagulation time. A combination of these two effects could account for thc observed results. TABLE 6.-cOMPARlSON OF EXPERlMENTAL AND CALCULATED COAGULATION TIMES (SECONDS).RUNSWITH DEVIATIOS MEASURES GREATER THAN 0.25 ELIMINATED exp1l t irnc no. o rnns quas,i-statictime s.d. Poiseuille time 82 20 71 22 89 154 59 127 47 I58 235 21 203 35 254 327 24 268 61 340 A question has been raised about the stability of the aerosol to evaporation during its passage through the coagulation tube. There is the possibility because of the Kelvin effect that material might distill to the walls or from the smaller to the larger particles or both of these effects might occur. The possibility of distillation to the walls has been checked repeatedly by collecting and weighing the aerosol prior to entrance and upon emergence from the coagluation tube and we were unable to detect any hold-up. Furthermore the light-scattering data can only be interpreted by an increase in average particle size which would not be the case were distillation to the walls to occur to a significant cxtcnt.Distillation from the smaller to the larger particles-for which the driving force is much less than distillation to the walls- BROWNIAN COAGULATION OF AEROSOLS would have the effect of shifting the size distribution to a greater average size just as coagulation. However since the effects which we have observed are accounted for by coagulation which must proceed in any case it seems highly unlikely that evaporation of these particles occurs to any significant extent in the course of these experiments. We have noted the much greater variation of these experimental results in nitrogen compared to earlier results in helium and have attributed this to convective storms in the nitrogen system due to its lower heat conductance.We doubt if this effect can be attributed to the possibility of evaporation of the dibutyl phthalate particles. The average particle size in the helium work was smaller (a = 0.24pm compared to 0.31 pm) and hence the Kelvin effect was greater. Furthermore the rate of evaporation is greater in helium than in nitrogen. Yet the kinetics of the process is accounted for in both cases by coagulation ;the agreement in helium was even more striking than in nitrogen. M. Smoluchowski 2.phys. Chem. (Lpg) 1917,92 129. C. N. Davies Proc. Phys. Sac. 1945 57 259. F. S. Lai S. K. Friedlander J. Pich and G.M. Hidy J. Colloid Interface Sci. 1972 39 395. G. M. Hidy and J. R. Brock The Dynamics of Aerocolloicial Systems (Pergamon New York 1970). H. L. Green and W. R. Lane Particulate Clouds (D. Van Nostrand New York 1957). G. Nicolaon M.Kerker D. D. Cooke and M. Matijevic J. Colloid Interface Sci. 1972 38 460. M. Kerker The Scattering of Light and other Electromagnetic Radiation (Academic Press New York 1969). * G. Nicolaon D. D. Cooke M. Kerker and E. Matijevic,J. Colloid Interface Sci. 1970,34,534. G. Nicolaon D. D. Cooke E. J. Davis M. Kerker and E. Matijevic J. Colloid Interface Sci. 1971,35,490. lo G. Nicolaon and M. Kerker J. Colloid Interface Sci. 1973 42 to be published. E. J. Davis and G. Nicolaon J. Colloid Interface Sci. 1971 37 768. I* N. A. Fuchs The Mechanics of Aerosols (Macmillan New York 1971).

ISSN:0301-5696    

DOI:10.1039/FS9730700133

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

A Contribution to the Theory of Fibrous Aerosol Filters BY N. A. FUCHS,A. A. KIRSCH and I. B. STECHKINA Karpov-Institute of Physical Chemistry Moscow 120 Obucha 10 Received 7th November 1972 Almost all properties of the “ parallel ” filter model-a system of parallel cylindrical staggered and regularly arranged fibres can be treated theoretically but these properties differ considerably from those of real filters. On the contrary the theoretical treatment of the “ fan ” model obtained by turning in the parallel model all fibre rows in their planes by an arbitrary angle is very difficult but its properties are the same as those of real filters with a perfectly homogeneous structure. The “ degree of inhomogeneity ” of a real filter is the reverse ratio of its resistance and of the particle capture coefficient on its fibres (in absence of inertial deposition) to those in an equivalent fan model.This makes it possible to calculate the filter efficiency from its resistance. In the past 30 years many papers on the theory of fibrous aerosol filters have been published beginning with the fundamental work of Sell Albrecht Kaufmann and Langmuir. However on the basis of these papers it has been impossible to calculate the main characteristics of these filters (i.e. their hydraulic resistance and their efficiency in respect to aerosols with various particle size and at various flow rates) from measurable filter parameters-the fibre width and the shape of their cross-section the volume fraction occupied by the fibres (packing density) their orientation the homogeneity of filter structure etc.-without resorting to a number of empirical equations and coefficients.For several years we have been working on the development of a theory which would make possible such a quantitative calculation of filter efficiency. So far we have been able only to approach this goal but not to reach it. However the results of this work seem to have led to a better understanding of the complex processes of aerosol deposition in fibrous filters. For the development of the theory we have used filter models approaching real filters combining in this work wherever possible theoretical deductions with experi- mental studies. At small flow velocities (not exceeding 10-20cm/s) at which the fibrous filters show a high degree of efficiency it may be assumed that all particles of size not greater than a few pm coming into contact with a fibre adhere to it.Besides at such small flow velocities the flow is automodel i.e. the pressure drop across the filter is proportional to the flow rate. We have excluded from considera- tion the effect of electrical forces i.e. the filtration of aerosols with not very small particle charges as well as filters charged or polarized by an external field. In modern filters in the shape of papers cardboard sheets and pads the fibres are oriented more or less parallel to the same plane and the packing density is usually less than 0.1. THE “PARALLEL” MODEL. RESISTANCE In Langmuir’s model-an isolated cylindrical fibre the effect of neighbouring fibres on the flow field is neglected and this model cannot be used for our purpose.The simplest model approaching real filters called by us the “parallel” model is a system of straight equal cylindrical parallel staggered regularly arranged fibres (fig. l) perpendicular to the flow direction. The flow field near the fibre surface in 143 FIBROUS AEROSOL FILTERS this model was calculated by Kuwabara.' For the flow function he obtained the following expression (in polar coordinates) accurate to the terms of a to the first power where Uois the face value of the flow velocity a the fibre radius and a the packing density. 0 0 Q 0 0 0 0 ____)_ FIG.1.-The " parallel "model. Kuwabara assumed the fibres to be arranged parallel but disorderly.In reality as shown experimentally by us (see below) and theoretically by Golovin and Lopatin,2 formula (1) can be used only for a regular staggered fibre arrangement shown in fig. 1. The accuracy of formula (1) was checked in our model experiments with glycerol flowing in a system of staggered parallel cylinders with diameters of 7 or 14 mm with a velocity 0.06-0.16cm/s (Re= 0.01-0.05). The velocity vector in each point was determined by photographing under intermittent illumination the trajectories of metallised spherical polymer beads suspended in glycerol having the same density as the liquid and therefore moving along the flowlines. The trajectories and velocities of the beads agreed accurately with those calculated by means of (1) at p/a<2 for a = 0.05 and at p/a< 1.5 for a = 0.2.Another question important to the filtration theory was solved in these experi-ments. It is usually assumed that the centre of a spherical inertia-less particle moves exactly along the flow lines. However under the action of the flow velocity gradient existing in the vicinity of a cylindrical obstacle the particle must rotate and we cannot assume apriori that no lateral drag is acting on this particle. In any case the larger the particle whose centre moves along a given flow line i.e. the smaller the minimal gap between the particle and the cylinder the larger must be the lateral drag In our experiments we found that spherical inertialess particles with diameters of 0.1 and 3.0 mm move around 7 to 14 1nm thick cylinders along quite identical trajectories i.e.along the flow lines. As the hydrodynamical forces in liquids are much larger than in gases the validity of this conclusion for aerosols cannot be doubted. N. A. FUCHS A. A. KIRSCH and I. B. STECHKINA From (1) the hydrodynamic drag F,’ acting on the unit fibre length in the parallel model can be calculated. It is more convenient to use the dimensionless drag FP= E’;/pU, where p is the viscosity of the medium. The following expression for FPcan be derived FP = ~x/K;K = -0.5 In a-0.75+a (2) (superscript P stands for the “ parallel ” model). For a single regular row of parallel cylinders Mijagi obtained the formula FP= 4x[-ln(na/h2)+0.5+(na/2h2)’/3+. . .]-I (3) where 2h is the distance between the axes of neighbouring fibres.The pressure drop across the model is related to FPby the formula Ap = FPUopuH/na2 (4) where H is the thickness of the filter (or of the model). For a single row Ap = FPUOp/2h2 (5) Formulae (2)-(5) were verified by model experiments with glycerol at very low Reynolds number. The fibres were modelled by wires and capron filaments with diameters 0.15-0.70 mm. A plot of FPagainst a drawn in accordance with formula (2) is shown in fig. 2 together with the experimental results obtained on models -2 -I I0 10 a FIG.2.-The dependence of FPupon cc in the parallel model. Theoretical curve eqn (2). Experi-mental points v 0 n v a/h2 0.41 0.365 0.21 0.074 with h1 = h2and a/h2= 0.067-0.41.Good agreement with the theory was observed up to a = 0.27. An equally good agreement was obtained for models with It <h,. Formula (3) for single fibre rows was valid up to a/h = 0.7. Approximately at hl/h2 = I the FPvalues for a single row and for a system of cylinders become equal i.e. at h > h the hydrodynamic interaction between the fibre rows vanishes and the resistance of the parallel model is equal to the sum of resistances of separate isolated rows. FIBROUS AEROSOL FILTERS In filters made of ultrafine fibres (a< 1 pm) or in filtration at reduced pressure the Knudsen number Kn = A/a (A is the mean free path of gas molecules) is finite and the gas slip at the fibre surface should be taken account of. In this case the following formulae can be derived for the parallel model,6 (FP)-' = (FE)-' +zKn(l -a)/47t (6) and for a single fibre row (FP)-' = (FOP)-' +zKn[l -+(r~a/2h~>~]/4n (7) where F is the value of Pp at Kn = 0 and z is the ratio of the slip coefficient at the fibre surface to A.Formula (7) was verified on a model with a = 4.45 pm 2h2 = 62 pm 2hl = 1.1 mm in the air and in CO at pressures 10 Torr. As follows from above in such a model the hydrodynamic interaction between fibre rows is absent. The results are shown in fig. 3. Experimental points were obtained at p-l Torr-' air 2 3 Kn c02 I 1 I 2 I 3 FIG.3.-(Fp)-' against p-l (Kn) in a single fibre row in air (1-7) and in CO (8-12).mental points refer to various Re values up to 6 x The experi- Re = 1 x -6 x The lines were drawn in accordance with (7) at z = 1.18 for air and z = 1.12for CO,.According to the latest data,8 in air z = 1.15. Thus formula (7) was valid up to large values of Kn (Kn x 3) but already at Re = 0.15 the relationship between (FP)-' and Kn begins to deviate from linearity (PP)-'increasing faster than Kn.* The absolute value of FPat Kn = 0 found in these measurements agreed exactly with formula (3). Real filters consist of fibres of different width. In order to estimate the effect of fibre polydispersity on the resistance of the parallel model a model consisting of a single row of fibres with alternately larger a and smaller a2radii and with the distance * Later experiments did not confirm this conclusion. N.A. FUCHS A. A. KIRSCH AND I. B. STECHKINA 147 between the fibre axes 2hzwas studied. The flow field in such a model was calculated and the following formulae were obtained for the drags 8' and F,P acting 011 thick and thin fibres respectively which are valid for small values of a,/h and aJh F = 8~51; F,P = 8x52; (8) = s12/(C21i22-K2); K = 2 In 2-(~a~/4h~)~-(na,J4h,)~; Ql = In (na,/4h2)2-1-2(na,/4h,)2/3 (9) and similar formulae for c2 and Q2. If Fp = (8':+F!)/2 is the averaged drag and 6 = (a,+a2)/2the mean fibre radius then as shown by calculations for d/h2G0.4 and a,/a2<5 Ppdiffers little (less than by 5 %) from the drag Ppin a mono-disperse grid with the fibre radius equal to d. This result was corroborated by model experi- ments with a viscous liquid at a2 = 22 pm a = 79 or 160 pm h = 500 pin I 2 Plal FIG.4.-Theoretical (1) and experimental (2) flow velocity profiles along the line joining the fibre axes at a/hz = 0.238 and and alla2 = 52.0 0 0 0 oo0 000 U FIG. 5.-A " perturbed " parallel model. FIBROUS AEROSOL FILTERS Re< 0.05. The values of FPdetermined from these experiments agreed within 1-2 % with those calculated for a monodisperse grid. From these results it follows with high probability that the resistance of not very polydisperse filters can be calculated from the mean fibre width. The validity of the flow field near the fibres calculated for the above model was also corroborated in these experiments. The calculated flow liries coincided with those determined experimentally at n/h2 = 0.133 up to p = 2a near thin fibres and up to p = 1.20~~ near thick ones.Even for a very large difference in fibre diameters the perturbing effect of thin fibres on the flow field is considerable as can be seen from fig. 4 showing the experimental and calculated flow velocity profiles along the line joining the fibre axes at 6/h2 = 0.238 and ul/a2= 52. The effect of the irregularity of the model structure on its resistance was also estimated. For that purpose a “ perturbed ” model (fig.5) with equal but irregularly arranged fibres was investigated by means of a viscous liquid and compared with a regular model with h2 = (hi+4)/2. Such a “ microinhomogeneity ” reduced the model resistance considerably and the more so the larger the degree of inhomo- geneity i.e.the quotient h’;/h;and a. The same result was obtained theoretically. The deviation from parallel orientation of fibres in the rows also lowers appreciably the model resistance. PARALLEL MODEL. EFFICIENCY The aerosol penetration through a filter is given by the formula P = exp { -2aql) = exp (-2qaH/na) (10) in which q is the capture coefficient of aerosol particles on the fibres and I is the total length of fibres contained in 1 cm2 of the filter sheet. In the derivation of this formula it is assumed that in each plane perpendicular to the flow direction the aerosol concentration is constant despite particle deposition on the fibres. In the absence of turbulence in the flow through the filter such equalisation of aerosol concentration in the parallel model is possible only under the influence of Brownian diffusion.When the particles are deposited on the fibres not by diffusion but by other mechanisms the error when using formula (10) can be significant. The capture coefficient for diffusional particle deposition in the parallel model qi can be determined by solving the differential equation of convective particle diffusion towards the fibres in the flow field expressed by formula (1). We assume that a< 1 ; Re<&; Pe = 2aUo/D$ 1 (Dthe particle diffusion coefficient). The second of these conditions means that the flow in the fibre system is automodel the third that the particles are deposited from a layer at the fibre surface whose thickness is very small in comparison to the fibre radius.Under these conditions the following formula lo* can be derived for q; q = [2.30(4~/Pe)* +0.312(4~/Pe)+ .. .]/2~. (11) The hydrodynamic factor K is the same as in formulae (I) and (2). At Pe> 10 formula (1 1) can be approximated with sufficient accuracy by a simpler expression q; = 2.9K-+Pe-*. (12) The experimental verification of these formulae was performed l2 using fairly monodisperse aerosols of NaCl and dioctylsebacate with the mean particle radii from 1.5 to 9 nm. The particle diffusion coefficient was measured by means of diffusion batteries. The relative particle concentration before and after a battery N. A. FUCHS A. A. KIRSCH AND I. B. STECHKINA 149 etc. was determined by means of a tyndallimeter after growing the particles by vapour condensation on them.The model filters were made of wires and filaments with a = 0.021-0.25 mm. The experimental results are shown in fig. 6 together with the theoretical lines drawn in accordance with formula (I 1). This formula is valid already at Pe values of the order of a few units and for a as large as 0.27 i.e. in a much wider range than imposed by the conditions of its derivation. 0.1 10 I00 I000 Pe FIG. 6.-The diffusional capture coefficient against Pe in parallel models. Theoretical curves ; I. a = 0.01 ; 11. a = 0.05; 111 a = 0.135; IV a = 0.27. Experimental points (1-4) a = 0.01 ; 1 r = 158,; 2 r = 18A; 3 r = 60A; 4 r = 83A; 5 a = 0.05; r = 70A; (6-8) IX = 0.135; 6 r = 41 A; 7 r = 708,;8 r = 558,; 9 a = 0.27; r = 55A.The diffusional deposition of aerosols in a polydisperse parallel model was studied by the same method as its resistance. In this case the aerosol penetration is expressed (instead of (10)) by the formula P = exp (-2qT,,a,~,-2q;,,a2l21 = exp (-2611 (13) where I = l2 is the length of fibres with radii a and a2 contained in a part of the model with 1 cm2 cross-section I = 1 +12. As shown by calculation based on the flow field in such a model at a,/a2<3.5 and 6/h2G0.2,the value of Zais not more than by 5 % less of that of via,calculated for a model with an averaged fibre radius CS = (a +a2)/2. This conclusion was corroborated by measurements with nionodisperse NaCl aerosols with Y = 1.5 nm at Pe = 10-48 on two models-with a = 0.79mm al/a = 3.59 (3/h2= 0.101 and with a = 0.16 mm ;a,/a2 = 7.27 ;6/h2 = 0.182 respectively.The capture coefficient due to interception in the parallel model qg (the sub- script R stands for '' interception ',) is expressed by Langmuir's formula q = [2(1+R) In (I+R)-(~+R)+(~ +R)-']/~K (14) where R = r/a is the ratio between particle and fibre radii. The deposition due to simultaneous effect of diffusion and interception was calculated by means of a computer l3 for the following conditions R< 1 ; 6 = (4~/Pe)*<1 where 6 is the FIBROUS AEROSOL FILTERS ratio of the thickness of the layer at the fibre surface from which the particles are deposited to the fibre radius. The results of these calculations can be expressed (with accuracy 2-3 %) by an interpolation formula qLR = q +y~ + 1.241c-+Pe-*R3.(15) This means that the total capture coefficient q:R is equal to the sum of the capture coefficients due to diffusion and interception plus a relatively small interferential term. Unfortunately formula (15) could not be verified experimentally due to the great difficulty of preparing filter models with the fibre width of the order of 1 pm necessary for such work. The inertial particle deposition in the parallel model has been also calculated by us but as the results have not yet been verified experimentally they are not included. THE “FAN” MODEL A great advantage of the parallel model is the possibility of theoretical treatment of almost all its properties.However when comparing these properties with those of real filters substantial differences were found. The pressure drop across real filters is much less than in the “ equivalent ” models i.e. with the same parameters. A I ~ I ‘Id- iki+ 0 +. 0 i-0 0 0 FIG.8.-A fan model with very small 8. The diffusional capture coefficient in the model increases considerably with a (see fig. 2) e.g. when the model is compressed but changes very little or not at all on compression of a real filter. After testing a series of models we found that the best agreement with real filters is shown by the “ fan ’’ model obtained from the parallel model by turning each fibre row in its plane by an arbitrary angle 6. The properties of the model proved to be independent of the values of 8 provided they were not zero.In fig. 7 photographs of thin layers of a fan model and of a real filter are given which show a similarity in their structure. From measurements with a viscous liquid the following empirical formula was FIG.7.-A photograph of a fan model (a) and an electron micrograph of a real filter (b). [Toface page 150 N. A. FUCHS A. A. KIRSCH AND I. B. STECHKINA obtained for the drag on the fibres in the fan model l2 when the ratio of the distance between the rows to that between neighbouring fibres in a row was less than 0.65 Ff = 471/1c’ K’ = -0.5 In a-0.52+0.64a (16) (f stands for the “ fan ” model). When this ratio exceed 0.65 the hydrodynamical interaction between the rows vanishes and the drag is given by formula (3).1.0 cn F 0.i to 100 1000 Pe FIG.9.-The diffusional capture coefficient in the fan model (1-6) and in real filters corrected for their inhomogeneity (7-1 1). The full curve is plotted according to formula (18). Experimental points 1 2 3 4 5 6 2altmm) 0.25 0.5 0.1 0.052 0.043 0.043 2hzl(mm) 1 .o 2.5 1 .o 2.0 1 .o 2.0 U 0.187 0.157 0.079 0.02 0.034 0.017 7 8 9 10 11 2al(llm) 7.14 18.1 13.4 32 3.6 E 1.05 1.8 1.3 1.1 2.0 A theoretical analysis of the flow field in a fan model is extremely difficuit but we were able to make an approximate theoretical evaluation of Ff making use of the fact that P‘ remains constant even at very small values of 8. We consider several adjoining fibre rows divided into short sections (in fig.8 for clarity only two rows are shown). At very small 8 each section can be approximated by a system of parallel grids shifted with respect to one another by various distances A. Calculation of the drag Ffas a function of A based on superposition of the flow fields generated by each separate grid and averaging this drag for all A values from 0 to hZ leads to the formula Ff = 4n/(-0.5 In ct-O.44) (17) which is similar to (16). Thus we obtained an explanation of the fact that the resi- stance of the fan model is less than that of the parallel model but we could not explain why F is independent of 8. The conclusions made above for the effect of fibre poly-dispersity and gas slip on the model resistance proved to be applicable to the FIBROUS AEROSOL FILTERS fan niodel as well but in the second term of formula (6) a numerical factor 1.22 had to be introduced.6 An especially sharp difference between the two models was observed for diffusional particle deposition.As shown by measurements,’ the diffusional capture coefficient in the fan model at a = 0.01-0.15 and Pe = l-lO00 is expressed by the simple formula (see fig. 9) 46 = 2.7Pe-*. (18) Thus the diffusional capture coefficient in the fan model does not depend on c( (as in real filters). This can be explained qualitatively by the mutual compensation of two effects on the one hand the concentration gradient of the aerosol at the fibre surface increases with rising a (as for the parallel model).On the other hand the aerosol stream flowing around each fibre is inhomogeneous both in respect to its velocity and concentration. Due to non-linear dependence of the diffusional capture on the flow velocity this leads to a decrease of the deposition. Doubts about the validity of formula (10) for aerosol penetration does not apply equally well to the fan model and to real filters as the non-constancy of aerosol concentration in a plane perpendicular to the flow direction is averaged over the fibre length and for deposition by interception has no significance. However for other deposition mechanisms where the capture coefficient depends on the flow velocity the lack of constancy both of concentration and flow velocity (hydro- dynamic screening) seems to affect the validity of formula (10).An accurate theoretical treatment of this question is complex but the experimental evidence tends to the conclusion that the error in the use of this formula is small. The effect F 10 t -3166 16~ I o4 r/cm FIG.10.-The total capture coeficient against particle radius in a fan mode! with a = lO-’cm a w 0.05. 1 uo = 1 cm/s ; 2 uo = 5 m/s ; 3 uo = 10 cmls ;4 uo = 20 cm/s. N. A. FUCHS A. A. KIRSCH AND 1. B. STECHKINA of fibre polydispersity on the diffusional deposition in the fan model is the same as in the parallel model. The capture coefficient by interception in the fan model can be expressed by a formula similar to (14) but because of the pecularity of the flow field in this model it is necessary to introduce the hydrodynamic factor k' (see formula (16)) into it instead of I,-.Thus The last term in (1 5) is small and depends relatively slightly 011 K. We may therefore retain it for the fan modei substituting k' for k in it and obtain the formula for the combined capture coefficient l4 For practical purpose the most important question in the theory of aerosol filtration is the filter efficiency in the range of maximum penetration. The values of qbR plotted against the particle radii calculated by means of formula (20) for the fan model with c1 = 0,05 and a = 10pm at Uo = 5 10 and 20cm/s are given in fig. 10. As shown by our calculations the inertial deposition in the range of particle size corresponding to maximum penetration is relatively small (Langmuir came to this conclusion intuitively 30 years ago) and the minima on the curves are due to increase of qk and decrease of r& with rising particle size at constant flow velocity.However in the curves qLR against Uo the minima are caused by the increase of inertial deposition and decrease of q; with rising Uo. REAL FILTERS. DEGREE OF INHOMOGENEITY For real filters notwithstanding a large number of published experimental data very few ofthese could be used in this work chiefly due to incomplete characterisation of the filters used. In all filters with cylindrical fibres as shown below the resistance is less than in the fan model with the same parameters. This is caused mainly by the inhomogeneity of the structure of real filters.As already pointed out the filter resistance decreases considerably in the presence of structural micro-inhomogeneities (on a scale of the mean distance between the fibres). A similar effect is produced by macro-inhomo- geneities such as fluctuations of the thickness and packing density of the filter by any deviation from the parallel fibre orientation and from the perpendicularity of the fibres to the flow direction. The presence of doubled trebled etc. fibres caused by incomplete dispersion of the fibres in the fabrication of filters must be regarded also as a kind of inhomogeneity. As shown by calculation and by experib ments with fan models when all the fibres in the filter are doubled the resistance decreases almost two-fold. Various types of inhomogeneity affect the values of the drag F in the formula (4) differently.As the determination of the magnitude of fluctuations of H and a in real filters is very difficult it is expedient to assume formally that the effect of inhomo-geneity of any kind on the filter resistance expressed by formula (4) consists in reducing the drag F. In fig. 11 the values of F' (the superscript r stands for " real ") calculated by means of(4) (the mean values of a were used) are plotted against o! for a number of real filters with cylindrical fibres together with the curve (Pya)for the fan model plotted according to (16). For all filters with cylindrical fibres tested by us or described in the literature together with necessary data for calculating F in the function of CI,the Fvalues were lower than in the " equivalent " (i.e.with the 154 FIBROUS AEROSOL FlLTERS r I I I ii I -a-20 m Ip -G -a-I -I-4 -a-5 0-6 8-7 e 21 1 1 I I1 FIG.11.-The hydrodynamic drag against a. Fan model formula (16) (curve I). Real filters according to Chen l5 (curve 11) Davies l6 (curve 111) Langmuir (curve IV). Our data for filters with 2u = 7.14; 18.1 ;32 and 13.4 pm respectively (1-4). Data of First (3,Wong l9 (6) and Blasewitz *O (7). The effect of gas slip on the resistance of real filters was studied on mono- disperse filters with a = 1.5-9 pm a = 0.03-0.14 and E = 1.08-2.2 at pressures 210 Torr. As shown by these measurements (PI-'increases linearly with Kn (as in models) in accordance with the experimentally found formula (Fr)-' = (&)-' +1.2lzQ(l-a)Kn/4n (21) in which z = 1.18 (in air) 1.21 is an empirical coefficient corresponding to the tran- sition from parallel to fan model and B a coefficient related to the inhomogeneity of filter structure.To the first approximation p = 83. In the efficiency of real filters we must take into account that in the expressions for Ff (formula (16)) and for I&(formula (19)) the same hydrodynamical factor IC' is included. It follows that the effect of inhomogeneity of the filters on both these quantities should be the same i.e. in real filters r& should be E times less than in the fan model. By investigating a large number of commercial filters as well as those prepared in our laboratory we found i2 that the diffusional capture coefficient in real filters as in the fan model does not depend on a i.e.does not change during compression of the filter. Moreover qD in real filters as a rule is less than in the fan model with the same parameters. There can be no doubt that the main reason of these differences is the inhomogeneity of real filters because any kind of deviation from homogeneity leads to increase in the aerosol penetration through the filter. We N. A. FUCHS A. A. KIRSCH AND I. B. STECHKINA made the simplest assumption that the effect of the inhomogeneity on the drag F and on the diffusional capture coefficient vD is equal (as for interception) i.e. that qf = ~qf-,. In order to prove this hypothesis the diffusional deposition of an aerosol with Y = 27 nm in the fan model and in the filters prepared in our laboratory from isodisperse glass fibres was measured.12 The values of qb for these filters as well as for filters described by Chen,Is multiplied by E (determined from the filter resistance) together with the values of qh for the fan model are plotted against Pe in fig.9. All experimental points lie on one straight line corresponding to formula (18) in com- pliance with our hypothesis. Due to the smallness of the last term in (20) we can generalize this result and assume that tlLR = EVLR* (22) An experimental check of these deductions was made 21 with monodisperse aerosols and a filter prepared from isodisperse terylene fibres in the laboratory (no. 1-14 in table 1) and on the basis of Whitby's 22 data obtained with glass-fibre filters (no.14-16) in the range of maximum penetration. The change of cx. in our filter was achieved by compression. The table lists the following parameters fibre diameter 2a filter thickness H packing density u degree of inhomogeneity E deter-mined by comparing the drag F' calculated from fiiter resistance (formula 4) with the drag Ff in an equivalent fan model. U,is the face velocity of flow r the particle radius Pt and Pi,aerosol penetration for upward and downward flows respectively. TABLE 1 .-CALCULATED AND EXPERIMENTAL VALUES OF THE CAPTURE COEFFICIENT IN REAL FILTERS no. 2n/pm H/cm U. E Uo/(cm/s) rhrn Pt PJ. ~DRIE VDR 1 23.1 3.7 0.042 1.53 5.2 0.67 0.73 0.65 0.0043 0.0045 2 23.1 3.7 0.042 1.53 3.8 0.72 0.73 0.63 0.0045 0.0047 3 23.1 3.7 0.042 1.53 2.6 0.63 0.73 0.61 0.0047 0.0048 4 23.1 3.7 0.042 1.53 4.1 0.85 0.62 0.53 0.0065 0.0056 5 23.1 3.7 0.042 1.53 5.4 0.88 0.65 0.53 0.0061 0.0057 6 23.1 3.7 0.042 1.53 2.7 0.73 0.65 0.50 0.0065 0.0052 7 23.1 3.7 0.042 1.53 3.8 0.55 0.72 0.65 0.0044 0.0039 8 23.1 2.0 0.077 1.53 1.7 0.70 0.65 0.45 0.0072 0.0065 9 23.1 2.0 0.077 1.53 1.6 0.70 0.62 0.54 0.0063 0.0060 10 23.1 2.0 0.077 1.53 0.53 0.35 0.38 0.26 0.013 0.01 1 11 23.1 2.0 0.077 1.53 0.92 0.35 0.55 0.43 0.0085 0.0082 12 23.1 2.0 0.077 1.53 1.4 0.35 0.55 0.50 0.0072 0.0065 13 23.1 2.0 0.077 1.53 2.3 0.35 0.66 0.60 0.0054 0.0050 14 10.0 2.0 0.03 1.4 2.1 0.04 0.835 0.014 0.01 3 15 10.0 2.0 0.03 1.4 2.1 0.3 0.937 0.0051 0.0054 16 10.0 2.0 0.03 1.4 2.1 0.55 0.855 0.01 3 0.010 The difference between Pf and Pi is caused by gravitational particle deposition.We excluded this effect by taking the mean penetration H = (Pt+PJ)/2. In the next column the values of qLR/&evaluated by means of (20) are given i.e. the theoretical values of the total capture coefficient and in the last column are the experimental values of this coefficient determined from B by means of (10). The fact that the experimental values are somewhat larger than the calculated ones is evidently due to the neglect of inertial deposition. It follows that when the geometrical parameters a a and H of the filter and its resistance are known we can calculate with an accuracy sufficient for practical purposes its efficiency when inertial deposition can be neglected i.e.in the particle size range FIBROUS AEROSOL FILTERS corresponding to maximum penetration and to the left of it i.e. for still smaller particles. We realize that there are still many gaps in our work. The most sigmficant is the lack of model experimental data on the inertial particle deposition and the too-small number of filters on which all conclusions were tested. We hope to be able to fill up these gaps in the near future. S. Kuwabara J. Phys. Soc. Japan 1959,14,527. A. M. Golovin and V. A. Lopatin Prikladnaya Mekharrika i Tehdinicheskaya Fizika 1969 no 2,99. A. A. Kirsch and N. A. Fuchs J. Phys. SOC.Japan 1967,22 12% T.Mijagi J. Phys. SOC.Japan 1958,13,493. A A.Kirsch and N.A. Fuchs Ann. Occup. Hyg. 1967,10,23. A. A. Kirsch I. B. Stechkina and N. A. Fuchs Kolloid Zhur. 1973,35 34. ’A. A. Kirsch I. B. Stechkina and N. A. Fuchs J. .Colloid Interface Sci. 1971,37,458. S.AJbertoni C. CeECignani and L. Gotusso Phys. Fluids 1963,11 217. A A. Kirsch and I. B. Stechkina J Colloid Inferface Sci. 1973,43,10. *O N. A. Fuchs and I. B. Stechkina Ann. Occup. Hyg. 1963,6 27. I. B.Stechkina Doklady Akad. Nauk. USSR 1966 167 1372. l2 A. A. Kirsch and N. A. Fuchs Ann. Occup. Hyg.,1968 11 299. l3 I. B. Stecbkina and N.A. Fuchs Ann. Omup. Hyg. 1966,9 59. l4 1. B. Stechkina A. A. Kirsch and N. A. Fuchs Ann. Occup. Hyg. 1969,12 1. Is C. Y. Chen Chem. Rev.,1955,55 595. I6 C.N.Davies Proc. Inst. Mech. Eng. B 1952,1 185. l7 I.Langmuir OSRD 1942 report no.865. M.W. First ef al. Harvard University Boston 1951 NYO-1581. l9 J. B. Wong W. E. Ranz and H. F. Johnstone J. Appl. Phys. 1956,27 161. *O A. G.Blasewitz et a/.,U.S. AEC Hanford Works 1951 HW-20847. 21 A. A. Kirsch 1. B. Stechkina and N. A. Fuchs Kolloirl Zhur. 1969,31,227. 22 K. T. Whitby et nl. J. Air. Poll. Contr. Ass. 1961,11 503.

ISSN:0301-5696    

DOI:10.1039/FS9730700143

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

GENERAL DISCUSSION Prof. M. Kerker (Clarkson Cull. Tech. Potsddm) said The measurement of the extinction cross section of a particle by attenuation measurements of a sample colIected on a glass slide is quite precarious. Among the difficulties are refiection effects due to the glass slide interference effects among the assembled particles and if the collection is somewhat dense multiple scattering effects. Also there is the purely optical problem of eliminating the forward scattered light from the detection system. What precautions did Howard take to assess these? And did he caIculate the refractive index that would correspond to his measured extinction cross-section for comparison with the literature values? Alternatively did he compare calculated values of the extinction cross-section for particles of the size he had with his measured values of the extinction cross-section? Prof.J. B. Howard and Dr. B. L. Wersborg (Depr. Chern. Eng. M.I.T.) said In reply to Kerker attenuation by reflection from the glass slide was adequately elimin- ated by directing the laser beam first at a clean spot adjacent to the particle deposit and then at the deposit. The recorded signal which was the difference between the second and first attenuation signals measured the attenuation by soot particles. Interference among particles was trivial a conclusion based on the fact that attenuation by the different deposits which ranged from less than a monolayer to only a few particle layers was a linear function of deposit depth. Calculations employing the ranges of possible values of the optical coefficients of the particles studied show that scattering is negligible compared with absorption for all values of the diameter/wavelength ratio encountered in the experiment.The optical measurements will be described more fully in a forthcoming publication. The extinction cross-sections cannot be calculated since data on the refractive index of young growing soot particles are not available. However data are available on the refractive index of aged soot and the values give extinction cross sections larger than those measured in this work. According to Dalzell and Satofim,' the complex refractive index of aged acetylene soot for the wavelength in question (6328A) is rn = 1.57-0.44i which gives an extinction cross-section larger by a factor of 28-3.8 than the values found in this study.This difference is qualitatively reasonable since young soot particles contain more hydrogen and have less crystal stucture than aged soot. Dr. C. N. Davies (University of Essex) said I think that aerosols of dibutyl phthalate are too volatile for use in the experiments of Nicolaon and Kerker. Since the aerosols were undiluted the gas phase must have been saturated with the vapour of dibutyl phthalate and eqn (2.9) and (3.1) of my paper are then suitable for calculat- ing rates of evaporation. Coagulation times from 82-327 s are shown in table 5 ; it will be supposed that the temperature of the aerosol in the ageing vessel was 20°C. Calculations of evaporation have been carried out for particles of radii as shown in table 3.' W. H. Dalzell and A. F. Sarofim J. Heat Transfer 1969 91 100. 157 GENERAL DISCUSSION It is evident that during the coagulation period vapour must be distilling isothermally from the smaller particles to the larger ones so that the ascribing of change in size loss of weight in particle radius/ aerosol Pm lifetimels 320 s 160 s DBP in helium DBP in nitrogen 0.235 0.314 940 1210 39 % 27.6 % 19 x 12.8 % distribution to coagulation alone is incorrect. Some of the vapour would also condense on the walls of the vessel which have an area much exceeding that of the aerosol particles; the authors state that they were unable to detect any hold-up on this account but an assessment of the amount of vapour concerned in relation to the accuracy of analysis is lacking.An assessment also of the accuracy of the rather indirect optical measurement of size distribution would be of interest. The mass concentration of aerosol measured by thermal precipitator sampling was 5 % less than the figure obtained with millipore filters. A thermal precipitator can be a very accurate instrument for sampling aerosols but it is possible for vapour to condense in the small cavities of filters due to the Kelvin effect. Prof. M. Kerker (Clarkson Coll. Techn. N. Y.) said In reply to Davies we have checked repeatedly for hold-up of dibutylphthalate in the coagulation chamber and have always found this to be negligible. Some recent results are presented here for three different flow rates.In this case the dibutylphthalate aerosol is in helium at a pressure of 0.50+0.01 atm so that any distillation to the walls would be expected to be more pronounced than for the aerosol in the paper which is for nitrogen at atmos-pheric pressure. The modal radius was 0.25pm. The aerosol was collected on millipore filters (pore 1.2 pm) just prior to entrance into and after exit from the coagulation chamber (volume 2570 ml ; wall area 1800 cm2). Residence time in the chamber varied from 1.28-2.57 min. As is apparent from the table the loss appeared to be about 2 %. The error in weighing the samples is about 1 % so that hold-up in the coagulation chamber is negligible. TABLE 1 .-HOLD-UP OF DIBUTYLPHTHALATE AEROSOL IN THE COAGULATION CHAMBER aerosol conctntration/(nig/l) flow 1.0 I/m flow 1.5 l/m flow 2.0 I/m initial aerosol 1.70 1.62 1.57 coagulated aerosols 1.68 1.59 1.55 One would expect that isothermal distillation from smaller particles to larger ones would occur even more slowly than distillation to the walls both because the wall area is larger than the surface area of the aerosol particles but more especially because these aerosols are quite monodisperse (even those which have coagulated for some time) so that the driving force which is derived from the range of Kelvin vapour pressures is much smaller.Accordingly we do not believe that distillation either to the walls or from particle to particle plays a significant role in the processes occur- ring in the hold-up tube.More direct evidence that the mechanism by which the aerosol ages is coagulation rather than distillation is contained in the two electron micrographs fig. 1 and 2. These depict a linolenic acid aerosol (modal radius a = 0.248 pm) prior to entry into the coagulation chamber and after exit (hold-up time 5.26min). The aerosol was "fixed " prior to collection for electron microscope observation by treatment with OsO,. (The apparent spots in the centre of each particle are due to penetration of the glossy photographic print in the process of obtaining the particle size distri- FIG. 1.-Electron micrograph of linolenic acid aerosol prior to coagulation; see table 2 for size distribution. FIG.2.-Electron micrograph of linolenic acid aerosol after coagulation (5.26 min) ; see table 2 for size distribution.[Tofacepage 158 GENERAL DISCUSSION bution with a Karl Zeiss particle counter.) The size distributions for each of these electron micrographs is given in table 2. It is significant that although the average particle size increases the smallest particles in the population are neither completely scavenged nor reduced to a smaller size as would be expected were the principal mechanism distillation from small to TABLE 2.-PARTICLE SIZE DISTRIBUTION OF INITIAL AND COAGULATED LINOLENIC ACID AEROSOL radius/pminitial (%) 0.18 - 0.21 13.9 0.25 58.1 0.28 23.3 0.32 3.8 0.35 0.6 0.38 - 0.41 - coagulate (%) 0.5 8.3 24.9 19.1 13.8 9.6 5.3 5.4 radius/pminitial (%) 0.44 - 0.47 0.2 0.51 - 0.54 - 0.57 - 0.60 - 0.63 - 0.67 - coagulated (%) 3.7 2.7 3.0 1.o 1.1 0.6 0.9 0.2 large particles rather than coagulation.Also examination of the distribution of sizes in table 2 shows that the frequency of the modal size decreases as would be expected for coagulation and does not shift to a smaller size category of the same frequency as would be expected for the distillation mechanism. 1 IJ 60 80 100 I20 8 FrG. 3.-Polarization ratio against scattering angle for initial aerosol (UM= 0.24pm uo = 0.10 N = 1.2 x 10’ ~m-~) for coagulation times 41 (--) 56 (-. -.) 78 (. . . . .) and 110 (-) s. Davies is surely mistaken when he characterizes the optical measurements as “ rather indirect.” They are most direct since they occur in situ without perturbing the system and can be interpreted in a straightforward method.The sensitivity of the light scattering to the evolution of the particle size distribution in the course of coagulation is illustrated in fig. 3 which represents the curves of polarization ratio GENERAL DISCUSSION against scattering angle for an initial aerosol aM= 0.24 prn c0 = 0.10 N = 1.2x lo7 ~m-~ for coagulation times 41 56 78 and 110s. The separation of these curves indicates that the light scattering canclearly resolve differences of 2-3 SI in coagulation time. Fig. 4 depicts graphically the. resolution in coagulation time attainable for a particular experimental run. In this case the initial particle size distribution was aM= 0.31pm cro = 0.10 N = 5.6 x lo6 ern? The experimental coagulation time was 82s.The figure is a plot of the deviation measure (eqn (5)) against the min FIG.4.-Deviation measure against coagulation time for initial aerosol UM = 0.31 pm uo = 0.10 N = 5.6 x lo6 ~m-~ after 82 s in hold-up tube. The minimum is at 2.50min. calculated coagulation time. The minimum at 2.50 min is certainly well resolved by these light scattering data to within no more than 1-2 s. The resolution becomes less at longer coagulation times when the aerosol becomes polydisperse and it is for that reason that the light scattering can no longer be used to monitor the process beyond about one-third to one-half a life-time. The criterion becomes the depth of the minimum in the curves of the deviation measure against time.Dr. C. N. Davies (Uniuersity of Esses) (communicated) I am grateful to Kerker for the details of his experiments but must admit that 1 am puzzled by the results. His fig. I and 2 which claim to show the coagulation of 0.25 pm radius aerosol of linolenic acid during 326s which may be due to incorrect sampling,' and many circular particles of about the same volume as the chain in the sample of coagulated aerosol. His table 2 shows that some 3 % of the final number of particles has twice the initial radius. T cannot see how so many multiplet particles could have formed ' J. 0.Irwin P. Armitage and C. N. Davies Nature 1949 163 809 ; S. A. Roach The Theory of Ratidotn Climtping (Methuen 1968). GENERAL DISCUSSION by coagulation while airborne.A rough calculation based on the half-life of the aerosol being 250 s indicates that there arc about 20 times too many eightfold multi- plets. The effect of evaporation might therefore have been obscured. Dr. G. H. Walker (Clark College Atlanta Ga.) said The techniques of light beating spectroscopy have been developed to the point where they offer a valuable supplement to the more traditional approaches. Recently Hinds and Reist have applied these techniques successfully to aerosol measurements. Does Kerker think that light beating spectroscopy can be applied profitably to the problems of aerosol growth and coagulation? Prof. M. Kerker (Clarkson Coll. Tech. Potsdani) said The use of in situ light scattering measurements to study dynamical processes of aerosols such ascoagulation appears to have many advantages.Would Brock please comment on the possibility of relaxing some of the present constraints on his method i.e. the restrictions of narrow size distributions and unimodality. On the same subject Some of the people at Clarkson are working on the problem of investigating diffusion battery measure- ments. Brock and his colleagues have done quite a lot on the related light scattering problem. We would be interested to learn about his numerical inversion techniques. Any information would be appreciated. Prof. J. R. Brock (Uniuersity of Texas at Austin) said The problem is that conventional light scattering may be quite inadequate to resolve unimodality versus bimodality for a narrow distribution.In fig. (7.35) of ref. (2) we have shown that if light scattering data corresponding to a bimodal distribution is assumed to be uni- modal one will obtain quite a good fit to the data. Accordingly it is necessary to know a priori whether the system is or is not unimodal. The same applies to the skewness of the distribution. Also we generally find that a unique fit to the data cannot be obtained for 0.1 pm particles when the standard deviation is greater than 20-30 %. For larger particles the conditions are even more stringent. Of course our techniques do not involve absolute intensity measurements which are often difficult to obtain. These might relax matters somewhat. Our numerical inversion technique is experimental and calculated measure-ments (for a two parameter distribution) are compared at each of 19 scattering angles.A deviation measure is obtained by summing the square of the differences between these quantities and plotting contours of equal deviation measures in atwo dimensional domain of the two size distribution parameters. If there is a " well ",the bottom of the " well " is selected as the solution. If the distribution is too broad one will ob-tain open valleys which means there is no unique solution. It is my view that light scattering can be a sensitive tool for particle size study but that it must be based upon observation of single particles such as we have carried out re~ently.~ Then one takes advantage of the high sensitivity of light scattering to particle size. Thus we were able to determine the size and refractive index of single glass fibres to 0.25 % and 0.01 R.1.units respectively. I believe the instrumentation recently developed by the late Prof. Gucker of Indiana University offers a great opportunity in this regard. ' Ao~osolSci. 1972 3 OOO. M. Kerker The Scatteritig of Light and Other Electromagnetic Radiation (Academic Press New York 1969) pp. 359-373. D. D. Cookc and M. Kerker J. Colloid Interface Sci.,1973 42 150. W. A. Farone and M. Kerker J. Opt. Soc. Anier. 1966 56 481. S7-6

ISSN:0301-5696    

DOI:10.1039/FS9730700157

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Deposition of Aerosols from Turbulent Pipe Flow BY I. WILLIAMS AND A. B. HEDLEY Dept. of Chemical Engineering University of Sheffield Mappin Street Sheffield Yorkshire Received 1 lth January 1973 Several approaches to the calculation of the rate of deposition of particles from a turbulent fluid stream on to the boundary walls are discussed. In a turbulent flow system containing suspended particles the need to consider the relationship between the particle eddy diffusivity and the fluid eddy diffusivity in calculating the deposition rate has been indicated. A quantitative estimation is made of the effect of temperature gradients between the fluid and the wall surface in inducing a radially- directed thermophoretic velocity on the particles. A flow system is described in which a turbulent air stream passes through a cylindrical duct.The flow was assumed to be two-dimensional and was characterized by measuring the mean velocities and the fluctuating turbulent velocities of the fluid in the axial and radial directions and also the shear stress profile in the radial direction. From the latter measurement the eddy diffusivity of the fluid was determined. The measurements were carried out at Reynolds numbers of 1.27 x lo5and 2.67 x lo4 and at several duct wall temperatures between 279 and 317 K. Droplets of approximately 1 pm diam. were injected into the turbulent fluid and the results indicate the effect of the flow conditions and wall temperatures on the particle deposition rates. The prediction of the rate of deposition of particles from a turbulent fluid on to boundary surfaces has many important applications.Examples include deposition in atomic reactors spray dryers particle sampling lines and in any flow system where suspended particles are transported from a generating source to the place of applica- tion. A straight smooth walled cylindrical duct offers the most convenient means for studying the rate of particle deposition in turbulent flow systems. The processes by which particles deposit on a pipe wall include,l eddy diffusion gravity settling thermophoresis diffusiophoresis electrostatic effects and inertial effects such as impaction and interception. The parameter K which describes the deposition rate has been defined as K=-amount of particulate deposited per cm2 of surface s-I ~-.the airborne particulate concentration above the surface The approach to the problem has usually been to evolve methods of predicting K for different systems and to correlate the predictions experimentally. In previous investigations the following assumptions were often made. The structure of the turbulent fluid in pipe flow consisted of a laminated boundary layer and a turbulent core. The boundary layer was characterized by three regions (i) laminar sub layer y + <5 ; (ii) buffer layer 5 <y + <30 ; (iii) main boundary layer y + >30 where y+ is the dimensionless variable yu /v y is the distance normal to the surface measured outwards and u is the fluid friction velocity defined as 1.WILLIAMS AND A. B. HEDLEY zo is the tangential shearing stress on the surface over which the fluid flows p is the fluid density and v is the fluid kinematic viscosity. The equation used to describe the rate R of transport of particles from the turbulent core to the wall is R = (D+c,)dC/dy (2) where D is the molecular diffusivity and E is the particle eddy diffusion coefficient due to the turbulence ;C is the concentration of the diffusing substance at a distance y from the surface. The particles were usually assumed to diffuse by eddy diffusion from a constant particle concentration in the turbulent core of the pipe up to and in some theories into the boundary layer. In the diffusion process the eddy diffusivities of the particle and fluid were assumed equal.At the point where the eddy diffusion process was assumed to end the particle was associated with a free flight velocity v and a stop distance ds where ds = vi+z and z is the particle relaxation time. For particles obeying Stokes law of resistance where r is the particle radius rn the particle mass ppits density and q is the viscosity of the fluid. The value of v was usually equated to a function of the root-mean- square radial resolute of the fluid fluctuation velocity vi+. Friedlander and Johnson derived deposition velocities on the basis of the above postulate. They assumed that 2’ = 0.9 u,. This figure seemed unreasonably high and according to the fundamental turbulence measurements made by Laufer this velocity existed at a distance y-t = 80 which was within the turbulent core and not within the boundary layer.Even using such a high initial velocity the particle stopping distance was often less than the thickness of the laminar sublayer. This led Friedlander and Johnson to use the hypothesis of Lin et aL6 who determined the following empirical expression for Ef the fluid eddy diffusivity within the laminar sublayer cf/v = (~‘/14.5)~. (4) According to this model eddies from the turbulent core at a distance y+ = 80 penetrated the boundary layer and retained their momentum until they were within a distance S+,from the wall where S+ = 0.9z+ and z+ the dimensionless particle relaxation time was equal to zu,2/v. A finite eddy diffusivity within the laminar layer was assumed.When S+ was calculated using the actual values of u’ at y+ = S+ transport coefficients were obtained which were four orders of magnitude lower than those found experimentally by Friedlander and Johns~n.~ Davies ’derived a deposition scheme in which he considered both inertial depo- sition and deposition by Brownian diffusion. The particle radius was taken as the distance of closest approach to the deposition surface. The main difference between this theory and that mentioned previously for inertial deposition was that Davies calculated his free-flight particle velocity from an analytical expression derived from the measured turbulent velocity data in fully-developed turbulent pipe flow derived by La~fer.~ He determined the free-flight velocity at a distance from the wall where he considered free flight began not as previ~usly,~ in the turbulent core.Lawrence and Huang * adapted this theory and obtained solutions valid for a cylindrical coordinate system rather than the rectangular coordinate system used by Da~ies.~In all the above work re-entrainment of particles from the boundary walls was assumed to be absent. Reviews of these theories and of others AEROSOL DEPOSITION FROM TURBULENT FLOW differing little from the above have been given by Montgomery and Corn l3 and Sehmel.14 In a recent theory Lawrence and Huang considered that the size of the particles relative to the scale of the turbulence was of importance and they defined a relative entrainment factor as x = ds/l (5) where I is the fluid mixing length I5 at a point within the fluid.If this ratio was greater than unity the concept of a particle stop distance was used; however if the quantity a was less than unity then the mixing length was used as a measure of the particle free flight distance. On the basis of work by Tchen l6 and So0 and Tien the authors assumed equality of particle and fluid diffusivities but included a specifi-cation of the particle root-mean-square turbulent fluctuation velocity uL+ with respect to the r.m.s. fluid fluctuation velocity u;+ in the form of a non-linear differential equation relating the latter two quantities and the particle relaxation time in the following manner (6) The authors calculated the discrete particle deposition flux for fully-developed turbulent pipe flow.The results deviated widely as did those in all the previous work reviewed from the small mount of experimentally obtained aerosol deposition data available from other sources. Rouhiainen and Stachiewicz used the concept of frequency response developed by Hjelmfelt and Mockros l9 to obtain a quantitative evaluation of ep!eF. They showed that for 30pm diam. particles of lycopodium spore a fourfold increase in Reynolds number Re of the suspending fluid which caused a more than fourfold increase in gF only resulted in a twofold increase in E,. A more important result of their work for small particles was their quantitative evaluation of the shear flow induced transverse lift force on a particle in the laminar sublayer. They considered that for a vertical flow system if the particle radial velocity was sufficient to carry the particle to such a distance from the wall that the particle velocity in the x coordinate direction was higher than the local stream velocity in this direction then the lift force was directed towards the wall.For lycopodeum spheres of 2 pm diam. they calculated that for Re> 1 x lo4 the particle velocity at the edge of the sublayer such that deposition on the wall took place was three orders of magnitude lower when considering the lift force effect than when a purely inertial mechanism was considered. Further work was needed to apply this mechanism to horizontal pipe flow to determine the distance from the wall at which the lift reversal takes place and to clarify the mechanisms which propel the particles to within the latter distance from the wall.Sehmel examined the effect of removing the assumptions of regarding an equality of diffusivity of the particle and fluid and an equality of particle and fluid root- mean-square turbulent fluctuation velocities. He determined what dependence these variables had upon other parameters of the problem in order that theoretical calculations agreed with the experimental data i.e. he described the combined effect of the two parameters as an " effective eddy diffusion coefficient " and gave empirical correlations for predicting this quantity for various flow conditions. He also made deposition measurements on all surfaces of a duct and introduced a gravitational factor into the correlations.Finally an effect was investigated by Byers and Calvert *O which had been subject to few previous investigations. They determined the particle deposition from turbulent streams by means of a thermal force. Experi- I. WILLIAMS AND A. B. HEDLEY mental work carried out measured the deposition rate of 0.3-1.3 pm diam. particles from pipe flows at Re = 1.376 x lo4 when the gas temperature was several hundred degrees above the pipe wall temperature. High particle collection efficiencies were measured and compared with negligible particle collection efficiencies under similar experimental conditions with the temperature gradient removed. Unfortunately there seems to be few experimental data relating to the thermal deposition of micron size aerosols from fully-developed turbulent pipe flow incorporating small tempera- ture gradients.It was apparent from the current state of aerosol deposition studies in turbulent flow that certain aspects of the problem warranted further investigation ;these were (1) more experimental results of particle deposition rates from turbulent pipe flow under closely controlled conditions were needed. (2) The relationship between the particle diffusivity and the fluid diffusivity needed clarification. (3) The relative importance of thermal electrostatic and diffusive forces should be investigated. (4) The reverse lift force l8 warranted further theoretical investigation along the previously suggested lines. VT/lO-* K m-* FIG.1 .-The dependence of the particle therrnophoretic velocity upon the temperature gradient.It was decided to construct a variable flow system in which fully-developed turbulent pipe flow was achieved. An initial investigation was designed to characterize the flow in terms of the mean and fluctuating velocities U,u’ V,v’ in the axial and radial directions respectively and to allow the determination of the shear stress -% as a function of y and hence the eddy diffusivity of the fluid from the relationship where AEROSOL DEPOSITION FROM TURBULENT FLOW and a is the pipe radius Uis the mean axial velocity at a point and U is the maximum mainstream velocity at the centre line. The measurement of the above quantities was carried out using hot-wire anemo- metry.Non-volatiledroplets were chosen as the disperse phase since in the deposition measurements particle evapouration would be minimized. By carrying out concen- tration traverses of the aerosol injected into the turbulent flow the diffusivity of the particles in the fluid was deter~ined.~~ The measurement of the aerosol concentration was carried out by sampling the aerosol isokinetically and using a multi-channel light-scattering counter which was developed for the purpose. 24 For the purpose of this experiment the effect of charge was minimized by generat- ing a condensation aerosol examining it for charge using a charge analyzer and if necessary neutralizing the aerosol using a charge generator designed to produce equal numbers of +ve and -ve ions. Fig.1 indicates the magnitude of the thermo- phoretic velocity V,, induced in a particle by a temperature gradient VT. The quantities were calculated from the equation of Brock l2 derived from the slip-flow region corresponding to Knudsen numbers Kn in the range 0.1-0.01 where Kn = A./r, and 1 was the mean free path of the gas molecules. The particles used in the present work varied from 0.8 to 4 pm diam. and correspond to Kn = 0.11 to 0.05. The equation is where the constants A Q and b are dependent upon the gas-particle system. T is the absolute gas temperature CT and C are constants related to the thermal and momentum coefficients respectively and k and k are the thermal conductivities of air and the particle respectively. In order to induce thermophoretic particle velocities within the duct provision was made for heating or cooling the duct walls within the temperature range 0-50°C while maintaining the fluid temperature constant.Fig. 2 shows temperature profiles obtained from the duct centre to the wall measured using a thermistor probe within the test section and thermistors embedded in the duct wall at that point. The temperature gradients were appreciable and are shown in table 1. Also shown in table 1 are the times taken for a particle to traverse the laminar sub- layer in turbulent pipe flow under the action of a temperature gradient. Since the thermophoretic velocity of a particle acts towards the cooler region the results obtained when the duct wall temperature was raised above the fluid temperatures are prefixed with a negative sign.In this case any particles within a distance r’laG0.05 or 0.25 cm from the wall were subjected to a thermophoretic velocity moving away from the wall. Appreciable thermophoretic velocities were induced when the duct wall and the fluid flow were ostensibly at room temperature. The velocity referred to acted on a particle from some distance into the flow although the maximum value occurred over a distance r’la-0.05 as shown where r’ is equal to a-r and r is the coordinate in the radial direction r = 0 is the pipe centre. This velocity was maintained through the laminar sublayer so no question of a stop distance arose. It was considered that the magnitude of the approximate velocities calculated were sufficient to warrant an experimental investigation of this additional driving force acting on the particles.The experimental unit is shown diagrammatically in fig. 3 and consisted of three units the flow system the aerodynamic analysis system and the aerosol generation 1. WILLIAMS AND A. B. HEDLEY I67 and analysis unit. A general view of the duct assembly is shown in fig. 4. The duct assembly consisted of a valve regulated blower which passed up to 0.4 m3 s-' of cooled air through an absolute filter unit a 0.6cm mesh screen and a 35-cm-long section of paper honeycomb into the first of six interlocking sections of 10.16 cm i.d. 154.2 cm long stainless steel tubes each of which was mirror polished internally. L, 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6 0.9 1.0 r'la FIG.2.-The distribution of the fluid temperature within a circular duct.For curve 1 wall temper- ature was 317.0 K and Re = 2.67x lo4; curve 2,313.0 K and Re = 1.27 x lo5; curve 3,295.2 K and Re = 1.27x lo5 ; curve 4 296.0 K and Re = 2.67 x lo4; curve 5 284.0 K and Re = 1.27x lo5; curve 6,279.8 K and Re = 2.67~ lo4. TABLE VELOCITY OF PARTICLES IN TURBULENTFLOW UNDER THE INFLU- 1.-THERMOPHORETIC ENCE OF A TEMPERATURE GRADIENT timejs taken to Reynolds number laminar sublayer thickness at y+ = 5.Ocm duct walltemp./K fluid temp./K at r' = 0.25 cm VT/K cm-1 Vmi/cm s-1 traverse laminar sublayer 2.67x lo4 4.18 x 296.0 296.6 2.6 4.5~10-3 9.29 2.67~lo4 4.18~ 279.8 292.6 51.2 9.2~lo-' 0.45 2.67 x lo4 4.18~ 317.0 304.2 51.2 -9.2~ 0.45 1.27x lo5 1.23x 295.2 297.3 8.4 1.6~ 0.79 1.27x lo5 1.23x 284.0 293.2 36.8 6.8~ 0.18 1.27~lo5 1.23~lo-' 313.0 302.2 43.2 -8.0~ 0.15 The turbulent boundary layer was instigated by an annular protuberance of 1.5 mm depth in the first section.Each tube was fitted with the facility to accommodate an aerosol injection point in the form of an airfoil wedge section across the duct. The last two sections of the duct acted as test sections and were fitted with 20 equispaced I68 AEROSOL DEPOStTtON FROM TURBULENT FLOW pressure tappings and each section had facilities for fitting a probe scanning unit shown in fig. 5. Around the periphery of the duct at the corresponding axial position to the internal probe tip eight thermistors recorded the internal wall temperature and eight adjacent removable plugs were fitted flush with the inside tube wall to act as droplet sample holders which were subsequently examined microscopically.The wall temperature of the last section of the duct was controlled by passing ethylene glycol through eight 1.27 cm i.d. copper tubes fastened to the outer tube wall. The flow Reynolds number range available with the unit was between 2.67 x lo4 and 1.27 x lo5 with wall temperatures between 279 and 317 K. AEROSOL HOT WRE FENLRATSR AkEhtOMETER AVERSING SAWLING PROBE STOR TFlRERATURE ESOLUTE AIR FILTER CIPCULT PROBE FIc;. 3.-A diagrammatic view of the experimental system. The second unit in the experiment a DISA hot-wire anemometer type 55D01 was used to determine the aerodynamic characteristics of the fluid flow.These quantities were the fluid shear stress -uV where u and v were the instantaneous values of velocity fluctuations in the x or y directions respectively the mean axial velocities U and U, and the root mean square fluctuating velocity components in the axial and radial directions u’ and v’. In order to determine v’ it was necessary to determine the double correlation coefficient uU/u‘v’. The probes used in the experiment were Disa gold-plated miniature probes types 55F14,55F12 and 55Fl1 to measure the average velocity profiles the shear stress and the fluctuating root-mean-square velocities respectively. The correlation coefficient was measured at several points during a traverse in the test section using a DISA cross-wire probe.In the aero- dynamic measurements two dimensional duct flow was assumed. The effect of the fluid temperature variation on the hot-wire results was taken into account by calibrating the probes at several temperatures within the range of interest. A plot of the calibration constants against the temperature was then made. For calibration purposes the DISA calibration wind tunnel was used with a modification. The air was heated or cooled by passing through an automobile radiator at the inlet to the tunnel. Ethylene glycol acted as heatant or coolant and the temperature of the air in the wind tunnel was monitored’using a thermistor. The third part of the experimental apparatus was the aerosol generation sampling and analysis unit. The aerosol was generated from two materials dioctyl phthalate and di-2-ethyl hexyl sebacate respectively.The generator is shown in fig. 6. This was a condensation generator a description of which had been given previou~ly.~~ Some modifications to the generator described 25 have been made. The two most important were the provision of additional flow controllers at the outlet of each gas supply and a more sophisticated temperature control system. The temperature controller incorporated an electronic proportional control circuit with a fine differ- ential control applied. The sensor units were negative temperature coefficient FIG.4.-A view of the duct showing the diffuser/sampling unit. FIG.5.-The end of the duct test section showing the scanning unit and thermistor and sampling plug positions.[Toface page 168 FIG.6.-The aerosol generator. I. WILLIAMS AND A. B. HEDLEY thermistors which were fitted into the boiler and reheater flasks respectively. This unit enabled temperature control within +_O.S"Cto be maintained. Two different nucleii sources were used in the condensation generator. Incoming air was passed over a heated wire coated with Apiezon W wax and an alternative method of introduc- ing anthracene into the boiler flask was also used. The use of a condensation generator precluded the formation of charged droplets. That this condition was satisfied was tested by passing the aerosol in a laminar air stream between two plates with a potential of -5 kV between them.The plates were examined for deposited droplets using photo-micrography. The aerosol could be neutralized by passing through a charge apparatus designed to generate equal numbers of +ve and -ve ions both the charge analyzer and charger were designed after Linger and Radnik.26 Particles were pumped through the sampling probe and then through a conical diffuser the included angle of which was 5". The diffuser reduced the velocity to a level acceptable to the sensing system. The particles were classified into ten size- ranges and total counts in each range were indicated digitally. The anemometer hot-wire data was processed using a statistical approach to the signal analysis developed by Dvorak and S~red.~' The spacial resolution of the velocity vectors acting on a hot-wire probe in each of three 45" mutually differing positions provided a set of three non-linear equations whose analytical solutions represented the three velocity components as functions of three random variables.The random functions were processed to obtain the mean velocities and the various turbulent components. This method was applied to the two-dimensional system under discussion and necessitated measurements from a straight wire probe in two 45" mutually differing positions. The equations were solved for the mean and fluctuating velocities in the axial and radial direction at a number of points on a traverse across the duct test-section. The correlation coefficient was measured at several points across the duct using a cross-wire probe.The shear stress component was evaluated from measurements I f I 11 r'la FIG.7.-The effect of wall temperature on the fluid velocity profile in turbulent pipe flow at Re = 2.67 x lo4. Curve 1 wall temperature = 279.8 K; curve 2 296.0 K ; curve 3 317.0 K. 170 AEROSOL DEPOSITION FROM TURBULENT FLOW made with a 45O-slant wire probe 28 rotated through 180° assuming that the heat transfer from the wire depended only upon the flow velocity normal to the wire. In a fully-developed pipe flow the velocity distribution across a pipe is independent of the stream wise position. Under these conditions the pressure drop along a pipe is balanced by the shear stress ZO = ~dP/2d~ (9) zo = laminar stress -pZ (10) + where -pZ is the apparent turbulent stress.Except very close to the pipe wall zo is composed entirely of the turbulent stress. In this experiment the static pressure tapping along the last two pipe sections enabled a measurement of dP/dx the pressure drop to be made and so a direct determination of the shear stress was possible. -. --. ‘ .r .-..I . ,. ,. I I I I I I I -0 0.2 0.4 0.6 0.8 I.o //a FIG.8.-The effect of wall temperature on the fluid velocity profile in turbulent pipe flow at Re = 1.27 x lo5. Curve 1 wall temperature = 284.2 K; curve 2 295.2 K; curve 3 313.0 K. This compared well with the values obtained from hot-wire anemometry. Fig. 7 shows the variation with temperature of the velocity profile across the test section at Re = 2.67 x lo4 and fig. 8 shows similar data for Re = 1.27 x lo5.The duct wall temperatures correspond to those shown in fig. 1. A plot of the shear stress non-dimensionalized with the friction velocity as a function of r’/ais shown in fig. 9. Four sets of data points and two curves are shown. The curves correspond to Reynolds numbers of 2.67 x lo4 (upper curve) and 1.27 x lo5 (lower curve). The data points shown as triangles and squares both correspond to a Reynolds number of 2.67 x lo4 but at wall temperatures of approximately 317 and 280 K respectively. The effect of an alteration in pipe wall temperature on the shear stress profile at a Reynolds number of 1.27 x lo5 was very small. The distribution of the axial root-mean-square fluctuating turbulent velocity component u’ non-dimensionalized with U,,is shown in fig.10. The upper curve shows the distribution of a Reynolds number of 1.27 x lo5 and the lower curve was determined for a Reynolds number of 2.67 x lo4. I. WILLIAMS AND A. B. HEDLEY The last of the turbulent quantities the distribution of the radial root-mean- square turbulent fluctuating velocity component u‘ is shown in fig. 1 1. This quantity is again non-dimensionalized with the friction velocity. The upper curve corre- sponds to a Reynolds number of 1.27 x lo5and the lower curve to one of 2.67 x lo4. 0.a 0.6 NCI ;s is 0.4 0.2 I I I I I I I OO 0.2 0.4 0.6 0.0 I.o t I I I I 1 I I 72 AEROSOL DEPOSlTION FROM TURBULENT FLOW I .6 $ 0.8 a 0 0 0.2 0.4 0.6 0.0 1.0 r'/a FIG.11.-The distribution of u' within turbulent pipe flow at Re = 1.27~lo5 and 2.67~lo4 res-pectively. Curve 1 represents c' at Re = 1.27~ lo5 curve 2 represents 13' at Re = 2.67~lo4. FIG.12.-The fluid eddy diffusivity distribution in turbulent pipe flow. 0 results obtained at Re = 1.27~10'; 0,results obtained at Re = 2.67~104; A are theoretically derived from a correlation in ref. (7). I x~64 1x162 1.0 1x102 rlv FIG. 13.-The fluid eddy diffusivity distribution in turbuient pipe flow. 0,Results obtained at Re = 1.27~lo5; + results obtained at Re = 7.03x lo4; 0,results obtained at Re = 2.67~lo4; A theoretically derived results from ref. (7). I. WILLIAMS AND A. 3. HEDLEY ref. (7). Fig. 12 shows the results at the elevated pipe wall temperatures shown in fig.1 ; fig. 13 gives the results with the pipe wall at nominal room temperature again shown in fig. 1 and fig. 14 shows the results obtained at the low pipe wall temperature and again the numerical wall temperature can be obtained from fig. 1. Due to the finite residence time of the fluid in the test section of the duct it was necessary to derive an approximate particle trajectory in order to evaluate the distance a particle travelled down the duct before deposition on the wall occurred due to its radial thermophoretic velocity. The trajectory of the particle has been considered in the following case to be a function of the axial velocity at the edge of the boundary layer denoted by the directional coordinate x and the thermophoretic velocity in the radial direction denoted by the directional coordinate r ; other diffusive forces were neglected.3 1x10 ' x lo2 + ?I I x 10 1.0 I 1x10 1x1,c2 1.0 1x102 EIV FIG.14.-The fluid eddy diffusivity distribution in turbulent pipe flow. 0,Results obtained at Re = 1.27 x lo5; 0,resuIts obtained at Re = 2.67 x lo4 ; A theoretically derived results from ref. (7). The axial velocity of the air equalized VJr) = dx/dt =f(r) (1 1) wheref(r) described the fluid velocity profile across the duct. It was assumed that the particle was completely entrained by the fluid and that the axial velocity of the particle was equal to the axial velocity of the fluid. The radial velocity of the particle drldt equals the thermophoretic velocity YTH hence On integration we obtain f(r)dr VTHdx, = rZL x=o where a is the distance from the duct centre line to the wall and r is the distance from the duct centre line to the edge of the laminar sublayer.L is the distance a particle moving under the axial velocity would travel from the time it was subjected to the thermophoretic velocity to time of deposition on the tube wall. The expression AEROSOL DEPOSITION FROM TURBULENT FLOW chosen forf(r) to represent the velocity profile across the duct was the empirically obtained expres~ion,~~ U/U = [(a-r)/a]l/". (14) According to Schlichting 29 the exponent has values of 7.0 and 6.6 at Reynolds numbers of 1.1 x lo5 and 2.3 x lo4 respectively. Substituting for Jlr) in eqn (13) for a Reynolds number value of 1.1 x lo5 which on integration gives 7 uo 7 uo --&a -r)817 =-T7(a-ra)8i7 = vTHL 8a 8a from which the length L was obtained.The results from eqn (1 6) are shown in table 2. Although these calculations were approximate they indicate that quite small temperature gradients cause particles to deposit within the duct system at points depending upon the position of the aerosol injection point. The establishment of known temperature gradients in the present work should help to determine experimentally the influence of thermophoresis on particle deposition. TABLE 2.-AXI[AL DISTANCE TRAVELLED BY DROPLETS SUBJECTED TO A RADIAL THERMOPHORETIC VELOCITY Reynoldsnumber duct wall temp./K distance L before impactionlcm 1.27~105 295.2 1931.3 1.27~105 284.0 443.4 2.67~104 296.0 6970.1 2.67~104 279.8 342.0 With regard to the determination of the fluid dynamic characteristics of the flow in the duct it was necessary to determine how closely the present system approached fully-developed turbulent flow and also the effect of the boundary wall temperature on the fluid turbulent characteristics in particular the fluid eddy diffusivity.That the fluid flow in this experiment did closely approach fully developed turbulent flow was indicated by several features. For both values of Reynolds number the velocity profiles were typical flat turbulent profiles as opposed to the parabolic profile expected from laminar flow. The effect of a decrease in the wall temperature in each case resulted in a "flatter " profile.The shear stress profiles shown in fig. 9. showed little dependence on Reynolds number and varied linearly across the duct cross-section. The dependence of the profiles on the wall temperature was only significant for the lower Reynolds number when an increase in the dimensionless shear stress corresponded to an increase in wall temperature. The dimensionless fluid eddy diffusivity profile was correspondingly affected by temperature E/V increasing with decrease in temperature. Fig. 10 indicated a significant decrease in the axial root-mean-square turbulent component with a decrease in Reynolds number although the radial component profiles were of a similar magnitude for both values of Reynolds number.The turbulent intensities u'/Uowere calculated for r'/a = 0.1 and 1.O for Reynolds number of 1.27 x lo5 and 2.67 x lo4. The intensities were compared with those calculated by Laufer for Reynolds numbers of 5 x lo5 and 5x lo4 and the compari- I. WILLIAMS AND A. B. HEDLEY son is shown in table 3. The similarity of the magnitude of the turbulent intensities in the present system and those measured by Laufer at higher Reynolds numbers indicated that fully-developed turbulent flow was achieved in our system. TABLE OF RELATIVE TURBULENT INTENSITIES 3.-COMPARISON Reynolds number r'ln 1ilUo 1.27~105 0.1 0.079 1.27x 105 1.o 0.029 2.67~104 0.1 0.069 2.67~104 1.o 0.021 5x lo5 0.1 0.070 5~ 105 1.o 5~ 104 0.1 5~ 104 1.o 0.027 The work so far has established reasons for and provided a system within which the relationship between the diffusivity of the fluid and of the particles can be deter- mined.Furthermore the dependence of particle deposition on a thermophoretic force due to temperature gradients existing between the duct wall and the fluid is clarified. The authors wish to acknowledge the financial assistance of Shell Research Ltd. and in particular the help of Prof. T. M. Sugden F.R.S. which enabled this work to be carried out. G. A. Sehmel Meeting SOC.Eng. Sci. (Tel Aviv June 1972). A. C. Chamberlain Proc. Roy. SOC.A 1966 290 236. C. N. Davies Aerosol Sci. 1966 1 418. S. K. Friedlander and H. F. Johnstone Znd. Eng. Chem. 1957 49 1151. J. Laufer The Structure of Turbulence in Fully Developed P@e Flow N.A.C.A.Report 1147 1954. ti C. S. Lin R. W. Moulton and G. L. Putnam Ind Eng. Chem. 1954 45 636. C. N. Davies Aerosol Sci. 1966 1 393. W. R. Lawrence and A. B. Huang A.Z.A.A. 10th Aerospace Sci. Meeting (San Diego Cali- fornia January 1972) A.I.A.A. paper no. 72-81. S. K. Beal Nucl. Sci. Eng. 1970 40 lo V. E. Levich Physiochemical Hydrodynamics (Prentice Hall New Jersey 1962) p. 155. ' A. C. Wells and A. C.Chamberlain Brit. J. Appl. Phys. 1967 18 1793. l2 P. R. Owen Int. J. Air- Water Pollution 1960 3 8 50. l3 T. L. Montgomery and M. Corn Aerosol. Sci. 1970 1 185. l4 G. A. Sehmel J. Geophys. Res. 1970,75 1766. l5 L. Prandtl 2.angew. Math. Mach 1925 5 136. l6 C. M. Tchen Ph.D. Thesis (Delft 1947).l7 S. L. So0 and C. L. Tien J. Appl. Mech. 1960 27 5. lS P. 0.Rouhiainen and J. W. Stachiewicz J. Heat Transfer 1970 29 C 169. l9 A. T. Hjelmfelt and L. F. Mockros Appl. Sci. Res. 1900 16 149. 2o R. L. Byers and S. Calvert Znd. Eng. Chem. Fund. 1969 8 646. 21 N. A. Fuchs The Mechanics 0fAerosol.s (Pergamon London 1964) p. 56. 22 G. M. Hidy and J. R. Brock The Dynamics of Aerocolloidal Systems (Pergamon Oxford 1970). 23 W. L. Towle and T. K. Sherwood Znd. Eng. Chem. 1939,31,457. 24 I. Williams and A. B. Hedley Aerosol Sci. 1972 3 363. 25 I. Williams M.Sc. Thesis (Sheffield 1970). 26 G. Langer and J. L. Radnik J. Appl. Phys. 1961 32 955. "K. Dvorak and N. Syred DZSA Conference (Leicester 1972); also Internal Report (Dept. of Chem. Eng. University of Sheffield).28 J. 0.Him Turbulence (McGraw Hill London 1959) chap. 2. 29 H. Schlichting Boundary Layer Theory (McGraw Hill London 1 1968) p. 563.

ISSN:0301-5696    

DOI:10.1039/FS9730700162

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Light-Scattering Instrument for Kinetic Measurements in Aerosols with Changing Particle Size Distributions BY M. D. CARABINE AND A. P. MOORE Department of Chemical Engineering and Chemical Technology Imperial College Prince Consort Road London S.W.7. Receiued 13th December 1972 The construction and use are described of a laser light-scattering instrument for kinetic measure- ments of the particle size distribution in a developing aerosol. In the present stage of development, the time resolution (of the order of seconds) is adequate fur the study of aerosols which are developing by growth and by coagulation. Such an in situ measurement is preferable for particles and for kinetic studies. The systems investigated are of importance in atmospheric pollution namely the formation of solid particles by interaction of ammonia and sulphur dioxide and the hygroscopic growth of sulphuric acid droplets in humid atmospheres.The precision of the data-analyzing procedure is such that it yields modal particle sizes and distribution spread parameters accurate to within 4 and 10 % respectively even with about 5 % random fluctuations in the measurements of the angular distribution of scattered intensity. The size distribution of particles or droplets in an aerosol suspension can be deduced from the variation of intensity of scattered light with either the angle of scattering the polarisation or the wavelength. The method of sizing has the advantage that the particles need not be disturbed by e.g. deposition before electron microscopic examination or by electrification prior to sizing.Minimal iiiterference with the aerosol is essential if it is required to observe the changes of particle-size distribution with time which can often be important in practical cases both in manufacturing of particulate products and in atmospheric pollution.2 Instan-taneous measurement of light intensity is a further feature which makes the technique particularly suitable for monitoring rate processes provided that the input parameters such as scattering angle or wavelength can be varied quickly enough. This paper describes a light-scattering instrument designed for kinetic measure- ments of size distribution in an aerosol with a time resolution in its present initial stage of development which is adequate for the study of aerosols which are developing growth and by coagulation of particles.Our particular interest is in systems in which a vapour from the suspending mediun is being transferred to the condensed phase e.g. a suspension of hygroscopic acid droplets which are growing in a humid atmos- phere or a suspension of solid particles being formed by interaction of gases such as ammonia and hydrogen chloride or ammonia and sulphur dioxide. The size distribution of the aerosol thus formed and its variation with time depend on such processes as condensation coagulation diffusion and sedimentation. In the range of conditions which are relevant to atmospheric pollution significant size change by condensation growth occurs in general'on a time scale of tens of seconds.3* Coagulation in a given aerosol causes time variation in both the number and the size of the particles.The number concentration varies predominantly according to second-order kinetics and at a inoderately high atmospheric concent ra-tion of say lox3m-3 the half-life would be of the order 100 s. 176 M. D. CARABINE AND A. P. MOORE The times involved in changes in size due to Brownian coagulation are illustrated in fig. 1 in which the successive distributions have been computed for intervals of 110 s. particle radiuz/prn FIG.1.-The particle size distribution at time intervals of 110 s resulting from the Brownian coagula-tion of a dispersion initially having a modal radius 0.25 pm and a zeroth-order logarithmic breadth parameter a.= 0.10. In the aerosol referred to above which is produced by interaction of ammonia and sulphur dioxide it has been shown by sampling on filters (with consequent uncertainties) followed by electron microscopy that the particles undergo growth typically from 0.03 pm to 0.2 pm in about lo3 s and then to about 0.5 pm in further 5 x lo3 s. The aggregates in the 0.2-0.5 pm range are formed of primary particles predominantly of size less than 0.1 pm. The proportion of small particles is aug- rncnted when traces of moisture or oxygen are added to the carrier gas. CRITERIA FOR THE CHOICE OF METHOD A tinic interval of about 1-10 s is considered short enough for meaningful size distribution measurements in the systems referred to above and if angular distri- bution of intensity is the chosen method a scan of the angles must be achieved within this time.To obtain sufficient intensity of scattered light from a dilute suspension of sub-micrometre particles a high-intensity light-source such as a continuous laser is required. Besides the high intensity it has the advantages for light scattering of monochromaticity and linear polarisation-and Harris et a!.$ have shown experi- mentally that there is no difference in scattering behaviour between conventional incoherent light sources and coherent laser sources. The scanning-speed requirement rules out the use of several techniques reviewed e.g. by Kerker which have been developed to study essentially time-invariant dispersions using conventional light sources.Thus the "polarisation ratio " method 'would require rotating the plane of polarisation of the beam through 90"at each observation angle ; while the methods using " scattering ratio " or " turbidity spectra " 8. at different wavelengths would necessitate repeated retuning of the laser. Hence the only technique compatible with the required scanning speed and the laser source is one using the angular variation of intensity. Angular scanning intro- duces its own problems which must be carefully considered in the design. The LIGHT-SCATTERING INSTRUMENT optically-effective volume is defined by the geometry of the light-receiver system and the incident beam and contains all the scattering particles which contribute to the measured intensity for a particular angle of scattering 8.Ideally if the detector receives only parallel light the optically effective volume varies simply in direct proportion to sin 8 if the cell containing the aerosol is cylindrical and free from flaws. However in practice a finite solid angle also means that data are recorded for an angular range 8+A8 rather than for the unique angle for which theoretical data are normally computed. Tabibian and Heller lo have shown that in the absence of steep maxima or minima in the intensity against angle curves a solid angle not in excess of steradian is permissible. Problems common to all light-scattering methods include multiple scattering and extinction of the beam. These interfere if the concentration of particles is above a certain limit whose value depends at a given wavelength in a given medium on the refractive index and the size of the scatterers.These two complications are respectively avoided by working at sufficiently low dilutions and by using relative intensities of light scattered at the various angles (see eqn (2) later). The more practical difficulties of inadvertent reflections of the incident and scattered beams are specific to individual scattering cells. The devices used to minimize them in this apparatus are described below. The essence of achieving precision in the size-distribution measurement is to record light intensity for a large number of scattering angles. Before considering the present design we examine the possible arrangements which are compatible with rapid scanning a laser source and a photo-multiplier detector.These alternatives are (a) to use a stationary light source and a single detector which is moved rapidly through a series of angular positions; (b) to use a stationary source and a separate photomultiplier stationed at each angle; and (c) to hold both source and detector static and to deflect the incident beam itself through the series of angles. Alternative (a) has been previously adopted l1 but mechanical movement of the detector must be relatively slow in a low-cost instrument. Alternative (b) is also unsuitable as it demands a number of photomultipliers of known relative sensitivities together with a complex and costly multichannel data-acquisition system. THE INSTRUMENT The present instrument based on alternative (c) achieves the measurement economically with one source one detector and several inexpensive mirrors.The arrangement is shown schematically in fig. 2. The plane mirror at position R rotated by a stepper motor about an axis perpendicular to the scattering plane (the plane of the diagram) reflects the source beam sequentially on to a series of static plane mirrors M at the positions marked. From each of the latter mirrors the beam is directed back to the centre of the scattering system at A and the photomultiplier detects the light scattered by the optically effective volume of aerosol. There is a slight divergence of the beam over the optical path (less than 1 mradian) and to keep it constant for all the beams the stationary mirrors are positioned on an ellipse with the principal foci at A and R.The laser beam and the line PM-A define the hori- zontal scattering plane of the instrument. The scattering angles which range from 8 to 172"have a precision of *0.33" determined by the stepper motor. A helium-neon laser with a 15 mW output at 632.8 nm is used as the light source. The photomultiplier has a "modified S-20 "spectral response yielding a high quantum efficiency at this wavelength compared with other photocathodes. Plane-front-surface mirrors are used throughout and precise adjustment of the stationary ones is M. D. CARABINE AND A. P. MOORE effected by three-point spring mountings. A special light trap has been constructed from black glass-fibre-reinforced resin to minimize back reflections from the trans- mitted light beams.Based on the conventional Rayleigh horn but having a wide curving aperture it traps any light entering within an angular range of 174". In this apparatus it is attached directly to the gas-tight scattering cell opposite to a thin semi-circular glass window which admits the incident beams with negligible distortion. FIG.2.-Schematic plan view of the optical system. The positions x are locations of stationary mirrors M ; R is the rotating mirror ; A is the scattering centre ; L and PM are the laser source and photomultiplier detector. ANGULAR SCANNING CONTROL AND DATA ACQUISITION Initial adjustment of the rotating mirror is made to a start position defined by an infra-red position detector situated under the main baseplate of the instrument.Thereafter the rotating mirror scans through the predetermined stepping pattern. A count of the number of steps taken determines the end of each scan whereupon the mirror is rapidly brought around to the start position and the sequence repeated. The mirror can be advanced in single steps to enable alignment of each stationary mirror and determination of the corresponding scattering angle. A block diagram of the control circuitry which governs the stepper motor is shown in fig. 3. The motor moves through 3.75'. at each step. When a full scan is required to have readings at eight angular stations four steps are necessary between each and for sixteen positions two steps. Provision is made for half scans and for the peripheral mirrors to be used in " odd " as well as "even " numbered positions.The control logic is performed by standard integrated circuit techniques the stepping rate and timing being derived throughout from the mains frequency with basic clock pulses at 100 Hz. The " start " command releases the clock inhibiting gate to enable the motor to step at this rate until the infra-red detector halts it at the LIGHT-SCATTERING INSTRUMENT start position. A delay of 300 ms foliows before the first reading and thereafter after each change of position giving time for internal resets. The time interval between readings of intensity is 200 ms derived like the delay by division of the clock rate. The motor is stepped to a new position each time the required number of readings is satisfied and this can be up to eight at each position.CONTINUOUS 4 SAMPLE 1 SCAhi PQ3GRAtJME FIG.3.-Schematic diagram of the electronic system controlling the angular scanning. "Even-Odd " selects which set of mirrors is to be scanned " 8-16 " selects the number of mirrors to be scanned "Full-Half " selects full (ca. 180 deg.) scan or half (cu. 90 deg.) scan. Selection of " End " inhibits the clock when the current scan is complete. The number of completed scans and angular position are visually displayed on serial counters and the intensity readings are recorded on paper tape for subsequent analysis. ANALYSIS OF DATA The theory of Mie l2 is used to compute the angular intensity functions (i and i2 for perpendicular- and parallel-polarised incident light respectively) for spherical particles of known size and refractive index.For a system of heterodisperse particles the scattered intensity at a particular angle is given for the perpendicular polarised case by Id@= 1h(a7QPb) da (1) M. D. CARABINE AND A. P. MOORE where p(a) is the normalised size-distribution function. The experimentally-deter- mined scattering signals are related to I,(@ as follows l,(O) = c sin 8[s,/so -sh/sb] (2) where the symbols are c a constant proportional to the number concentration; sin 8 factor for the change in observed volume at different angles ; so photomultiplier signal from aerosol at angle 8 ; $4 correction term for background light e.g.stray light scattering from edges of stops etc. ; so sh incident beam intensities at time of measur-ing so s;. For convenience the two-parameter zeroth order logarithmic distribution (ZOLD) of Espenscheid et aZ.13 has been adopted in this work after experimental checks that such a distribution does describe the aerosols under study.14 Typical theoretical curves of intensity against the scattering angle are shown in fig. 4 for spherical particles of refractive index 1.52. Readings at suitably chosen angles discriminate well between the different distributions of sizes in this sub-micro-metre range. The method is inapplicable if the greater part of the distribution is in the Rayleigh scattering regime i.e. with diameter <0.06 pm. A computer programme has been devised to solve the complex probleni of inverting the light scattering data to give the corresponding size distributions.First the theoretical intensities are computed for an assumed distribution (using eqn (1) and producing curves such as those in fig. 4) and the percentage differences for all angles found between these values and the recorded experimental data. The parameters of this "first-guess" distri-bution are then adjusted in successive steps to minimize the sum of squares of these differences according to the method developed by P~well,'~ until a final estimate for the aerosol is reached. In order to evaluate the accuracy of the light-scattering inversion programme theoretical intensity values for a set of eight angles were computed for several chosen -1.5 -0 45 90 135 angle/deg.angle/deg. FIG.4.-Theoretical intensity against scattering angle for fight plane-polarised perpendicular (I,) and parallel (I,) to the scattering plane. Curves (a-f)are for distributions having a modal diameter 0.40 pm and the following ZOLD spread parameters (a)uo = 0.50 ; (b) uo = 0.40; (c) u0 = 0.30 ; (d)oo = 0.25 ; (e)uo = 0.20; (f)uo = 0.10. I82 LIGHT-SCATTERING INSTRUMENT distributions. These were then used as experimental input data on which to perform the routine search analysis. The resulting "best fit " distributions were within 4 % of the modal diameter and 10 % of ao even when the input intensity data were subjected to 4 % random fluctuations. The authors acknowledge generous provision by Courtauld's Educational Trust Fund of equipment and a maintenance bursary and assistance from L.Tyley and T. Hunt in the design of the electronic control system. B .Y. H. Liu and A. C. Verma Anulyt. Chem. 1968,40,843; B. Y.H. Liu V. A. Marple and H. Yazdani Environmehtal Sci. Tech. 1969 3 381. M. D. Carabine Chem. SOC.Reu. 1972,1,411. B. J. Mason Discuss. Faraday SOC.,1960,30,20. L. Coutarel E. Matijevic M. Kerker and Chao-Ming Huang J. ColZoid Interface Sci. 1967 24,338. F. Harris G. Sherman and F. Morse I.E.E.E. Trans. Antenna Propagation AP-15,1967 p. 141. M. Kerker The Scattering of Light and Other Electromagnetic Radiation (Academic Press N.Y. and London 1969). 'M. Kerker E. Matijevic W. Espenscheid W. Farone and S. Kitani J. Colloid Interface Sci.1964 19 213. W. Heller and M. Wallach J.Phys. Chem. 1963 67 2577. W. Heller and M. Wallach J.Phys. Chem. 1964 68,931. lo R.Tabibian and W. Heller J. Colloid Interface Sci. 1958 13 6. J. E. L. Maddock M.Sc. Thesis (Univ. London 1970). G. Mie Ann. Phys. 1908 25 377. l3 W.Espenscheid M. Kerker and E. Matijevic J. Phys. Chem. 1964 68 3093. l4 M. D. Carabine J. E. L. Maddock and A. P. Moore Nature Phys. Sci. 1971 231 18. M. Powell Computer J. 1965 7 303.

ISSN:0301-5696    

DOI:10.1039/FS9730700176

出版商:RSC    

年代:1973

数据来源: RSC