摘要:

DISPERSED CARBQN FBRNTATION IN ACETYLENE SELF-CQI%IBUSTION BY P. A. TESNER All-Union Institute of Natural Gas (Vniigaz), Moscow Received 29th July, 1960 Acetylene self-combustion results in the formation of hydrogen and dispersed carbon or carbon black. This process has been investigated by many authors;X-12 however, the mechanism of dispersed carbon formation is not understood well enough. The present paper is an attempt to perform a theoretical calculation of the process of dispersed carbon formation in self-combustion of acetylene, i.e. when flame propagates in acetylene contain- ing no oxygen. The calculation is based on representations developed by the author 1 3 ~ 1 4 involving two-stage formation of dispersed carbon (nucleation and particle growth). A comparison of the calculated results with the experimental data shows good agreement.GENERAL Flame propagation in acetylene differs from similar processes in other gaseous substances or their mixtures in that the process yields not only a gas, but also dis- persed solid carbon. The basic idea of the method applied by us for process analysis consists in the fact that the structure and size distribution of particles of dispersed carbon formed in acetylene self-combustion characterize the totality of the processes which took place in the explosion. Therefore, a study of distribution curves for the dispersed carbon formed enables one to obtain data on the mechanism of the processes taking place at the combustion front. This is feasible because the structure of the dispersed product formed remains unchanged after the termination of the process, due to the high thermal stability of carbon.Acetylene self-combustion is characterized either by explosion or by combustion features, depending on the conditions attending this process. The self-combustion of acetylene contained in a closed volume under a pressure of over 2 atm is followed by an explosion which rapidly develops into a detonation. The heating of acetylene to a temperature 8 of above 500°C causes a spontaneous thermal decomposition of acetylene at atmospheric pressure as well. Thereafter under certain conditions there exists a possibility of the continuous thermal decomposition of acetylene similar to the stationary combustion of a pre-mixed gas mixture. However, the process should progress on essentially identical lines in each ele- mentary volume of acetylene both in the case of explosion and of continuous steady-state decomposition.Our conception of this process is as follows. The initial act of acetylene decomposition accompanied by the formation of hydrogen and carbon black consists in the nucleation of carbon particles. The nucleation, the mechanism of which we do not consider here, starts after some critical temperature is attained. As soon as the first nuclei are formed they grow rapidly by direct decomposition of the acetylene molecules on their surface. Along with this process and with a further rise in temperature, new nuclei are formed and grow, and so on. We find it plausible to assume that in any elementary volume where the tem- perature and composition of the gaseous phase at any point are identical, all particles grow at the same linear rate.In other words, given the same temperature and composition of the gaseous phase, the linear rate of particle growth is inde- 170I?. A. TESNER 171 pendent of the particle diameter. Hence, as decomposition proceeds, the differ- ence between the diameters of two growing particles remains constant at all times, and the relative sizes of the particles can serve to determine the time of their formation. It is obvious that the largest particles were the first to form in a given elementary volume, and vice-versa, the smallest were the last. This representation of the process permits easy determination of the number of particles and the construction of particle-size distribution curves for any degree of decomposition of the acetylene.Thus, such calculation may be helpful in con- structing curves expressing the dependence of the number of particles €Formed and the thickness of the carbon layer produced on the degree of acetylene decomposition. Let the particle size distribution be as follows : diameter number of particles dl n1 d2 n2 rii ni dm nm where di > di-1. Then, at the moment when dn-sized particles were formed, particles having diameters equal to dn or less were non-existent, while all the other particles had a diameter which was smaller by d, than the ultimate one. Consequently, the distribution of all the particles existing at that moment (hereafter it will be referred to as the " n-distribution ") should be : diameter number of particles The total volume of all the carbon particles resulting from a complete acetylene decomposition is i=m Vm = in: d?ni.i = 1 The total volume of all the particles of the n-distribution corresponding to a certain intermediate stage of acetylene decomposition will be i=m Vn = (di-dJ3ni. i = n + 1 Thus, the percentage degree of acetylene decomposition corresponding to this particle size distribution will be VJ VJOS. (3) The total surface area can be found for each distribution similarly to the total volume. The total particle surface area for the n-distribution (S,) is expressed by the following equation : CALCULATIONS The calculation has been performed for Schawinigen acetylene carbon black which is obtained as a result of continuous thermal acetylene decomposition at172 DISPERSED CARBON FORMATION atmospheric pressure.Watson 15 carried out thorough electron-microscopic measurements of particle sizes of this carbon black. Table 1 gives the results of these measurements covering 1 1,576 particles. TABLE 1 .-SIZE DISTRIBUTION OF PARTICLES OF ACETYLENE CARBON BLACK ACCORDING TO WATSON lS interval diameter number of particles in the interval (nj) index, di i A' units % 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 50 108 200 300 400 500 600 700 800 900 1000 1250 1500 1750 2008 7 62 3 69 1088 1968 2255 1956 1548 954 593 336 303 101 27 9 0060 0.535 3.187 9407 17.007 19.478 16.888 13.472 8.242 5-122 2.902 2.617 0.873 0.23 3 0.077 Table 2 shows the results of calculating the total volume and the total surface area of the particles, the total number of particles and the degree of acetylene decomposition for distributions from 1 to rn.The calculation made use of eqn. TABLE 2.-cALCULATEON OF THE DEGREE OF DECOMPOSITION, SURFACE AREA AND NUMBER OF PARTICLES FOR DIFFERENT DISTRIBUTIONS thickness no. of dis- of the tribution. formed n 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 carbon layer, A 125 250 375 500 550 600 650 700 750 300 850 900 950 975 100 total volume of particles eqn . (21, A3 8.10 X 108 1.97 X 1010 3-33 x 1010 5.45 x 1010 8.79 X 1010 1-41 X 1011 2.26 X 1011 3.60 X 1011 5.73 x 1011 8-92 X 1011 1.35 X 1012 1.64 X 1012 1.99 x 1012 7-38 x 107 4-58 x 109 degree of decompo- sition eqn. (3), % 0.00371 0.04070 0.2301 0.9934 1.676 2.743 4.419 7.087 11-369 18.133 28.826 44.834 67.955 82.748 1000 total particle surface area eqn.(41, cm2 ml-1 0052 0.364 1.67 6.33 9.9 15.5 24.5 39.2 627 99.3 152.0 224.0 3340 373.0 435.0 total number of par- ticles, m1-1 2.64 X 109 1.06 x 1010 4.03 x 3010 1-29 X 1011 2.28 x 1011 4.03 x 1011 6.85 x 1011 1.13 x 1012 1 . 7 2 ~ 1012 2.96 x 1012 3.28 x 1012 3.39 x 1012 3.40 X 1012 3-42 x 1012 238 x 1012 (1)-(4). The total surface and the total number of particles are not absolute values referring to the totality of particles measured in the electron-microscopic investigation, but values related to 1 ml of the initial acetylene. These values were obtained by multiplying the values given by eqn. (2), (4) times the ratio (K = 2 . 9 4 ~ 108) of the weight of carbon in 1 ml acetylene to the total weight of the carbon particles measured by means of an electron microscope, i.e.to the weight of carbon contained in the carbon particles corresponding to the 0-distribution. Fig. 1 is a graphical representation of the results and suggests a few interesting conclusions. The curves of the total nvmlxr of particles show that the formationI?. A . TESNER 173 of new particles takes place only at the beginning of the decomposition. Thus, 10 % decomposition results in the formation of 1 . 6 ~ 1012 particles which is about 50 % of all the particles formed. Of a similar shape is the curve for the thickness of the carbon layer formed, indicating that the initial stages of decomposition are attended by a more intensive growth of the carbon layer than in the subsequent stages.Conversely, the curves for the total particle surface area show a prac- tically linear dependence of the surface area on the degree of decomposition. Thus, the curves obtained provide an idea of the process of dispersed carbon formation and therefore is of interest. These curves, however, are not kinetic curves, since they represent the dependence of the process parameters, not on time, 0 25 5 0 75 I 0 0 decomposition of acetylene, % FIG. 1 .-Development of formation of dispersed carbon by self-combustion of acetylene. Curves 1, total number of particles ; 2, total surface area of particles ; 3, thickness of the carbon layer. but on the degree of decomposition. To obtain kinetic regularities from these curves, the time element should be added to them in some way or another.To achieve this, the following attempt was made initially. In order to cal- culate the early stage of the process we used the direct measurement data on the rate of growth of the carbon surface area in thermal decomposition of acetylene and assumed the activation energy of this process at low temperatures (50I)-60O9C).16 It was also assumed that, because of the adiabatic nature of the process, the system temperature is determined by the amount of heat released in the reaction, which is proportional to the degree of decomposition. However, this calculation showed that the rate of surface area growth at a temperature corresponding to the bzginning of the explosive decomposition of acetylene was so low that the formation of the first particles would require a few hours, and not fractions of a second as is actually the case.This unexpected result has led us to the conclusion that the actual process of the growth of the particles which were the first to form in the explosion is 6 to 7 orders faster than that process at a temperature of 500-700" which corresponds174 D IS 1’ ER SED C A R B 0 N F 0 R MAT 10 N to the low initial degree of acetylene decomposition. There can be only one explanation of such a discrepancy. At the moment of nuclei formation a growing carbon particle has a considerably higher temperature than would correspond to the degree of acetylene decomposition attained at that moment. Inasmuch as the interaction between the acetylene molecules and the nuclei, and their decom- position on the surface of the growing particle, result in the release of a large amount of heat which has no time to be transferred to the gas owing to the high rate of the process, such a supposition seems reasonable.Therefore, it was assumed as a first approximation that the particle temperature, starting from the moment of nucleation, is equal to the maximum temperature of the process (about 3000°K) developing when the decomposition of acetylene is complete. In addition, it was assumed that the gas layer which is the closest to the surface has a temperature equal to the surface temperature and that each collision of a hydrocarbon molecule with the surface leads to an elementary act of decomposition. In other words, it was assumed that the process under con- sideration has an activation energy E = 0 and that the reaction rate depends only on the number of collisions of acetylene molecules with the surface.Naturally, a calculation based on such assumptions yields a maximum possible decomposi- tion rate and a minimum reaction time. The number of collisions of acetylene molecules with the surface was determined from the equations of the kinetic theory. d I 2 3 4 5 6 time, microseconds FIG. 2.-Kinetic curves of the process of formation of dispersed carbon by self-combustion of acetylene. Curves 1, rate of particles formation ; 2, total surface area of the particles ; 3, degree of acetylene decomposition. Such a calculation produces a correct result for the number of collisions of the molecules with the surface only at the first moment of nucleation. Subsequently, the number of collisions decreases, because the concentration of acetylene falls off and the concentration of hydrogen grows in the surface layer as a result of the reaction.In a steady-state process the growth rate would be determined by the diffusion of acetylene molecules towards the surface. However, we are dealing with an essentially non-steady-state process, and it is very difficult to estim- ate the role of diffusion in slowing-down the process. Therefore, as a first ap- proximation, we also ignored diffusion and assumed that the concentration of acetylene near the surface of the particle and throughout the volume was the same during the whole period of particle growth. This assumption, as well as theP. A .TESNER 175 previous ones, should lead to an over-estimation of the growth rate. The maximum rate of particle growth obtained in this manner proved to be w = 2.09 x lO-'C cm/sec, (5) where C is the acetylene concentration in vol. %. formation will be If the thickness of the carbon layer formed is 6 (A), the time necessary for its t = S/249C x 106 sec. (6) Using this equation the curves of fig, 1 were converted to the kinetic curves given in fig. 2. To do this, we determined the growth rate from eqn. (3, then obtained graphically the thickness of the formed carbon layer, 6, and finally calculated the reaction time from eqn. (6) for a certain range of variation in the degree of decom- position. Then we found graphically the number of newly-formed carbon particles, An, and determined the absolute rate of formation of new particles or the rate of nucleation (in units of cm-3 sec-1) using the known reaction time.DISCUSSION The graph of fig, 2 represents kinetic curves of the process of dispersed carbon formation. Of special interest is that the particle formation curve shows a con- siderable induction period and a sharp peak in the particle formation rate. Of the total duration of the process (about 7 psec), the time from the moment of formation of the first particles to the beginning of the rapid growth of the formation rate is about 2psec. The sharp peak on the curve of the formation of carbon particle nuclei is due to the rapid rise in the rate oi nucleation at the beginning of the process and the similar rapid fall-off in this rate which is observed when the acetylene concentration is still high.The cause of the rapid rise in the nucleation rate is not entirely clear. Tbis rise can hardly be explained by the rapid rise in temperature because the maximum gradient of the growth rate corresponds to the initial degrees of decomposition. The maximum rate of particle formation corresponds to about 10 % of the degree of acetylene decomposition. This leads to the conclusion that nucleation takes place essentially in the temperature range from 500 to SOOOC, As far as the drop in the nucleation rate is concerned, it is attributed to the competing reaction of particle growth, whose activation energy is close to zero, whereas the activation energy of the nucleation process is 60 to 70 kcal/mole.As was indicated above, the calculation was based on assumptions that led to the maximum possible rate of the process and hence the minimum possible duration of the reaction. The kinetic curves of fig. 2 permit an &timation of the total duration of the explosion of 7pec. It would be of interest to compare this value with direct experimental results. For this purpose we used the measure- ments of the rate of acetylene detonation based on the data of Bonn and Framr.17 These measurements were carried out at atmospheric pressure. The detonation was produced by means of a detonator placed in acetylene. The initial flame velocity over a length of 0.5 m was 2135 m/sec, the length of the incandescent head of the detonation front being about 10 cm. Based on these results, the dura- tion of the chemical reaction in detonation may be estimated as 0.1/2135~47 x sec.This value is only about 7 times the one found by calculation. Since the length of the region of incandescent carbon particles should exceed that of the chemical front of the reaction, because some time is needed for the cooling of the particles, the actual divergence between these values is still smaller. This suggests the unexpected conclusion that the extreme assumptions used in the calculation176 DISPERSED CARBON FORMATION have not led to a considerable overstatement of the reaction rate and, consequently, are close to the actual values. Indeed, if one assumes that the divergence is due only to slowing-down by diffusion, then, considering the tremendous absolute reaction rate, this slowing- down should be regarded as insignificant.Conversely, if slowing-down by diffusion is assumed to be zero, it should be concluded that the reaction does not involve each of the acetylene molecules hitting the surface, but only one of every four or five molecules. In other words, the activation energy of the growth process is not zero, but 6000 to 8000 cal/mole. If we assume, however, that the actual process involves slowing-down both by diffusion and kinetic processes (which is more realistic), the conclusion must be drawn that the activation energy of the process does not exceed a few thousand calories per mole, and slowing-down by diffusion is quite insignificant. Conse- quently, in acetylene explosion, the growth of carbon particles is, indeed, due to the direct destruction of acetylene molecules hitting the carbon surface, and the reaction involves practically each of the colliding molecules.In this case the heat released in the exothermic decomposition reaction has 110 time to dissipate, and the growing particle has a considerably higher temperature than the ambient gas during the major part of the reaction. Owing to the aval- anche-like and highly unstable nature of the process, in spite of its tremendous rate, the slowing-down by diffusion decreases its rate but only slightly (less than by one order of magnitude). As regards the mechanism of nucleation in the process considered, the following may be stated. Because of the short reaction time, nuclei cannot result from polymerization reactions, as was shown convincingly by Porter.4 Hence, nuclei are simply carbon particles-radicals formed from active acetylene molecules.The computed absolute rates of carbon particle formation allow an estimation to be made of the activation energy of the nucleation process. The curve of fig. 2 shows that the maximum rate of nucleation is 2.3 x 1012 ml-1 sec-1. This value makes it possible to estimate the activation energy of the nucleation process as about 60 kcal/mole for a birnolecular process and 70 kcal/mole for a monomolecular process. The high values of the activation energy of nucleation in molecular reactions suggest that the chain mechanism of nucleation is more probable. The problem of the possible chain mechanism is treated in ref. (8) and (9). It should be emphasized that the formation of carbon radicals is needed only to obtain nuclei of carbon particles, regardless of the mechanism of this formation. The further growth of these nuclei proceeds as a purely molecular process. It should also be noted that the considerable excess of the temperature of the growing carbon particle over the temperature of the ambient gas is characteristic only of the explosion decomposition of acetylene.Of course, no such effect exists in the formation of carbon black from other hydrocarbons and from dilute mixtures of acetylene, where the temperatures of the growing carbon particle and the gas should be identical. CONCLUSIONS (1) The growth of carbon particles in acetylene explosion results from the direct decomposition of acetylene molecules on the surface of the growing particle.The activation energy of the process is close to zero ; thus practically each collision of an acetylene molecule with the surface leads to reaction. (2) The total rate of the chemical reaction at the front of the acetylene ex- plosion is determined by the rate of the reaction of acetylene molecule decomposition on the surface of the carbon particles which, in turn, depends on the rate of nucleation. (3) The temperature of the growing carbon particle from the moment of nucle- ation and during the major part of the reaction considerably exceeds the equilibriumP. A . TESNER 177 adiabatic temperature of the gas corresponding to the degree of decomposition achieved. (4) Because of the avalanche-like nature of the process the rate of particle growth is determined by the rate of the chemical decomposition reaction and is only slightly inhibited by the rate of hydrocarbon diffusion. (5) The nuclei of carbon particles in acetylene explosion represent the simplest carbon particles-radicals formed by a molecular and/or a chain process from the molecules of acetylene. 1 Alekseev, Proc. Shelaputia Inst., Moscow, 1915, 4, 167. 2 Rimarski and Konschak, Autogene Metallbearbeitung, 1931,24, 51. 3 Frank-Kamenetzky, Acta physicochim., 1943,18, 148. 4 Porter, Combustioi~ Research and Reviews (Butterworths Sci. Publ., London, 19551, 5 Jones, Kennedy, Spolan and Scott, Bur. Mines. Report, no. 4695, 1950. 6Gaydon and Fairbairn, 5th Symp. Combustion (Reinh. Publ. Corp., N.Y., 19551, 7 Robertson, Magee, Fain and Matsen, 5th Symp. Combustion (Reinh. Publ. Corp., 8 Westbrook, Hellwig and Anderson, 5th Symp. Combustion (Reinh. Publ. Corp., 9 Stehling, Frazee and Anderson, Gth Symp. Combustion (Reinh. Publ. Corp., N.Y., p. 108. p. 324. N.Y., 1955), p. 628. N.Y., 1955), p. 631. 1957), p. 247. 10 Green, Taylor and Patterson, J. Physic. Chem., 1958, 62, 238. 11 Aten and Green, Faraday Soc. Discussions, 1956,22, 162. 12 Hooker, 7th Symp. Combustion (Buttenvorths Sci. Publ., London, 1958). 13 Tesner, Viziigaz Proc. Gostoptehisdat., Moscow, 1958, N3 (1 1), p. 34. 14 Tesner, 7th Symp. Combustion (Butterworths Sci. Publ., London, 1958), p. 576. 15 Watson, Anal. Chem., 1948, 20, 567. 16 Tesner, 8th Symp. Combustion, (1960). 17 Bone and Frazer, Proc. Roy. Soc. A , 1932,23Q, 363.

ISSN:0366-9033    

DOI:10.1039/DF9603000170

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

LIGHT SCATTERING OF COATED AEROSOLS PART 1.-SCATTERING BY THE AgCl CORES" BY E. MATIJEVI~, M. KERKER AND K. F. SCHUEZ Clarltson College of Technology, Potsdam, New York, USA. Received June, 1960 The preparation of silver chloride aerosols consisting of spherical particles of narrow size distribution by a condensation technique is described. The particle size distribution was determined by electron microscopy. Excellent agreement was obtained between the polarization ratio from light-scattering measurements and that calculated from the particle size distribution and theoretical scattering functions. Since the light scattering itself was insensitive to particle size distribution over a wide range of sizes studied (radius, 208-800 mp), the determination of particle size distribution from light scattering is not feasible for this range.However, there is an optimum range of size (r,,,-55.0 mp) where particle size distribution can be obtained from light scattering. The primary objective of this investigation is to study the light scattering of coated aerosols, i.e., aerosol particles consisting of a core encased in a shell of second material. The theory of scattering of electromagnetic radiation by such systems was worked out a number of years ago 1 and has been applied to problems in radar meteoro- logy,ZJ scattering of microwaves by dielectric coated spheres 4 and astrophysics.5 The theory is restricted to a spherical core and a concentric spherical shell, but is general for any size or any optical parameters, provided the latter are homogeneous. We have successfully prepared aerosols consisting of a solid spherical core on which a liquid shell is condensed.Silver chloride is used as the core and various organic substances such as octanoic acid, linolenic acid and dibutylphthalate as the shell. However, in this first part we shall report only the light-scattering data on silver chloride " cores ". Silver chloride aerosols consisting of spherical particles with average radii ranging from 5 to 1000 mp were obtained using a condensation technique. The mean particle size depended upon the " boiler " temperature and the flow rate of the carrier gas. Although the aerosols were not monodisperse, they were of reasonably narrow size distribution. The size distribution was determined by electron microscopy.The intensity of the vertical and horizontal components of the scattered light from these aerosols at various angles of observation was measured and the experimental polarization ratio compared with the values calculated from the size distribution and the light-scattering functions. The light- scattering €unctions were computed for this specific case on an IBM 704 digital computer . EXPERIMENTAL GENERATION OF SILVER CHLORIDE AEROSOLS Silver chloride aerosols were generated using a " boiler " technique whereby solid AgCl was successively evaporated and condensed in a stream of helium. The generator equip- ment is schematically represented in fig. 1. Two multiple heavy-duty hinged type com- bustion furnaces (1 and 2) were employed. The first served as the boiler for AgC1, and the second as the reheater or cooling regulator.Solid AgCl (1-4 g) was evaporated from a combustion boat (4) which was inserted into a silica or a Coors Sillimanite combustion tube (3). The temperature was controlled using Variac resistors and measured with a chromel-alumel thermocouple in connection with a Wheelco portable potentiometer, * supported by U.S. Army Chemical Corps Contract DA 18-108-405-Cml-201. 178E . MATIJEVI6, M. KERICER AND K. F. SCHULZ 179 series 300 (5). The furnace temperature could be kept constant to f l " C of the desired temperature, which ranged between 850 and 1100°C. Helium of 99.9 % purity from a cylinder was used as the aerosol carrier. It was filtered through a fritted disc Pyrex filter before entering the flowmeter (8) and the combustion tube.The aerosol was diluted, when necessary, using a branch line for helium (9) which terminated in the second furnace. The flow rate of the dilution gas was controlled by another flowmeter (10). The aerosol formed could be observed in a three-neck-flask which served as a viewing chamber. Collection of aerosol for the particle size distribution counts was performed either by direct impingement in the viewing chamber on cooled microscope slides on which electron microscope grids were fixed or by thermal precipitation. In the latter case, a model B thermopositor obtained from the American Instrument Company was used. Collodion- coated electron microscope grids were arranged in a suitable pattern on top of an alum- inium foil in the thermal precipitation chamber. The flow rate through the thermopositor was kept the same as through the generator and was controlled with the aid of an addi- tional flowmeter (13): ELECTRON MICROSCOPY The particle size distribution of the aerosol samples was obtained with the aid of an RCA model EMT and a Phillips model EM-100 electron microscope. Small silver chloride aerosol particles were unaffected by the electron beam, and remained spherical and unchanged for long periods of observation in the electron microscope.Larger 12 ib o5 6 7 FIG. 1 .-Schematic diagram of the equipment : 1 , boiler furnace ; 2, reheater furnace ; 3, silica combustion tube ; 4, combustion boat ; 5, thermocouple and potentiometer ; 6, helium source ; 7, gas filter; 8, 10, 13, flowmeters; 9, gas dilution line; 11, viewing chamber ; 12, thermopositor collector ; 14, light-scattering instrument ; 15, light- scattering cell.particles, however, melted and partly evaporated under the influence of the electron beam. In order to prevent this, they were shadowed at vertical incidence with gold in a RCA type EMV-6 Vacuum Shadowing Unit. The gold-coated particles were suffciciently stable in the electron microscope so that electron micrographs could be obtained. However, after an extended time, the coated particles also evaporated. The electron micrographs were projected for counting purposes and the size of several hundred particles measured directly on the projection screen. LIGHT-SCATTERING MEASUREMENTS The light-scattering measurements were obtained with a Brice-Phoenix Photometer, 1000 series, which was tested and adjusted as described previously.6 A special light- scattering cell for aerosols was designed and built in our laboratory.It was made of brass with one flat glass window for the incident beam and a glass arc as the exit window for angular measurements of the intensity of the scattered light. A Rayleigh horn was mounted in the 180" position in order to reduce stray light. The opening of the receiver tube was fitted with a special nose piece with a circular slit 1 mm in radius in order to reduce the solid angle viewed by the photomuItiplier. The intensities of the vertically and horizontally polarized scattered light were measured at angles from 50 to 140" at 10" intervals using the 436 fzi)rc line of the mercury spectrum.Light-scattering measurements were obtained under a constant flow of the aerosol through the cell. As long as the180 LIGHT SCATTERING OF COATED AEROSOLS flow rate of aerosol during these measurements was very carefully controlled, the in- tensity of the scattered light was quite stable. COMPUTATIONS The light-scattering intensity functions were computed on the IBM 704 computer for single spheres of refractive index 2.105 which corresponds to AgCl at 436mp.7 The values of these functions will be presented in detail in a subsequent publication.8 L' C.... RESULTS AND DISCUSSION The aerosol particles appeared spherical in the electron microscope, indicating that they probably consist of supercooled, glassy AgCl. The absence of an electron diffraction pattern confirms the amorphous character of the material.Some typical electron micrographs are shown on plates 1-5. In plates 1-4 the average sizes are 15, 55, 370 and 580 mp, respectively. These aerosols were obtained at the same flow rate (930 ml/min) but different temperatures (850, 930, 1045 and llOO°C). Temperatures between 930-1045°C give aerosols of intermediate particle sizes (see also fig. 4). What may appear as coagula in plates 1 and 2 are actually aggregates which are formed by deposition upon preferential sites on the -1 COLLECTION: THERMOPOSITOR DIRECT 850°C 930 ml/min AgCl '1 I Oo lo 20 30 40 COLLECTION TIME: 15 sec 30 sec - --- radius in mp FIG. 2.-Effect of the type of the aerosol collection (left) and the collectioii time in thermopositor (right) on the particle size distribution of silver chloride aerosols.electron microscope grids. By collecting for a shorter period of time such coagula are no longer encountered. However, in order to obtain a large number of particles for counting we have routinely obtained micrographs with such a high particle concentration. The deformation of particles in the electron micrograph on plate 4 occurs after they have been in the electron beam for a minute or so and is due to the beginning of evaporation of the original spherical particles as discussed earlier. The electron micrograph on plate 5 is from the same aerosol as plate 4 but here the collection time has been increased and this clearly shows aggregation upon the electron microscope grid. In the last three samples, the particles have been gold-shadowed at vertical incidence in order to retard the evaporation process.In plate 4 the deformation due to evaporation has proceeded to a greater extent than in plate 5 where there are only small serrations at the edges of the particles.PLATE 1.-Electron micrograph of AgCl aerosol obtained at 850°C and a flow rate of 930 ml/min, diluted 4.3 times ; thermopositor collection 30 sec ; electron microscopic magnification 3000 x ; photographic enlargement 2 x . PLATE 2.-Electron micrograph of AgCl aerosol obtained at 930°C and a flow rate of 930 ml/min ; thermopositor collection 10 sec ; electron microscopic magnification 1450 x ; photographic enlargement 2 x . [To face p. 180PLATE 3.-Electron micrograph of AgCl aerosol obtained at 1045°C and a flow rate of 930 ml/min; thermopositor collection 10 sec; sample gold-shadowed ; electron micro- scopic magnification 1450 x ; photographic enlargement 2 X .PLATE 4.-Electron micrograph of AgCl aerosol obtained at 1100°C and a flow rate of 930 ml/min ; thermopositor collection 10 sec ; sample gold-shadowed ; electron micro- scopic magnification 1450 x ; photographic enlargement 2 x .PLATE 5.-Same conditions as 4 ; thermopositor collection 30 sec,E . M A T I J E V I ~ , M . KERKER AND K . F. SCEIULZ 181 Both methods of sampling, direct impingement and thermal precipitation, gave the same size distribution. As an example, the two histograms compared in fig. 2 (left) were obtained from samples of the same aerosol collected in the two different ways.We also ascertained that neither the position of the grids in the thermo- positor nor the collection time influenced the particle size distribution (fig. 2 (right)). If all experimental conditions were kept constant and especially if traces of AgCl from previous experiments were completely removed from the combustion tube and the thermocouple, very good reproducibility was obtained. Fig. 3 gives the histo- grams for two pairs of runs performed under quite different conditions, one at 930°C and a flow rate of 930 ml/min (solid lines) and the second at 1010°C and 540 ml/min (dashed lines). Each pair represents two completely independent aerosol preparations obtained over a considerable time interval and in both cases almost identical particle size distribution were obtained.10 I00 radius in mp (log) In00 FIG. 3.-Examples of reproducibility in preparation of AgCl aerosols. Full lines repre- sent two independent preparations performed at 930°C and 930 ml/min. Dashed lines represent two other preparations at 1010°C and 540 ml/min. If aerosols were prepared at low temperatures (t850") some coagulation did take place but this could be eliminated by a four-fold (or higher) dilution of the aerosol with helium. With larger average particles (higher temperatures) coagula- tion was not encountered. The primary factors controlling the size distribution are the boiler temperature and the flow rate. Fig. 4 shows five histograms obtained at the same flow rate but at five different temperatures.The mean particle diameter increases considerably with increasing temperature. The radius is plotted on a logarithmic scale in order to be able to compare the wide range of sizes obtained. The influence of flow rate is shown in fig. 5 where the histograms are for aerosols prepared at 1010°C and at various flow rates of the carrier gas. With increasing flow rate the mean particle size increases. Since increasing flow rate corresponds to a more rapid rate of cooling, this would suggest that the proportion of material condensing on the walls is reduced as the rate of cooling increases. Although these aerosols are not monodisperse to the same extent as systems such as certain polystyrene preparations or La Mer's sulphur sols,g their size distribution is relatively narrow, e.g., the standard deviation from the mean radius182 LIGHT SCATTERING OF COATED AEROSOLS is about 20 to 25 %.Attempts to obtain greater monodispersity by varying the boiler temperature or by using nuclei, such as sodium chloride or silver chloride, did not succeed. . . -. . . . -1.. .. L, I, I I I I I : I I 1 I ,i;'; , , I : L, ----J 40 FLOW R A T E 930ml /min 3ol AgC' I 7 l o t I 930' I I r--1 - , . . . . . . . . . . . . a . * * . . 1046' i r I I L l : I ! I i t i..... I i I i t l A t I : 1 :.... t i 1 : : I : I I I I L1 I I I I I I 1 I-, I I 10 radius in mp (log) FIG. 4.-Effect of the temperature on the particle size distribution of silver chloride aerosols ; flow rate constant (930 ml/rnin). TEMP - IOlO'C FLOW RATE: 240 ml /min Ag C1 % radius in mp (log) FIG.5.Effect of the flow rate on the particle size distribution of silver chloride aerosols ; temp. constant (lSIO°C). The light-scattering results are summarized in table 1. The angle y of observa- tion is the angle between the direction of propagation of the scattered light and the reversed direction of propagation of the incident beam. The experimental polariza- tion ratio is the ratio of the intensities of the horizontally to vertically polarized scattered light and was obtained with Glan-Thompson prisms, appropriately oriented, in both the incident and scattered beams. There was no depolarizationE. M A T I J E V I ~ , M. KERKER AND K . F. SCNWLZ 183 by the aerosol in the sense that when these prisms were crossed there was complete extinction.The reproducibility of successive polarization ratio determinations on the same aerosol was such that the average deviation was about 1 to 2 %. The solid angle subtended by the photometer receiver was sufficiently small (7.6~ 10-3 steradians) so that no appreciable error would be encountered from this factor. TABLE 1 TABLE 1 .-COMPARISON OF CALCULATED AND angle of rav= 55.0 rnp rav = 246 rnp observation o=20.3 u= 80 m p caIc. expt. calc. expt. 50 a90 *go 1.17 1.49 60 *83 -80 204 1-65 70 4 1 *76 239 1.73 80 -50 -66 2-42 1-75 90 -51 -65 1-56 1.51 100 -74 -66 1.20 1.43 110 -82 *69 1.07 1.27 120 *91 *74 1.15 1.14 130 -76 *79 -92 1.06 140 -97 -85 1.06 1.03 EXPERIMENTAL POLARIZATION RATIO rav= 389 m p rav=563 m p a= 143 m p calc. expt. calc. expt. 1-17 1.27 1.43 1-24 1.97 1.40 1-84 1.40 1-82 1.59 219 1.53 2.38 - 221 1.50 1.57 1-53 1.76 1.49 1.47 1.39 1.65 1-32 1.30 1.35 1-31 1.20 1-20 1-20 1.18 1.04 1.03 1.09 1.02 -99 *9 1 -94 1-02 -97 u= 104 mp r,, = average radius ; (r = standard deviation from the average.The calculated results were obtained from the light-scattering intensity functions il(y, a, m) and iz(y, a, m) which are functions of particle index of refraction m, angle of observation y, and the quantity a = 2741 where r is the particle radius and A is the wavelength of the light in the medium. These functions are proportional, respectively, to the intensity of the vertically and horizontally polarized components of the scattered light. If the aerosol is characterized by a size distribution Prdry which is the fraction of particles with values of r between r and r+dr, then the polarization ratio is given by The light-scattering functions were available in increments of 0-4 from a = 0.2 to 6.0 and in increments of 0.2 from a = 6.0 to 15.0.Intermediate values were obtained by graphical interpolation. Since the values of the functions oscillated quite sharply and erratically with a, there was a substantial element of uncertainty in some of the interpolations which in turn might affect the h a 1 result, especially when they occurred in the neighbourhood of the peak of the size distribution curve. We expect, eventually, to obtain additional light scattering functions which will eliminate this source of error. The size distribution was obtained by drawing a smooth curve through the histograms.The agreement between size distributions obtained by direct impinge- ment and thermal precipitation would indicate no appreciable systematic sampling error. However, the systematic error in size determination of electron microscopy might be of the magnitude of about 10 %. Despite the possibility of experimental error discussed above, the agreement between the calculated and experimental values of the polarization ratio in table 1 is remarkably good. In the worst cases the deviation is only 25 % and the average deviation is 8 %. It is interesting that for the three aerosols of larger size, the polarization ratio is insensitive to the size. Were these systems perfectly monodisperse, this would184 LIGHT SCATTERING OF COATED AEROSOLS not be the case and the polarization ratio would vary over orders of magnitude.However, the scattering functions do oscillate so sharply that the integrated polariza- tion ratio over even the relatively narrow size distributions which we encountered is much the same over the entire range of from 200 to 800 mp in radius. This, in turn, means that for this range of sizes measurement of the polarization ratio cannot be used for particle size determination. Although we do not have experimental dissymmetry data, the calculated dissymmetry indicates that for this size the same situation prevails for this type of measurement, i.e., the angular intensity pattern is quite insensitive to size in this range of particle sizes. For aerosols consisting of very small particles, i.e., average radius less than 30 mp, we were unable to get a correlation between the experimental and calculated polariza- tion ratio. For this size range, the scattering functions are increasing exceedingly rapidly with particle size (il-r6) so that the scattering by just a few large particles completely swamps out that due to large numbers of smaller particles. There is an optimum particle size range, such as that corresponding to the smallest aerosol given in table 1 (Y, = 55-0 mp) where it is feasible to determine the particle size distribution from light-scattering data. We are very much indebted to Miss Elizabeth Wallace and Dr. R. Ward from the Department of Zoology, Columbia University, New York, for taking some of our electron micrographs. We would also like to thank Dr. Norman Loud for his assistance in the early stage of this work. 1 Aden and Kerker, J. Appl. Physics, 1951, 22, 1242. 2 Kerker, Langleben and Gunn, J. Meteorology, 1951, 8, 424. 3 Atlas, Kerker and Hitschfield, J. Atm. Terr. Physics, 1953, 3, 108. 4 Scharfman, J. Appl. Physics, 1954,25, 1352. 5 Guttler, Ann. Physik, 1952, 11, 65. 6 Kerker and Matijevib, J. Opt. SOC., 1960, 50, 722. 7 Int. Crit. Tables (McGraw-Hill, New York, 1930), vol. vii, p. 13. 8 Kerker and Matijevib, J. Opt. SOC., 1961, 51, 87. 9 Kerker and La Mer, J. Amer. Chem. SOC., 1950,72, 3516.

ISSN:0366-9033    

DOI:10.1039/DF9603000178

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

BY FRANK T. GUCKER AND ROBERT L. ROWELL? Dept. of Chemistry, Indiana University, Bloomington, Indiana, U.S.A. Received 27th June, 1960 The light-scattering diagrams of single aerosol droplets of dioctyl phthalate $ have been determined by charging them, suspending then1 in an electrostatic field, illuminating them with monochromatic light of wavelength )I and measuring the light scattered into a photo- meter moving over the range of 40 to 140" from the direction of illumination. Particle radius r was calculated from rate-of-fall measurements and the Stokes-Cunningham- Millikan equation. Good agreement was obtained with scattering diagrams calcuIated from the Mie theory, which indeed provide a more sensitive measurement of particle size than do rate-of-fall measurements. Detailed calculations of scattered intensity according to the Mie theory have been made at angular intervals of 1" over the range of size parameter a = (27~rlA) = 01(0*1)30-0 for a refractive index of 1.486 and at several values of a for a refractive index of 1.50.The number of maxima in the scattering diagrams increases with a. Graphs of the angular position of the maxima in the two polarized components show that new maxima are formed by splitting where the curves for the two polarized components intersect and the size parameter is approximately divisible by ~14. Gustav Mie, in 1908,l obtained the first complete theoretical solution to the problem of the scattering of a plane electromagnetic wave by a spherical particle. A brief statement of some of the results of Me's work introduces the present investigation.A dielectric sphere of radius r is illuminated by a plane wave of natural (un- polarized) light of unit intensity and wavelength A. The intensity of the scattered light I observed at a distance R which is large compared to 2, at an angle 8 measured from the forward direction of propagation of the incident beam is given by I = (A2/8~2R2)(i1 + iz), where il is proportional to the intensity of light plane polarized with the electric vector perpendicular to the plane of observation (including the incident beam and the point of observation) and i2 is proportional to the intensity of light plane polar- ized with the electric vector perpendicular to il. The intensity functions, il and 2'2, are expressed in terms of infinite series dis- cussed by Gucker and Cohn 2 and given in the notation they suggested as The augmented angular functions, IIn and Tn, are formed from the first and second derivatives of Legendre polynomials of argument cos 0 and the amplitude functions, a, and b,, are derived from Wiccati-Bessel functions of arguments a = 2nr/A and * contribution no.958. 7 present address : Department of Chemistry, University of Massachusetts, Amherst, Massachusetts, USA. i.e., bis-2-ethylhexyl phthalate. 1852 86 LIGHT SCATTERING BY SINGLE AEROSOL DROPLETS ma, where rn is the re€ractive index relative to the medium. Penndorf and Gold- berg 3 found that the series converge rapidly after about (73- 1.2~) terms, and the summation is stopped at about that point, when further terms become inappreciable. The present work combines an experimental and theoretical study of light scattering from aerosol particles.We have made precise measurements of the angular variation of monochromatic light scattered by single droplets of dioctyl phthalate @QP) (bis-2-ethylhexyl phthalate), and computations OF the Me-theory intensity €unctions over the angular range 0" (1 ") 180", and size parameter a = 0.1 (0.1) 300. These detailed calculations allow a careful comparison of experi- ment with theory, and have revealed some unsuspected new relationships between size parameter and scattering diagrams. EXPERIMENTAL METHODS The object of the experimental work was to produce an apparatus capable of precise measurement of the angular intensity-distribution curve for a particlc of radius in the micron range.Such an instrument enables a quantitative test of various scattering theories and eventually the possibility of studying the scattering from substances with a complex index of refraction or of intricate shape, which are dimcult or impossible of theoretical evaluation. A detailed description of the first model of the apparatus, developed by Dr. James J. Egan, is given elsewhere.4 5 The principle of the measurement is to suspend a charged droplet of DOP in the electrostatic field of a Millikan-type apparatus, illuminate it with an intense beam of light, nearly parallel (0.8 O half-angle of divergence), and monochromatic (34-0 A half-band width) and measure the scattered light over the angular range (d = 40' to 140") with a photometar having an entrance aperture 4.1" wide and 6.0' high.The improved apparatus used in this work employs a precision goniometer (0.2" accuracy) and dual photometers, a measuring photometer which responds to the scattered light and a reference photometer which monitors the attenuated incident radiation. Each photometer employs an RCA type 1P21 multiplier phototube, the output of which is fcd into a bucking circuit (based on Egan's design) which allows cancellation of the back- ground current. The resultant signals are amplified by Leeds and Northrup type 9836 micromicroampere amplifiers and fed into a factory-modified Leeds and Northrup Speedo- max 6 recorder capable of recording the output from either channel or their ratio. An advantage of this arrangement is that the ratio of the scattered light to the attenuated incident light is independent of fluctuations in the intensity of the incident beam.The angular position of the measuring photometer at each end of the range is indicated on the recording paper by means of a solenoid marginal pen actuated by an electromechanical trigger pulse from the precision goniometer and associated electronic circuit. COMPUTATIONS The augmented angular functions, IIn and Tn, have been calculated at intervals of 1" to fifteen decimal places for orders n = 1 to 43. Amplitude functions, a, and b,, given to ten digits, for refractive indices 1.33, 1.40, 1.44, 1.486 and 1.50 and for size parameters a = 0.1 (0.1) 30.0 have recently been published in five parts by Penndorf and Goldberg.3 We used the amplitude functions (part 4, rn = 1.486; part 5, m = 1.50 corresponding to the refractive index of DOP for two wavelengths of visible light) along with our augmented angular functions, to calculate the complex amplitudes of the intensity functions, il and i2, the functions themselves (equal to the square of the modulus), and their sum, il+ i2 = ie.The calculations for m = 1.486 cover the range of a = 0.1 (0- 1) 30 and 6 = 0" (1") 180" and are recorded on 54,300 ( 3 0 0 ~ 181) IBM cards, each containing the complex amplitudes, Re(il), Im(il), Re(i2), and Im(i2), and the intensity functions, il, i2, and is, for a particular a and 6. The work was done in double precision and the results are in floating-point notation with eight sig- nificant figures and the floating point index punched for each number.Similar calculations for rn = 1.50 have been made over the complete angular range at intervals of 2 9 for ct = 10.0, 12.0, 15.8, 19.2, 20.5 and 209, in connectionF. T . GUCKER AND R. I,. ROWELL 18; with Egan's measurements,s and at intervals of 1" for a = 15.4 (0.1) 18.8 anc 20.2 (0.1) 20.6 in connection with OUT experimental work (see below). The results of the calculations show that the shape of the angular intensity distribution curves and the angular positions of the maxima are very sensitive tc small changes in the size parameter a and in the refractive index rn. l ~ i ~ [ 0 angle, 0 FIG. 1 .-Mie-theory scattering diagram showing total intensity function, ie = i~ +i2, over the range in scattering angle 0 = 50" to 120" for a size parameter a = 18.4 and refractive indices m = 1.486, dashed curve, and 1-50, solid curve.angle, 6' FIG. 2.-Angular position of the maxima in the total intensity function, it, = i l f i 2 , for a refractive index of 1-486 over the range in size parameter, a = 18.0 to 22.0, and scattering angle, 0 = 50" to 100". Fig. 1 shows a comparison on a semi-logarithmic scale of a portion of the angular intensity distribution for size parameter a = 18.4 and refractive indices of 1.486, dashed curve, and 1-50, solid curve. A logarithmic scale seemed ap- propriate for the intensity functions because of the large range in the values of the resonance peaks and valleys. Although the curves are roughly the same, the small difference in refractive index appreciably affects both the amplitude of the resonance peaks and the angular position of thezmaxima.188 LIGHT SCATTERING BY STNGLE AEROSOL DROPLETS The junior author 6 has compared the scattering diagram for io over the corn- plcte angular range for a = 20.9, m = 1-58 with five scattering diagrams for m = 1-486: a = 20.9, 21.0, 21.1, 21.2 and 21.5, and found best agreement for a = 21.1, which suggests that diagrams having the same valuc of ma (31.35 in these cases) would have about the same structure.The behaviour of the maxima for different size parameters can be coiivenieiitly summarized by plotting the angular position of the maxima on a size-angle diagram. A limited region is shown in fig. 2, which covers the angular range, 8 = 50' to lQQ", and the size range a = 18.0 to 22.0.The pattern is somewhat irregular but shows that the increase in number of maxima with particle size is due to their migration away from the centre and the appearance of new maxima in the centre. COMPARISON OF EXPERIMENT WITH THEORY FOR io The problem of obtaining a precise comparison of experiment with theory was complicated by the facts that the particle diameters were so small that a cor- rection had to be applied to Stokes's law, the light was nearly but not precisely monochromatic, and the observing aperture had a small but finite width. From measurements of the rate of fall of the DOP particle we calculated its radius from the Stokes-Cunningham-Millikan (SCM) equation, Here u is the terminal velocity, p2 and p1 the densities of the particle and medium (air), g the acceleration of gravity, r the particulate radius, q the coefficient of viscosity, and ~ C M the Cunningham-Millikan correction lactor, v = 2 ( ~ , - p1)8r2/9v(1 + f C d (4) fcM = (l/r)(A+Be-Cr/'), ( 5 ) where I is the mean free path.For DOP particles in air we used Millikan's values 7 for the constants A , B and C which he determined for oil drops falling in air and which Rosenblatt and LaMer 8 have found applicable to tricresyl phosphate droplets falling in air. The value of rn = 1.486 was first chosen as most representative of the refractive index of DOk for visible light, and this value was used for our complete calculations. Later, however, we found the refractive index of a sample of DOP at 25°C was 14840 for sodium-D light, but 1.4980 for light of wavelength 4371.3A.6 Ac- cordingly, we used our detailed calculations for m := 1.486 as a first approximation and made selected new calculations for nz = 1.50 to improve the cornparison of experimental results with theory.One particle we studied had a radius of 1.44,~ as determined by rate-of-fall mcasurements and the SCM equation, and a value of a = 20.8 based upon the mid-band wavelength of 4371 8, for A. Comparison of the positions of the light- scattering maxima with fig. 2 gave as a first approximation good agreement for a = 20.4 (m = 1.486). The IBM 650 programme of Gucker and Engle and the published amplitude functions of Penndorf and Goldberg 3 were then used to cal- culate intensity functions for a refractive index of 1-50 in this region. The experimental and theoretical curves were compared on a semi-logarithmic scale similar to fig.1 in an intermediate graph (not shown). The principal ad- vantage of the logarithmic scale is that it allows comparison of the shape of the experimental and theoretical curves without the necessity of a normalizing factor ; its chief disadvantage is that it gives too much weight to the smaller experimental numbers. The comparison gives the best agreement for a light scattering a of 20.3 (rn = 1-58). The result is consistent with the previous approximation using data based on m = 1.486. The difference of 0-5 a between the SCM value of 20.8 and light- scattering value of 20.3 is within the expected range of error inasmuch as Millikan 7 believed his constants to be accurate to f 2 %, the error in the time-of-fall measure- ment was about 1 %, and accurate Cunningham-Millikan constants (whichF.T. GUCKER AND R. L. ROWELL 189 depend on the mean free path and the nature of the collision between the molecules of the medium and the particle) have never been determined for DQP. Fig. 3 shows a comparison of the experimentd (solid) and theoretical (dashed) curves on a linear scale. The experimental curve was obtained from the difference of two measurements: the angular response with the particle illuminated by intense blue light (4371.3 A with half-band width of 344 A) minus the background, which is the angular response with no particle in the cell. The background con- sisted of dark current arid photocurrent from light scattered by the solid parts of the cell and the air, Most of the d.c.component of the background was reduced with the bucking circuits during a run. Similar experimental scattering diagrams have been obtained 4 for three other particles of DOF with radii 0.4, 1.3 and 2.3 p. angle, 0 FIG. 3.-Comparison of experiment, solid curve, with theory, dashed curvc. The curves in fig. 3 have been normalized by equating the areas shaded by the first two maxima, which are the most reliable. The disagreement is due chiefly to low signal-to-noise ratio and the strong dependence of the shape of the curves on the scattering angle and the particle size. Work is now in progress on a more refined comparison made by integrating the theoretical curves first over the range of size parameter a (approximately 0.2 a) corresponding to the small band-width of the incident radiation and then for each angular position over the range of angle corresponding to the finite width of the observing aperture (4.1").The self-consistency of the present results strongly substantiates the angular intensity distribution predicted by the Mie theory and independently confirms the Stokes-Cunningham-Millilcan law. Indeed, precise analysis of more of the light- scattering data should enabIe us to test the correctness of the relative angular intensity distributions predicted by the Mie theory for different sized particles, and calculate accurate values for the Cunningham-Millikan constants using a particle radius determined from the angular position of the maxima in the intensity dis- tribution. The method of using light-scattering data to determine particle size is promising since an uncertainty of 0-1 a corresponds to only 0.807 p in r.190 LIGHT SCATTERING BY SINGLE AEROSOL DROPLETS BEHAVIOUR OF THE MAXIMA IN il AND i2 The migration of' the maxima on the size-angle diagram for the total intensity (fig.2) coupled with the several abrupt changes and " splittings " in the pattern, led us to conclude that there might be two strong and opposite trends corresponding to the two plane-polarized components. Investigation of the data for the plane-polarized components revealed un- dulating curves, similar to fig. 1, and a plot of the angular position of the maxima on a size-angle diagram in fig. 4 showed the expected trends : general migration of the maxima in il, solid curve, toward the forward direction and general migration of the maxima in i2, dashed curve, toward the backward direction.In addition, some regions of the i2 data and more regions of the il data showed splitting with increasing size parameter. angle, 6 FIG. 4.-Angular position of the maxima in il, solid curve and i2, dashed curve, €or a refractive index of 1.486 over the range in size parameter, a = 18.0 to 22-0 and scattering angle, 0 = 50" to 100". Fig. 5 shows a photograph of a three-dimensional model of the intensity function il over the range of 18.5 to 19.1 in a and 50" to 100" in 8. Here the maxima form the ridges, and the model gives some insight into the nature of the splitting process. The first two ridges on the left are fairly uniform in height over this small range in size parameter, while the others slope down through cols which shift toward larger values of 8 and a.As the size parameter increases from 18.5 to 18.7, the last two ridges on the right slope down and a deep valley develops between them. With further increase in a, a shoulder appears on the right slope of the col in the second ridge from the right, and grows into a new ridge. The two ridges formed by the splitting then migrate in opposite directions as do those on either side. An inspection of fig. 4 shows that splitting occurs approximately where the curves for il and i2 intersect at a value of a divisible by n/4, which corresponds to " standing-wave positions " for both polarized components of the scattered light, i.e., where 1 sphere diameter equals $, +, etc., the wavelength of the incident light in air.For the region studied, the splittings were found to occur within the angular range 8 = 78-93' for il, 50-54" for i2, and 66-76' for i,g. We are now engaged inFIG. 5.-Mie-theory intensity iunctlon il over the range in size parameter, cc = 18.5 to 19.1 and scattering angle, 0 = 50" to 100". [To face p. 190F. T. GUCKER AND R. L. ROWELL 191 determining the pattern of the maxima for the complete angular range, 8 = 0-180", and for the size parameter range, a = 0.1-30.0. It is a pleasure to acknowledge the support of the National Science Foundation for a grant that made this research possible, and the courtesy of Dr. Rudolph Penndorf of the Geophysics Research Division of the Air Force Cambridge Research Center who sent us the theoretical values of the amplitude functions before their publication. We also should like to thank Ora May Engle of the Research Corn- puting Center of Indiana University for the computations of the scattered in- tensities on the IBM 650, and Maurice Williams for his help in the design and construction of the apparatus. 1 Mie, Ann. Physik, 1908, 25, 377. 2 Gucker and Cohn, J. Colloid Sci., 1953, 8, 555. 3 Penndorf and Goldberg, Nevi Tables of Mie Scattering Functions for Spherical Particles, Geophysical Research Papers No. 45, Parts 1 through 5 (as ASTIA docu- ments from U.S. Department of Commerce, Office of Technical Services, Wash- ington 25, D.C.). Parts 4 and 5, for refractive indices 1-486 and 1.50 respectively, are ASTM documents no. AD-98778 and AD-98771. 4 Egan, P k D . Thesis (Indiana University, 1954). 5 Gucker and Egan, J. ColZoid Sci., accepted for publication. 6 Rowell, P h B . Thesis (Indiana University, 1960). 7 Millikan, Physic. Rey., 1911, 32, 349; 1923, 22, 1. 8 Rosenblatt and LaMer, Physic. Rev., 1946, 70, 385.

ISSN:0366-9033    

DOI:10.1039/DF9603000185

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

BY S. W. CHURCHILL, G. C. CLARK,* AND C. M. SLIEPCEVICH 7 Dept. of Chemical and Metallurgical Engineering, The University of Michigan, Ann Arbor, Michigan, U.S.A. Received 20th June, 1960 The effect of particle separation distance on the light-scattering properties of dispersions of closely sized spheres was investigated by measuring the transmission as the concentra- tion was decreased by dilution. The data were corrclated in terms of a two-flux model. The coefficient in this model was observed to be essentially constant down to a centre- to-centre distance of about 1.7 diameters between particles and to vary less than 10 % down to a centre-to-centre distance of about 1.4 diameters, corresponding to 28 % solids by volume. Direct simulation of dilute aerosols having dimensions of the order of kilo- metres is therefore feasible with very dense hydrosols having dimensions of the order of millimetres.The intensity of radiation within or at the boundaries of a dispersion of uniformly-sized, non-absorbing spheres can be described in terms of the angular distribution for single scattering, the dimensions of the dispersion expressed in mean free paths for scattering, the source distribution, and the boundary con- ditions. The mean free path for scattering where Nis the number of spheres per unit volume, us is the scattering cross-section, K, is the scattering coefficient (the ratio of the scattering to the geometrical cross- section), and d is the diameter of the spheres. If the spheres are sufficiently far apart, the angular distribution for single scattering and the scattering coefficient are functions only of n, the refractive index of the sphere relative to the surrounding medium, and a = nd/A, where ;I is the wavelength of the radiation in the continuous medium.It is then possible to scale a dispersion in terms of mean free paths if the same n and CI are established as illustrated by Scott and co-workers;ls 2 Sinclair 3 stated without documentation that optical interference between par- ticles would be expected if the particles were less than 5 diameters apart. No measurements of interference or theoretical expressions for the effect have been found in the literature. The objective of this investigation was to determine the separation distance at which interference becomes appreciable and to measure the magnitude of the effect.Several possible methods of investigation were considered : (i) development of theoretical expressions for the two-body and multiple- body problems ; (ii) measurement of the radiant field around a set of two or more spheres with dimensions of the order of millimetres, using a beam of millimetre waves ; (iii) measurement of the transmission of a beam of monochromatic light through dense dispersions with particle concentration as a variable. * present address : Continental Oil Company, Ponca City, Oklahoma. -f present address : University of Oklahoma, Norman, Oklahoma. 192s. w. CHURCHILL, G. c . CLARK AND c . M. SLIEPCEVICH 193 Method (iii) was chosen because of its comparative simplicity and the more direct applicability of the results. EXPERIMENTAL APPARATUS The equipment consisted of a source and collimating system, a receiver and amplifying unit, and a cell and traversing mechanism, all located in a dehumidified dark room at 18°C.The source was a SO-candlepower, auto-headlight bulb operated with a regulated power supply. The light beam was monochromaticized with interference filters, yielding a transmission of 45 % at 5460flSOA and a band width of 120-140A at the 225 % transmission points. The collimating system is shown in fig. 1. Diaphragms D1 and D2 reduced the stray D, Ds FIG. 1 .-Schematic diagram of collimating system. light reaching the collimating lens, and diaphragm D3 limited the size of the collimated beam. The condensing lens L1 and L2 had focal lengths of 150 and 100 mm, respectively. The shutter was closed except during measurements.The collimating lens L3 was an achromatic, coated, telescope objective, 51 mrn in diameter and 191.5 rnm in focal length. FIXED PART OF CELL OTOMULTIPLIER MOUNTIN 3emm 1.0 x 114mm HIGH MOUNTING RING G G SCREWS MOVABLE PART / GLASS WINDOW OFF CELL f!'Ei::tA&E azmm I o x 63mm HIGH ALL PARTS ARE PLEXIGLAS EXCEPT GLASS WINDOWS FIG. 2.-Experimental cell. With a 1/16-mm pinhole P the final beam had a diameter of 32 mm and a divergence of only 14.2 min. Such a high degree of collimation was not necessary for the transmission measurements but was desirable for the determination of particle concentration. The Du Mont 6291 photomultiplier used as a receiver is a ten-stage multiplier, 38 mm in diameter, with a flat, end-window type photocathode.The photocathode has a S-11 response characteristic; the maximum response is at A = 4400f250A with 10 % of the maximum response at h = 3250f250A and 6175f275 A. Voltage from a variable G194 LIGHT-SCATTERING BY DENSE DISPERSIONS power supply was fed to the photomultiplier through a step attenuator with resistances chosen to give an amplification of about 3 : 1 per step. The anode current was determined by measuring the potential drop across a 1000 52 resistor. The amplified signal was fed to the Y channel of an X-Y recorder. The cell is shown in fig. 2. The fixed part of the cell served as the receiver housing and as the upper boundary of the dispersion. The photomultiplier was optically coupled to the upper glass window of the cell with immersion oil.The movable part of the cell was attached to a platform which travelled on a screw turned by a hand crank. The screw was geared to a Helipot which served as a potentiometer with the output fed through a cathode followed to the X channel of the recorder. The recorder thus produced a continuous record of transmission as a function of cell thickness. As the cell thickness decreased, the excess dispersion flowed up around the lower plate of the fixed part of the cell and was thus optically decoupled from the dispersion remaining in the cell. All cell surfaces except the receiver window and the portion of the source window illuminated by the incident beam were painted with flat, black, acrylic resin. For determination of the particle concentration a camera with an achromatic, coated, telescope objective lens, 83 mm in diam.and 914 mm in focal length, was located at the outlet window of the cell. A pinhole in the back of the camera opened to an opal glass optically coupled to the window of the photomultiplier. This receiver system was sur- rounded by a black, light-tight housing. MATERIALS The dispersions were prepared from very uniformly sized polystyrene-latex spheres supplied by the Dow Chemical Company, Midland, Michigan. One batch had a mean diameter of 0.814 p with a standard deviation of 0.011 p ; the other, a mean diameter of 1.171 p with a standard deviation of 0.013 p. At X = 5460A (in air), the latex has a refractive index of 1.205 with respect to water and a negligible absorptivity.The spheres are stable in water and, since they are charged, do not agglomerate. PROCEDURE After optical alignment, the cell was closed to a thickness of about 0-5 mm and the Helipot shaft was adjusted to indicate a zero signal on the X channel of the recorder. About 50 ml of distilled water were added to the cell and the cell was opened until full deflection occurred on the X channel, corresponding to a cell thickness of about 4 mm. The amplified photomultiplier signal was then recorded as the cell was slowly closed to a zero signal on the X channel. This experiment provided the reference signal I0 for calculation of the transmission. After cleaning and drying the cell, 50 ml of a concentrated dispersion were added and the photomultiplier signal was again recorded as the cell was closed.The concentrated dispersion was next withdrawn from the cell to a reservoir, diluted with a measured quan- tity of water, mixed and returned to the cell, and a new traverse was carried out. Tests were made at twelve stages of dilution over a 10 : 1 range of concentration. All traverses were repeated as necessary to assure reproducibility and complete mixing. DETERMINATION OF PARTICLE CONCENTRATION AND SEPARATION Samples of the dispersion were withdrawn at the end and at two intermediate stages of dilution. After great dilution, traverses were made on these samples with the camera between the cell and the photomultiplier. The particle concentration was determined from these data and the modified form of the Bouguer-Beer law : -dI = R N ~ J d l , (2) where I is the collimated radiant flux density, R is a correction factor for the finite angle subtended by the receiver, and 1 is distance.Eqn. (2) can be integrated and rearranged in the form In (1011) = RNa,(l,+ 10) (3) where 20 is the unknown reference thickness for which the X channel of the recorder was set to zero, and I, = (I-lo) is the measured distance. RNys and lo were calculated from eqn. (3) and the data by least squares. Nus was then calculated taking R = 0.998, corresponding to the angle of 47.8 min subtended by the receiver, N = 1.205 and the appropriate value of a. It should be noted that in water,s. w. CHURCHILL, G. c. CLARK AND c. M. SLIEPCEVICH 195 and hence in this value of a, h = Xair/nwater = 5460/1.33 = 4105A.N was in turn calculated using the theoretical values of 2.48 and 3.57 for K, for the 0.814 and 1.171 p particles, respectively. The volume fraction of solids x = N7rd3/6 was next calculated from the known particle diameters. The centre-to-centre distance between particles was calculated from the following expression for a rhombohedra1 array : 6 = (J21N)) = (~/3J2x)*d. (4) Since the particles are charged, this arrangement, which gives the maximum possible distance between particles for a given concentration, may be approached as the particle concentration increases to the limit. This limit for 6 = d is N = 2/%/d3 and the cor- responding maximum x is q / 2 / 6 = 0.7405. The computed properties for the initial, undiluted dispersions are given in table 1. TABLE 1 .-PROPERTIES OF UNDILUTED DISPERSIONS 4 P N, particIes/cm3 X 0.814 9.81 x 1011 0.278 1.385 1.171 3.23 X 1011 0.272 1.395 Values for the other traverses were obtained by multiplying the concentration by the corresponding dilution factor. RESULTS The data were correlated in terms of the two-flux model which has been’discussed by Chu and Churchill 5 and others, and successfully used by Larkin and Churchill 6 and others for multiple scattering.In this model the angular distribution of radiation scattered by a single sphere is represented by forward and backward components. The integro- differential equation describing the radiant intensity in a dispersion then reduces to two ordinary differential equations for the forward and backward components of the intensity.The idealized experiment would have consisted of an infinite layer of dispersion with an infinite, collimated source at one face and a totally absorbing surface at the other. A finite source and dispersion of the same diameter with a perfect specular reflector at the circumference would produce the same transmission as the infinite system. The experimental transmission obtained in this investigation would be expected to be somewhat less than in the idealized case because of the finite dimensions of the source and dispersion, and the failure of the dispersion beyond the circumference of the source to act as a perfect reflector. A correction for the net sidewise loss of radiation was therefore incorporated in the two-flux model. The resulting equation describing the forward component 11 and the backward component 12 of the intensity are and where B is the backward scattering coefficient for single scattering and S is the net sidewise scattering coefficient.The boundary conditions are I1 = 1.0 at I = 0, and 12 = 0 at I = Zt where It is the thickness of the dispersion. Solving these equations yields the following expression for the transmission : I,(&> 1 11(0) - cosh [p(Z, + lo)] + q sinh [-(I, + lo)]’ T=-- (7) where p = Nos JS(2B + S ) and q = (B + S)/d S(2 B + S). Values of the parameters p and q and the unknown reference distance lo were deter- mined by least squares on an IBM 650 computer using the method proposed by Scar- borough 7 for non-linear equations. Values of BK, and SK, were then computed from the previously determined values of N and the dilution factors.Although the computed values of BK, were in all cases about 1000 times the values of SK,, the inclusion of S in the model resulted in a distinctly better representation for the data.,196 LIGHT-SCATTERING BY DENSE DISPERSIONS t- i 1 I I 0 I 2 3 4 cell thickness, mm FIG. 3.-Experimental transmissions. 0.814 p particles. I , 0 .,4 !3 WJ *i 3 5 -2 10 -3 10 0 I 2 3 cell thickness, nun FIG. 4.-Experimental transmissions. 1.171 p particles.S . W. CHURCHILL, G . C. CLARK AND C. M. SLIEPCEVICH 197 The experimental transmissions and curves representing eqn. (7) are plotted against 2, for the two particle diameters in fig. 3 and 4. The precision of the data and the excellent representation obtained with eqn.(7) are apparent. The standard deviations for the 26 traverses averaged about 1.2 %. The experimental transmissions are replotted against NK,7rd2Zt/4 in fig. 5 and 6 using values of K, for isolated spheres. For a dilute dispersion, this abscissa corresponds to the cell thickness in mean free paths for scattering; for concentrated dispersions K,, and hence the mean free path, may be somewhat different. Due to compression of the data in this form, only data for selected concentrations and curves for the extreme trans- missions are included. It should be noted that the data for different concentrations N&?rd21/4 FIG. 5.-Effect of particle separation on transmission. 0.814 p particles. S/d: 299 0 1.65 0 1.55 A 1.47 + >O 1.39 cover different ranges of the abscissa ; for example, the data for the most dilute dispersion extend only over the lowest tenth of the abscissa. If there were no optical interference between particles, all data for a given particle size should lie along a single curve.Thus the spread of the data and curves indicates the magnitude of the interference in so far as sidewise losses and other non-idealities in the experiment are negligible or the same from traverse to traverse. The transmission appears to increase and' then to decrease as the particle separation distance is decreased, but the magnitude of the variation is less than f20 % for both particle sizes. A more critical test of interference is provided by fig. 7 in which the product of the coefficients B and Ks is plotted against 6/d for both particle sizes.This plot should be independent of sidewise losses from the cell. In so far as the modified two-flux model represents the physical situation, BK, is the fraction of the geometrically obstructed light which is scattered into the backward hemisphere by a single particle. Since B, S and K, occur in eqn. (7) only as the products BK, and SK,, the separate effects of particle separatio198 LIGHT-SCATTERING BY DENSE DISPERSIONS 10 ,,.f I I I I I I 0 1000 2000 3000 4000 5 0 0 0 6 0 0 0 7( NKsrrd21J4 ? - FIG. 6.-Effect of particle separation on transmission. 1.171 p particles. 8 / d : 3.01 0 1.67 1-56 A 1.48 + 1.39 @ 1.0 1.5 2 0 2 5 30 W FIG. 7.-Effect of particle separation on back scattering parameter. 0, d = 0.814 p ; 0, d = 1.171 p.S .W. CHURCHILL, G . C. CLARK AND C. M . SLIEPCEVICH 199 on B and Ks cannot be deciphered from the data of this experiment. For both particle sizes, BK, appears to be essentially constant down to a 8/d of about 1-7, then to decrease to a minimum, to increase to a maximum and finally to decrease again. The magnitude of this variation is only about j l 0 % and undoubtedly is due in part to experimental error. The uncertainty in the computed values of BK, is greater than the uncertainty in the measurements of transmission and distance, but is difficult to estimate because of the non-linearity of the equations from which BK, is derived. Additional details concerning the equipment, procedures and data are given by Clark.* CONCLUSIONS The modified two-flux model was found to provide an excellent representation for the data. The observed variations in BK, and T with concentration are sur- prisingly small, considering the very small distances separating the particles. The limiting 6/d above which optical interference between particles can be neglected is apparently about 1-7 rather than 5 as postulated by Sinclair.1 Therefore dis- persions of spheres as concentrated as 15 % solids can be used to simulate dilute dispersions without correction for interference between particles. This research was supported in part by National Science Foundation Research Grant G1006. Computer time was donated by the Continental Oil Company. The suggestions of Prof. C. M. Chu, and the assistance of Dr. R. H. Boll, Dr. J. H. Chin, Dr. 13. K. Larkin, Dr. J. A. Leacock, and- Messrs. P. H.! Scott and J. Chen are gratefully acknowledged. 1 Scott, Clark and Sliepcevich, J. Physic. Chem., 1955, 59, 849. 2 Scott and Churchill, J. Physic. Chem., 1958, 62, 1300. 3 Sinclair, Handbook on Aerusuls (U.S. Atomic Energy Corn., Washington, D.C. 4 Gumprecht and Sliepcevich, J. Physic. Chem., 1953, 57, 90. 5 Chu and Churchill, I.R.E. Trans., 1956, AP-4, 142. 6 Larkin and Churchill, J. Amev.!Inst. Chem. Engrs., 1959, 5, 467. 7 Scarborough, Numerical Mathematical Analysis (Oxford Univ. Press, 2nd ed., 1950). 8 Clark, Ph.D. Thesis (Univ. of Michigan, Ann Arbor, Michigan, 1960). 1950), chap. 5-8.

ISSN:0366-9033    

DOI:10.1039/DF9603000192

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

THE AGGREGATION OF SMALL ICE CRYSTALS BY C. L. HOSLER AND R. E. HALLGREN Dept. of Meteorology, College of Mineral Industries, The Pennsylvania State University, University Park, Pennsylvania Received 7th June, 1960 The growth of small aggregates of ice crystals has been observed between -6°C and -25°C by mounting an ice sphere in a moving cloud of ice crystals. The density of the aggregate formed increased with increasing temperature, and observations of the aggregate growth showed that the bonds between ice crystals permit folding of crystal towers. The higher the temperature, the more folding was noted. The proportion of the ice crystals in the path of the aggregate that became attached to it was temperature-dependent, show- ing a maximum collection efficiency at -11°C. Plates formed aggregates at a greater rate than did columnar crystals ; hence, when the cloud composition changed from plates to columns as the temperature increased above -11”C, the amount of aggregation diminished.These data and other evidence are interpreted as indicating that the aggrega- tion of the ice crystals depends upon the existence of a liquid film on the ice surfaces. The film thickness is greater at higher temperatures. A large part of the precipitation falling in middle and high latitudes goes through a stage involving the formation of aggregates of a great number of indi- vidual ice crystals to form the “snowflakes” observed at the ground. These aggregates, upon melting, give rise to much larger raindrops than would otherwise be observed if the ice crystals remained detached.In clouds composed entirely of ice formed at low temperatures, the formation of precipitation particles capable of high rates of fall and rapid subsequent growth may, to a large extent, be de- pendent upon aggregates of individual ice crystals. Knowledge of the degree to which ice crystals cohere on contact is important in evaluating some mechanisms suggested for explaining charge generation and separation in clouds. The follow- ing experiments were aimed at determining the factors acting to limit aggregation in clouds. Systematic experimentation on the ability of ice to stick to ice was begun in September, 1 842, by Faraday. His investigations were periodically resumed and described in his diary as late as February, 1860. 1-3 J.Thomson 4-6 and W. Thomson 7 attributed the phenomenon to melting of ice on contact with ice due to pressure and subsequent freezing. Faraday, however, by careful experimental design, succeeded in producing regelation under conditions where the pressures were negligible and, in his mind, insufficient to produce melting. In fact, Faraday 3 noted flexible adhesion so that torsion forces actually tended to separate the pieces of ice involved. This led him to conclude that water exhibited a property that made it possible for a water film to remain liquid in contact with ice, so long as ice was only on one side of the water ; but when surrounded by ice on both sides, it became solid and formed a bond between the two pieces of ice. In the years since the work of Faraday, many experiments have been performed which bear upon the nature of the surface of ice.Some of these have dealt with the cohesion of pieces of ice 8 or the adhesion of ice to other solids,9 others with the slipperiness of ice.10 A considerable amount of evidence has now been ac- cumulated which indicates the untenability of the concept that these phenomena are the result of pressure-induced melting. A number of these observations were summarized by Jordan et aZ.10 in a Report on Friction on Snow and Ice. It seems 200C. L . HOSLER AND R . E. HALLGREN 201 clear that the hypothesis of Faraday can now be supported by some physical- chemical reasoning, such as that proposed by Weyl, and is most likely the correct explanation of the several surface properties of ice.Nakaya and Matsumoto,s in an interesting experiment in which ice spheres were manipulated, noted the ability of two cohering ice spheres to rotate when in contact with one another prior to separating, indicating the presence of a liquid film on ice at temperatures below the melting point. Laboratory measurements of aggregation of ice crystals at -336OC12 lend support to radar observations indicating aggregation in natural clouds at temperatures this low.13 Fig. 1 presents some of the results of an experiment in which the force required to separate temp., "C FIG. 1.-Plot of the force required to separate manipulated ice spheres against temperature at saturation vapour pressure over ice (ref. 12). two ice spheres was measured after the two spheres had been carefully placed in contact with one another with a minimum of force.12 Each point represents the mean of from 10 to 15 measurements.The ice spheres were at the same temper- ature, and the vapour pressure was equal to the saturation vapour pressure over ice at that temperature. Two interesting features in these data were the con- sistency of the observations and the fact that measurable cohesion of the ice spheres was noted at temperatures down to -25°C." Presuming some degree of roughness of the surface of the spheres used to obtain the data in fig. 1, one could expect a great variation in the area of contact of the spheres and, hence, in the force required to separate them. However, the ease with which a smooth curve can be drawn in fig. 1 suggests the presence of a liquid film of sufficient thickness to give a rather uniform area of contact.The thickness of the film is temperature- dependent, increasing exponentially with:temperature. When the same experiment * Faraday apparently did not work below 0°C or, if he did, the cohesive forces were so small that he could not detect them, for he does not mention the phenomenan of regelation below 0°C. a*202 AGGREGATION OF ICE CRYSTALS wasperformed in an environment flushed with dry air, no sticking was observed below - 3°C. Apparently, when rapid evaporation occurs, the quasi-liquid film is absent or greatly reduced in effectiveness. Hori et al.14 have also gathered evidence of the possibility of thin liquid water films coexisting with ice at low temperatures. More recently, Jellinek,g in ex- tensive measurements of the adhesive properties of ice with metals, concluded that the best explanation for the observed variation in tensile strength of the bond between ice and metal was the existence of a liquid film whose thickness diminished with decreasing temperature, leading to a linear increase of the strength of the bond with decreasing temperature down to - 25°C.One reason for the existence of a layer of " distorted " water on the surface of an ice crystal has been explained by Weyl. His hypothesis states that, in order to keep the surface-free energy at a minimum, the surface ions must be polarized and the protons must be slightly recessed to form a dipole layer on the surface. Further- more, some finite distance below the surface is required as a transition between this distorted surface layer and the bulk structure of water or ice.This transition layer may retain the characteristics of a liquid at temperatures below the melting point of ice. We have suggested that such a distorted layer in a water surface is responsible for the radius-dependence of the spontaneous freezing of water droplets and that the degree of inhibition of ice formation may be a manifestation of the depth of penetration of a distorted structure originating in the surface.ls~ 16 Pertinent experiments 15 tended to show that freezing temperatures of water in capillaries was dependent solely on the capillary diameter and not upon volume or surface area. High-speed stereoscopic motion pictures 17 indicated that nucle- ation of the ice phase in capillaries occurred not at the surface, but in the interior.Kachurin 18 also noted that ice formed first in the centre of a droplet and radiated outward toward the surface, In spite of the experimental evidence that points toward peculiarities in the surface of water and ice, lack of quantitative evidence of Weyl's ideas has deferred wide acceptance of this concept to explain such phenomena as the cohesive properties of ice. In order to study the factors governing the amount of aggregation in an ice cloud, a vertical wind tunnel was constructed 19 within a cloud chamber in which both temperature and vapour pressure could be varied. A schematic diagram of the apparatus is shown in fig. 2. In the test section of the vertical wind tunnel, air speeds, temperatures, and vapour pressures were produced to simulate those which are encountered in the atmosphere.A small ice sphere (127p or 360p diam.) was suspended on the end of a fibre pointing into the air stream and observed while cloud particles were drawn past it at speeds approximating the terminal fall velocity encountered by an ice particle of comparable size falling through a cloud. The cloud particles were from 7 to 18 p diam. in concentrations of 3,000 to 20,000 cm-3. The ice sphere, which subsequently became an aggregate of from 200 to 100Op diam., was observed during its growth, and its dimensions were periodically measured. At the end of an experiment the aggregate was melted quickly and its liquid water content determined. The concentration, crystal type mass and dimensions of the cloud particles were measured. Plastic replicas of ice crystals were counted and measured with an optical microscope, and electron photomicrographs of shadowed replicas were used to obtain the thickness of the crystals.Hence, it was possible to observe the growth of an aggregate of ice, knowing those parameters that would presumably have some effect on its rate of growth. It was then possible to calculate the percentage of ice crystals in the path of the ice sphere that collided with, and adhered to, the sphere. This collection efficiency and the density of the aggregate were studied as a function of temper- ature, relative fall velocity, crystal type, mass of the collected crystals, and size of the collector. Because of the velocity of the small crystals, the collision between two crystals could not be actually seen, The growth of the aggregates was quite interesting.C .L. HOSLER AND R . E . HALLGREN 203 but the overall growth of the sphere could be closely observed. Very frequently the growth was in the form of a tower of crystals. Some towers would extend COMMERCIAL I FREEZER (20"X 24'X 72") Blower T FIG. 2.-Schematic diagram of vertical wind tunnel within a freezer. c t l 0 Q-l 0 -066 A 0 5 4 6042 a 0 3 0 7 -6 -8 -10 -12 -14 -16 -10 -20 -22 -24 temp., "C FIG. 3.- Plot of aggregate density as a function of temperature for collectors of 127 and 360 p initial diam. 0 collector of 360 p diam. x collector of 127 p diam. (standard deviation indicated beside points) as much as 1 0 0 ~ before collapsing or folding.In general, extended towers were more common at the lower temperatures than at the higher temperatures. They204 AGGREGATION OF ICE CRYSTALS also seemed to be more rigid at the lower temperatures and had a greater tendency to collapse as a unit, whereas at the higher temperatures they seemed to fold into the aggregate. In other words, the bonds were more mobile at the higher tem- peratures, an observation which parallels that by Nakaya and Matsumoto men- tioned above.8 In our experiment, the aggregate after being rotated ninety degrees showed that the aggregate, although of a very low density, did not actually have holes where a crystal could pass through without being captured. Although there may not have been crystals on the immediate surface of the aggregate, collision would occur somewhere within the aggregate.The aggregates appeared quite fragile in many cases ; but, at least on the scale that could be observed through the microscope, fracturing of the aggregate occurred on only a few occasions. The fact that the aggregated towers folded to consolidate the mass illustrates the flexibility of an ice-to-ice bond as noted by Faraday. Fig. 3, a plot of aggregate density against temperature, shows further evidence of this flexibility and con- solidation. The density increases as the temperature increases. In order to define FIG. -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 temp., "C cloud, as a function of temperature. 4.-Collection efficiency of an ice sphere of 127 p initial diameter in an ice crystal more precisely the reason for the temperature dependence of aggregate density, the effect of changing ice-crystal mass was evaluated.At - 8°C and - 9°C there was a rather large variation in ice-crystal mass from one experiment to the next. When the episodes with large crystal mass were compared to those with small crystal mass, it was found that there was no systematic variation in density due to changing mass. Between - 11°C and - 24°C the change in mass was insignificant, but there was a quite significant change in density. From these facts we are led to conclude that the aggregate density is determined by the temperature at a given collection rate. Fig. 4 shows the collection efficiency obtained from 98 measurements for a sphere of 127 ,u initial diameter with a relative fall velocity of 43 cmlsec.Fig. 5 gives the collection efficiency using 102 measurements for a 360,~ sphere with a relative fall velocity of 107 cmlsec. The deduction can be made from fig. 4 and 5 that some degree of sticking took place at all temperatures investigated in this experiment. When one considers the masses and the speeds of the particles involved, it becomes difficult to conceive that, at -220°C and below, the sticking was occurring at points where contact pressures exceeded the 2000 atm required for melting. In order to achieve the necessary high pressures on contact, in- conceivably small contact areas would have to have been effective in holding the crystals together and preventing them from continuing in the air stream in theC.L . HOSLER AND R . E. HALLGREN 205 face of the drag by the air stream and the buffeting by other crystals. Also, the folding of the crystal towers would be difficult to explain on the basis of pressure- induced melting. In the lower temperature range the collection efficiency or the degree of sticking was proportional to the temperature-the lower the temperature, the less sticking. However, at a temperature of - 11°C the collection efficiency unexpectedly reached a maximum, and as higher temperatures were approached, the collection efficiency fell to the value obtained for the lowest temperatures investigated. Several phen- omena associated with ice occur close to the temperature of - 11 "C. There was the possibility that we were seeing a manifestation of the maximum vapour pressure gradient between water and ice, although there was no evidence of the presence of supercooled water.Examination and re-evaluation of our apparatus and technique eliminated this possibility, because at no time did we observe ice crystal growth in the test section of the wind tunnel ; the vapour pressure was apparently very close to that for ice at the temperature of the test section. The average mass 0 - - - - 1 I I I I l I I I I I I I I I I I G ,206 AGGREGATION OF ICE CRYSTALS The procedure was to use runs at the same temperature but with different per- centages of plates and columns. The data from two runs with a small percentage of plates were averaged and inserted into an equation with two unknowns : the collection efficiency of plates and that of columns. Another equation was then obtained from another two runs having a higher percentage of plates.The two equations were then solved for the individual collection efficiencies. The results from eight such pairs of equations for temperatures of - 6°C to - 11°C showed a higher collection efficiency for the plates than for the columns. The collection efficiencies for the plates alone were higher than those observed at - 11 "C in fig. 4 and 5, whereas the collection efficiencies for the columns were lower than observed at -6°C. These experiments were designed primarily to shed light upon the fate of an ice particle falling through an ice cloud. The complete explanation of the results will have to wait for experiments specifically designed to determine the surface properties of ice under various conditions.The fact that aggregation occurs at the temperatures investigated, together with the observation of folding of crystal towers and of increased aggregate density with increased temperature, provides additional evidence of the existence of a quasi-liquid film on the surface of ice between 0°C and -25"C, and perhaps at lower temperatures. (The thickness of the film is apparently greater at higher temperatures.) According to earlier experiments, the bond between two ice spheres is stronger at higher temperatures up to 0°C; increased area of contact results in increased bond strength, but, in the case of the collision of small ice crystals, once the contact area or bond reaches some critical size, they will stick, and further increase in contact area does not contribute to greater collection efficiency or better sticking.In our experiments the collection efficiencies de- creased from - 11°C toward higher temperatures. The most important factor in determining collection efficiency above - 11°C is the change in crystal type from plates to columns. Perhaps we should expect plates and columns to behave differently, but we are not able to state with any assurance what is responsible for the difference. The possibilities include the aerodynamic characteristics, the mechanical forces acting at the time of the collision and the change in the dominant type of crystal face available to engage in the collision process. In the light of the evidence pointing to the existence of a quasi-liquid film on the ice surface and the possibility of explaining the existence of such a film on the basis of minimizing surface energy, we would be inclined to suggest that the change in the dominant type of crystal face involved in the collisions may cause the change in collection efficiency.This increased sticking may be due merely to the larger area of contact, which would increase the likelihood of bonding between the two surfaces. On the other hand, there are structural and energy differences between the two types of ice crystal faces. Moreover, the faces grow at different rates depending upon temperature, in the range in which the aggregation was measured. This suggests that, if a liquid film exists on the crystal, such a film would have different characteristics on the two crystal faces. These experiments may indicate that the basal plane is stickier than the planes parallel to the c-axis and that the decreased probability of basal planes colliding at the higher temperatures more than compensates for the tendency for increased aggregation with increased temperature that is in evidence at tem- peratures below - 11°C.This hypothesis could be tested by producing clouds consisting of only plates and columns, respectively, and then introducing them into the test section of the wind tunnel at varying temperatures to observe collection efficiency. This would require a rather elaborate apparatus. 1 Faraday (Bell a- d Sons Ltd., London), 1933, 4, 79 ; 7, 382. 2 Faraday, Phil. Mag., 1859, 17, 162.C. L. HOSLER AND R . E. HALLGREN 207 3 Faraday, Proc. Roy. Soc., 1860, 10, 440. 4 Thomson, Proc. Roy. Soc., 1861, 11, 198. 5 Thomson, Proc. Roy. SOC., 1859, 10, 152. 6 Thomson, Trans. Roy. SOC. Edin., 1859, 16, 575, 7 Thomson, Phil. Mag., 1850, 37, 123. 8 Nakaya and Matsumoto, SIPRE Res. Paper, # 4, 1953. 9 Jellinek, J. Colloid Sci., 1959, 14, 268. 10 Jordan, SIPRE Report Friction on Snow and Ice (U. of Minnesota, 1955), p. 286. 11 Weyl, J. Colloid Sci., 1951, 6, 389. 12 Hosler, Jensen and Goldshlak, J. Meteol., 1957, 14, 415. 13 Douglas, Gum and Marshall, Stormy Weather Research, Group Report MW-21 14 Hori, Teion and Busuri, Low Temp. Sci. Lab., ser. A, 1956, 15, 34. 15 Hosler and Hosler, Trans. A. G. U., 1955, 36, 126. 16 Hosler, Proc. Toronto-Met. Conf., 1953, 253. 17 Hosler and Spalding, Penn. State Univ. Final Report AF Contract 19(604-140), 18 Kachurin, Izvest. Akud. Nauk U.S.S.R., ser. Geofiz, 1951, 2, 43. 19 Hosler and Hallgren, Penn. State Univ. Final Report NSF G-3477, 1960, p. 39. (McGill U., July 1956), p. 45. 1955, p. 7.

ISSN:0366-9033    

DOI:10.1039/DF9603000200

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

COMBUSTION OF LIQUID AND SOLID AEROSOLS BY R. H. ESSENHIGH AND IAN FELLS Dept. of Fuel Technology and Chemical Engineering, The University of Sheffield. Mappin Street, Sheffield, 1: Received 16th June, 1960 In this paper are discussed the mathematical similarities and chemico-physical dis- similarities between the combustion mechanisms of liquid and solid aerosols. The similarities are a consequence of the accepted nature of the respective rate-controlling steps of the reaction mechanisms, conduction and diffusion, which are governed by differential equations of the same form. The mass burning rates and burning times in both systems can be shown, therefore, to be proportional respectively to the radius and square of the radius. The dissimilarities of the systems are to be found chiefly in the different physical positions of the reaction surfaces : for liquid drops this is at a flame surface which is a finite distance from the liquid surface; for solid particles it is on the surface of, or inside, the solid itself.If experimental techniques become sufficiently sensitive, these dissimilarities may be found to generate second-order differences in the rate equations. The reaction control mechanisms are discussed with particular emphasis on the alternate theory of surface rate control for solids leading to a linear burning-time law in place of the accepted square law. Also considered are the possible role of micro- turbulence in enhancing reaction by thinning the diffusion film, and the significance of macroturbuIence in aiding ignition and flame propagation.1. INTRODUCITON Most of the drops or particles found in aerosols are less than 1OOp diam. and this size range can be divided in two. The mists, smokes and grit clouds encountered in atmospheric pollution studies are mostly in the sub-micron range, whereas the fuel sprays and dust clouds used in combustion systems are to be found in the super- micron range. In this paper, space limitations make it impossible for us to cover the complete range of phenomena ; we have therefore restricted it to combustion phenomena in the super-micron range since the solid and liquid systems in this range have elements of similarity and contrast a that make them particularly appropriate subjects for simultaneous study. 6 2. GENERALIZED THEORY The elements of similarity in the combustion of liquid and solid aerosols are found mainly in the simplified mathematical theory of the combustion.In the first place, the combustion mechanism of either system is assumed to depend primarily on that of the individual drops or particles since the individual units (drops or particles) are regarded as being effectively independent and perturbed to only a minor degree by the surrounding units. Secondly, the burning rate of the individual units is predicted by theory, for both liquids 1-20 and solids,21-37 to be inversely proportional to the radius ; thus where B is a constant. By appropriate integration this gives the well-established square-law relation for the burning time of the units in an infinite atmosphere : where tb is the time for the units to burn out ; do is their initial diameter and K is the burning constant.Some of the experimental results obtained in testing this 208 dr/dt = -B/r, ( 2 4 tb = Kd;, (2.2)R . H. ESSENHIGH AND I . FELLS 209 equation are presented in fig. 1, and the appropriate values of the burning constant for these results are listed in table 1. This table shows that for liquids and solids the values of the burning constant are of the order of 100 and 1000 respectively; the volatiles from coal particles behave as though evaporated from liquid drops. TABLE l.-Vmms OF THE BURNING CONSTANT K investigator 1. Burgoyne and Cohen 38 2. Godsave 3 3. Hall and Diederichsen 39 4. Kobayasi 10 5. Kumagai and Isoda 8 6. Masdin 20 7. Masdin and Essenhigh 40 8. Simpson 6,7 9.Spalding 4 10. Wise, Lorell and Wood 9 11. Godsave 29 12. Masdin 20 13. Masdin and Essenhigh 40 14. Simpson 6,' 15. Spalding 4,313 fuel (A) LIQm tetralin (in flame) various (16) (i) kerosine (ii) tetralin various (15) n-heptane kerosine (i) kerosine (ii) gas oil various (5) kerosine (on 1-in. spheres) ethanol K (sec/cmZ) 312.5 100-130 300 195 55-180 (variations with temp.) 117.5 (variations with temp.) 100-225 100-117 111-140 (variations with temp.) 150 185 60-100 (B) CARBON coke residues from (i) pitch creosote (E) heavy fuel oil coke residue from 350 pitch creosote coke residue from 3 30 (predicted) 2060 833 at 800°C 400 at 920°C production oil (predicted) 2000 size,range, mcrons 8 to 50 1000 to 2000 150 to 600 700 to 1700 (not given) 500 to 2000 500 to 2000 350 to 650 (eqn.tested in- directly) lo00 to 6000 (on porous spheres) I 500 to 2000 500 to 2000 135 to 220 (c) PULVERIZED COAL 16. Essenhigh 37, 41 (i) volatiles (10 coals) 45-135 775 to 4000 (ii) residues (10 coals) 990-2125 300 to 40oo (captive particles) 17. Griffin, Adams and (single free 625 80 to 200 18. Rosin 22 equation-particles 8000 [1.8 power law] [1.8 to 2 2 power law] Smith 42 particles) in flame For units in an enclosed flame the oxygen supply is restricted ; the burning times are therefore increased by a factor F, which is a function of excess air alone and was first derived for particles in solid aerosols by Nusselt.21 Eqn. (2) thus becomes tb = FKdi where Fmay be written,432 10 COMBUSTION OF AEROSOLS where E is the fractional excess air.This function has been calculated :43 it rises from 2 to 4 as E drops from 50 % to 10 % ; it then rises to infinity as E drops to 8 v1 FIG. 1. particle diam., ,u diameter. -Variation of burning time of various liquid and solid fuels with drop or particle FIG. 2.-Schematic representation of model of burning drop. zero. So far as we are aware, a similar function has not been derived for liquid drops though their burning times clearly will be influenced by similar considerations. This possibly explains the difference in burning constant values obtained for tetralinR . H . ESSENHIGH AND I. FELLS 21 1 in flames by Burgoyne and Cohen 38 and for single drops by Hall and Diedrichsen 39 (see table 1). The reason for the similarity of eqn. (2.1) and (2.2) for both liquids and solids is that the assumed rate-controlling factors of the two combustion mechanisms lead to differential equations of the same form.In the liquid system, the individual drops are surrounded by flame surfaces, fed by evaporating liquid, at a finite distance from the liquid surface as illustrated in fig. 2 ; and the reaction rate control is assumed to be the rate at which heat is conducted back from the flame surface to the liquid surface to evaporate fresh fuel. In the solid system, the rate control is assumed to be the rate at which fresh oxygen is transported to the solid surface through a diffusional boundary layer surrounding the particles. In the first case, therefore, the controlling factor is the rate of heat transfer governed by the equation 4' = -A(dT/dx) ; in the second case, the controlling factor is diffusion, governed by the equation = - D(dp/dx) : where, at any radius x from the unit centre, 4' or k are the heat and mass transfer fluxes respectively ; il is the thermal conductivity of the ambient gas and D is its diffusion coefficient; (dT/dx) and (dpldx) are the thermal and concentration gradients respectively.Thus, in the liquid system, if the drop radius is r and the conditions have reached a steady state, then the total heat arriving at the drop surface in unit time is 4nr2 4,. = 4nx2i. If Q is the heat required to evaporate unit mass of the fuel, then by appropriate substitution and integration, the following rate equation is obtained : where AT is the temperature difference between the evaporation temperature and the flame temperature ; x is the radius of the spherical surface from which the heat (or mass) is assumed to originate; m is the mass of a drop or particle, given by (4/3)ncr3a7 Q being the density of the unit.Differentiating with respect to time and substituting appropriately, eqn. (2.5) becomes (2.6) dr dmldt 1AATlQa dt 4nr20 r ( l - r / x y This equation holds also for the mass transfer when the appropriate parameters are substituted (see Q 4) ; it has the same form as eqn. (2.1) provided only that the ratio (r/x) is constant. To show that this is so, requires a closer examination of the physical systems involved. This more detailed study shows that, in spite of the mathematical elements of similarity in the liquid and solid system, their dissimilarity is considerable and becomes increasingly apparent on closer examination ; this is the subject of the next three sections of this paper.-=-- - -_- 3. LIQUID SYSTEM The burning-drop model of a spherical flame surface at a discrete distance from the liquid surface, has been established by photographing single drops as they burn, both in 3% 449 45 and out 46,479 33 4,6-145 17-20 of flames. The flame studies demon- strated two things ; first, the validity of the model down to drop diameters of 8 p ; and secondly, since the square-law burning-time equation was still obeyed in the flame, that the validity of the assumption of independent reaction was substantiated, though the burning time was increased as described above. For drop diameters of less than 8 p, the heterogeneous nature of the flame vanished and the drops evaporated completely into a homogeneous mixture before reaction started.389 44 This seems to be a consequence of drop instability below a given diameter at any212 COMBUSTION OF AEROSOLS given temperature and pressure, by virtue of which the drops will evaporate completely without any further supply of heat. A superficially similar phenomenon also occurs with larger drops that associate randomly in a cluster. This has been studied48 on a macroscopic scale using a captive drop at the centre of a cage at the corners of which were further drops. Initially the drops burned independently but, as the distance bctween them was reduced, a critical distance was reached at which the mixture in the cage became too rich and a single flame surface was formed surrounding the cage; this change is clearly a function of the ratio of drop diameter to inter-drop distance.The smaller drop sizes, however, constitute only a fraction of the total weight in a polydisperse spray ; most are of the larger diameters (> 10 p) and the combus- tion mechanism of these is therefore of the greater importance. The essential theory is outlined above ( $ 2 ) and eqn. (2.6) applies if the radius of the flame surface is substituted for x. This implies that the flame surface is thin and in most theories this implication is accepted since the fuel and oxidant are assumed to react immedi- ately. This convenient theoretical fiction is based on the assumption of zero activation energy for the reaction.The effect of finite activation energy has been shown 49 to introduce a finite thickness for the flame ; for activation energies of 25 and 50 kcal the calculated flame thicknesses were about 50 and 100 p respec- tively, which are of the same order as the drop diameters. If, however, we assume the flame to be thin, then for a flame radius a, eqn. (2.6) becomes For this to integrate to the square law of eqn. (2.2), the ratio @/a) must be small or constant. Levy16 argues that this condition must be so by inference from the experimental results in which the square law was found to be obeyed. Wise and Agoston 17 disagree, stating that it is the Werence (a-r) that is constant, not the ratio ; but since the square law does not follow, then as fig.1 and table 1 illustrate, Levy’s inference would seem to be valid. The position is not, however, entirely clear : Hall and Diedrichsen 39 are quoted by Wise and Agoston in support but they do not quote figures ; Wise, Lorell and Wood 9 give figures showing a con- stant (a-r) difference but these are for combustion data on a simulated drop in which the fuel was supplied through the surface of a porous sphere (cf. Spalding 4) and may well be therefore a fundamentally different system. Other measure- ments 143 15.18 show an approximately constant ratio, but with deviations. The theories, however, substantiate Levy. These 1-20 mostly depend on a heat balance at the flame surface ; the heat of reaction is lost from the flame surface by conduction away from it on both sides.For the heat conducted away to infinity an equation of the form of (2.5) will hold, with r = a and x = co ; this can be used to eliminate terms in a and leads to an equivalent form of eqn. (2.5) and (3.1) : m/r = fn(T), where rh is differential w.r.t. time and fn(T) is a complex function of temperature that includes such terms as specific heat and thermal conductivity of the gases, latent heat and calorific value of the liquid ; and to a first approximation it should be constant for a given fuel. These various parameters all vary with temperature and some of the variations have been included in some of the theories ; the most common omissions seem to be : variation of latent heat and calorific value of the liquid ; and the variation of vapour pressure and therefore of boiling point, with radius.Integration shows that the temperature function is reIated to the burning constant K, which can therefore be predicted theoretically. The theoretical dependence is, however, complex. Godsave3 established the importance of latent heat over volatility as a factor influencing the value of the burning constant, but prediction of K still requires moreR. H. ESSENHIGH AND I. FELLS 213 detailed knowledge; the significant factors involved have now been examined in greater detail according to a recent report 19 but unfortunately this report is not yet available in the published literature. The relation for (air) may also be established by a mass balance across the flame front.15 The flux of fuel and oxidant are assumed to be in their stoichiometric ratio i.Applying the diffusion equations based on (2.5),and (2.6) we get a]r = 1 + (Dfi/Dop,)(l - a/6), (3.3) where f and 0 are the subscripts to the diffusion coefficients D for fuel and oxidant respectively and po is the,oxygen partial pressure in the mainstream outside the boundary layer of thickness 6. The diffusion coefficients also vary with temperature, but if their temperature histories are substantially similar, then their ratio is insensitive to temperature. Kumagai and Isoda 8 make a similar point in their theory of the radius ratio with respect to the variation of thermal conductivity. Values for the radius ratio can be calculated from eqn. (3.3) ; fuels commonly used are of medium carbon content (e.g. tetralin, CloH12) ; if the carbon contents are much higher there are complications from cracking.46,479 5 9 6s20s40 Diffusion coefficients of these medium carbon fuels are roughly 1/3 that of oxygen; the stoichiometric ratios (air to fuel by numbers of atoms) are in the range 10 to 15. In a quiescent system 6 is generally assumed to be infinity so, for an oxygen partial pressure of 1/5, the ratio of (a/r) is about 25. This can be compared with Goldsmith and Penners 5 values of 10 and experimental values quoted by Levy 16 of about 3. These, however, refer to large diameter drops and it is clear from the published photographs 43 5 9 20939 that the ratio a/6 for these is not negligible ; it could well be around 0.9, which reduces the predicted values to 3 or 4. Also, Miesse 15 shows that the ratio rises from 2 to 20 as the drop diameter-and therefore the relative magnitude of the disturbance-falls from 1000 to 10 p. Aerodynamic studies are clearly of considerable importance in controlling second-order effects in the rate equations and in this connection Kumagai and Isoda’s 8 experiments on the influence of a vibrating field are of considerable relevance. They found that the burning constant K of eqn.(2.2) varied with the field intensity (I = square of vibra- tion amplitude) as follows : where I0 and a are constants, fis the field frequency and KO is the zero intensity value. This indicates the probable effect of microturbulence in the flame ; by reducing 6 the burning rate is increased and the flame front may move closer to the liquid surface. However, if the microturbulence is excessive this might so accelerate the mixing of the vapour and fuel that the fuel/air ratio in the space between the drops would not support combustion; this may possibly explain the phenomenon of flame extinction in droplet combustion in conditions of forced convection of high intensity.Distinction must be made here between the local fuellair ratio in the flame round the drops and the fuellair ratio of the complete assembly. As might be expected, with small drops (< 10 p, which are likely to evaporate completely) the low limit of combustion approximates to that of the vapour ; when larger drops were present this was progressively reduced @om 46 mg/l. for 10 p drops to 18 mg/l. for 45 p drops).38 4. SOLID SYSTEM In solid aerosols the number of dusts capable of supporting flames is now known 50 to number 100 or more, but of all these the only ones of technological importance are the coal dusts ; for this reason most of the research on the reaction mechanism has been confined to the study of carbon as being generally representative of coals.214 COMBUSTION OF AEROSOLS This section is therefore concerned almost exclusively with the mechanism of the carbon oxidation reaction under conditions of solid aerosol combustion.Although the reactions of carbon with gases have been under investigation for 100 years or more, the first major advance in the quantitative analysis of the system was provided by Langmuir. The Langmuir adsorption isotherm was originally derived specifically for the carbon oxidation reaction 51 and the specific reaction rate R, may be written : where kl and k2 are the velocity constants for chemisorption and for the oxygen monolayer desorption respectively and ps is the surface oxygen concentration. From this equation it has been predicted that at low temperatures the reaction order with respect to oxygen should be zero; at high temperatures, it should be unity, so that at flame temperatures the reaction rate can be written as These predictions have now been confirmed by experiment ;243 523 53 at intermediate temperatures a transition region exists in which the reaction order is fractional and is rising from zero to unity.54-57 If a diffusion film exists above the solid surface then we also have the condition, where ko is the velocity constant (and also the mass transfer coefficient) 57 for oxygen transport and po is the main stream oxygen concentration.Eliminating ps between eqn. (4.2) and (4.3) we have l / R s = l/koPo + l/klpo = Wo + Wig (4.4) Because of the form of this equation the two quantities WO and W1 have long been known as the diffusion and chemical " resistances "249 58 Applying this analysis to carbon combustion in a solid aerosol system, the assumption stated above (that at flame temperatures WO> Wl) leads to Rs = koPo9 (4.5) which implies that ps is effectively zero. The velocity constant ko can be related to the diffusion coefficient by an analysis similar to that for the heat transfer, leading to eqn. (2.5) and (2.6). In this instance the equation becomes ko = D(P0 - p,)lr(l- rl@, (4.6) where 6 is the boundary layer thickness.In the quiescent system involving only molecular diffusion, when 6 is large and ps is effectively zero, we get Rs = -odr/dt = Dpolr, (4.7) which has the form of eqn. (2.1). This is Nusselt's 21 result that, in the quiescent system, the Nusselt number is 2 and the eflective boundary layer thickness is equal to the particle radius. By integration and appropriate substitution this has been shown 37 to give the following relation for the burning constant K : wherep is the air density and other factors are as previously defined ; the subscript zero refers to s.t.p. This equation has been used to predict the value of K for the carbon residues of a set of coal particles. TabIe 2 compares the predicted and experimental values ; the discrepancies are attributed to swelling and photographic measurements have now established a swelling factor of about 1.5.59R .H . ESSENHIGH AND I . FELLS 215 TABLE 2.VALUES OF BURNING CONSTANT K FOR COKE RESIDUES OF CARBONIZED COAL PARTICLES ; COMPARISON OF EXPERIMENTAL AND CALCULATED VALUES coal 1. Stanllyd 2. Five ft. 3. Two ft. Nine 4. Red Vein 5. Garw 6. Silkstone 7. Winter 8. Cowpen 9. HighHazel 10. Lorraine %C (d.m.f.) 93.0 91.8 91.2 89.7 88.9 86.9 84.0 82.7 81.9 79.3 square-law index 202 1 *94 225 209 201 225 2.18 1-94 2 14 2.20 K (expt.1 2125 1290 1470 1475 1410 1110 1125 1060 1450 992 ratio K (calc.) 2720 1.28 2620 2.03 2070 1.41 2275 1.54 2030 1.44 1655 1.49 1710 1.52 1775 1.68 1725 1.19 1890 1.91 mean ratio 1.55 Now derivation of eqn.(4.7) is based on the assumption that reaction takes place at a smooth exterior surface. In practice, experiments 60-64 have shown that pore diffusion takes place with consequent internal reaction. This has been treated theoretically 64-68 and it has been shown 68 that, for a first-order reaction, eqn. (4.7) becomes (4.9) where S is the specific internal surface. This in effect is substituting ki for kl in eqn. (4.4) where (4.10) k; = kl -I- Jk,DS= kl(I -I- JDSlk,). In another derivation 653 36 quoted by Popov,69 ki is given as k; = k , +aD(coth r - llar), (4.1 I) where a = dD/IGlS and r is the particle radius. Blyholder and Eyring,64 following Wheeler,66 established similar equations but also derived a further equation for the low-temperature case (T< lOOO"C), viz., (4.12) where rp is the pore radius and is related to the specific internal surface S.Without pore diffusion, the reaction order with respect to oxygen is zero ;249 52 Blyholder and Eyring proved that when it was present, and under low-pressure conditions to eliminate boundary layer diffusion, the reaction order changed to 1/2, in agreement with eqn. (4.12). This can be significant for ignition. Other modifying factors so far omitted from this discussion include: the influence of back reactions, e.g. resorption of CO and C02; other reactions, e.g. reaction with water vapour ; and gas-phase reactions, e.g. oxidation of CO. Studies of the carbon+ COz and carbon+ steam reactions with resorption have shown 70-77 that the simple Langmuir isotherm is modified as would be expected and takes the form (4.13) where k3 and ps2 are the velocity constants and surface partial pressure for the resorbed components.There is still argument, however, concerning the detailed sequence of the steps in the mechanism.68 Other dusts that burn as aerosols are mostly like coals in that, being carbon- aceous dusts, they k s t lose volatile components which burn as though evaporated from liquid drops, and then the carbon residue burns as indicated above. Heavy fuel oils that crack, to give a carbon residue, behave in a similar manner. Of other dusts, many change phase and have more in common with liquid fuels so far as the controlling reaction mechanism is concerned. Some, such as sulphur, become liquid, then evaporate and burn to gaseous combustion products ; others, mainly216 COMBUSTION OF AEROSOLS the metal dusts such as aluminium, magnesium, titanium, zinc, become liquid, evaporate, but then burn to give solid combustion products (these latter may be molten at flame temperatures.The boiling point of the metal oxides gives the upper flame temperature limit). 5. RATE: CONTROL In aerosol reactions the important parameter for theoretical purposes is the nature of the rate-controlling step in the reaction sequence since this will determine the value of the burning constant K of eqn. (2.2). In liquid aerosols, theory and experiment are in accord with the assumption of rate control by heat transfer to the drop by conduction from the drop flame; the chemical processes, however, still determine the combustion limits.Determination of these is not easily predictable from theory, but Qehley’s somewhat empirical argument seems to give good results.78 It is clear also that the burning rates are influenced, at least to a second order of magnitude, by microturbulence and by radiation. The latter can materially affect the temperature distribution in the drop. It has been observed,7Q for example, that radiation can initiate boiling well below the liquid surface and this clearly will affect evaporation rates. Radiation in particular may also affect high carbon fuels in other ways ; residual fuel oils for example polymerize and crack and the carbon- aceous residues thus formed then burn out as solid and not as liquid aero~ols.67~~0~40 In this respect they resemble coal.In solid aerosols the position is less clear. Values of the burning constant given by eqn. (4.8) and table 2 show the reasonable agreement between theory and experiment for the residues of single coal particles in an infinite atmosphere ; as a further check, the burning times closely obeyed the square law of eqn. (2.2) (see table 2). However, the assumption of diEusiona1 rate control under all flame conditions has recently been questioned,go the alternative proposal being that, in flames, the rate control is the chemisorption step. The basis of the argument is essentially that certain data may have been misinterpreted‘due’to confusion between the velocity constants kl and k2. For example, Tu, Davis and RottelN derived the ‘‘ resistance ” equation (4.4) without clearly specifying that it held only at high temperatures because of the approximation of eqn.(4.2). Inevitably, therefore, they chose the wrong activation energy for kl and them interpreted their experimental data on spheres in terms of chemical control (kl<ko) at low temperatures (< lOOWC), and diffusional control (kl>lco) at high temperatures (>2O0O0C‘). The source of this confusion is now clear but their argument has been generally adopted by nearly all subsequent theorists. In fact, the activation energies measured at the low temperatures, which have values in the range 20 to 40 kcal, have been identified 81 as those for oxide film decomposition by forming an oxide film and decomposing it again in a vacuum over a range of temperatures so that only one reaction could have been involved.In the high-temperature range, the activation energies assigned 8*,82 or measured64 are a factor of 18 less, being in the region of 4 kcal, and this indicates a second source of confusion. One of the arguments used to favour the diffusion control theory is that the temperature coefficient of the carbon reaction at flame temperatures is too low to fit an Amheniens exponential, but it can be represented by a T2 law which is to be expected from the diffusion theory. Unfor- tunately, however, if the activation energy is only 4 Bcal, the Arrhenius exponential can afso be represented to a g ~ o d approximation by a T2 law in the flame tempera- ture range (1080” to 2000°C). This means that the two resistances WO and Wl of eqn.(4.4) are indistinguishable by this test; so also is the distinction between external reaction (governed as kl) and internal reaction (governed as dkiD,$. What does change, however, is the law governing the burning-out time of individual particles since ko is inversely proportional tp radius (eqn. (4.6)), bat kl is independent of it. Neglecting pore diffusion we then have, for kl<ko, . __ drldt = -k,/a.R. H. ESSENHIGN AND I. FELLS On integration this gives : (i) in an infinite atmosphere (single particle), t b = K c d o , where Kc is the new burning constant given from kinetic theory by where MO is the mean molecular weight of the gas mixture. (5) In a finite atmosphere (flame), 21 7 (5.4) where Fc is the multiplying factor given by an equation of a form similar to that of eqn.(2.4).37 Calculation of K, gives values of the order of unity so that for isolated particles of 1 cm diam. we should expect diffusion to control the reaction. As the particle size drops and the air supply is increasingly restricted, we should expect a reversal of the respective roles as indicated in fig. 3, This has now been put to experimental test by comparing predicted 83 and measured 84 degrees of combustion on carbon particles derived from anthracite in a special reactor.85 This comparison is shown in fig. 4 which shows that the chemical control prediction fits the measured values better than does the diffusional control prediction. Whilst this is not conclusive, it supports the result implied by Hottel and Stewart 26 who wrote the equation for the specific reaction rate in the form where d was the particle diameter and m a constant having a value between zero (for chemical control) and unity (for diffusional control).This equation was then fitted to a collection of experimental data on flames from a variety of sources and the best fit was obtained when, contrary to expectation, rn had the value zero. It is also of interest that in current Russian work no significant distinction is drawn between the two resistances ; both are given similar weight.349 36 R, = const./dm, (5.5) 6. AERODYNAMIC EFFECTS Aerodynamics plays a part in two-ways : as microturbulence influencing the reaction kinetics of the systems and as macroturbulence or forced convection, related to the combustion chamber as a whole, influencing the ignition and stabiliza- tion of the flames, The possible role of microturbulence in promoting and then hindering the reaction of the liquid aerosols has already been discussed (0 3).It is reasonable to expect that a similar promotion effect will also operate in solid aerosols though the hindering effect of intense microturbulence is not expected. Microturbulence is in fact encouraged in solid aerosol systems, the object being to " scrub away " the diffusion film. Evidence that this may occur is provided by experiments on the influence of low-frequency ultrasonics on the combustion rates, which are increased thereby.86-89 In allowing quantitatively for microturbulence, Spalding,30 for example, applied Frossling's equation 90 and obtained a multiplying factor for the rate equation of the form 1 + 0.246 Re*&%, where Re and Sc are the Reynolds and Schmidt numbers respectively.This can be compared with Popov's use 69 of a modifying factor for the Nusselt number (Nu) suggested by Katsnelson and Timofeev 9121 8 COMBUSTION OF AEROSOL§ Id 18 to Id Id Id Captive P F range I particle range Excess Air 10% 100 */* Qb a3 particle diam., p PIG. 3.-Comparison of calculated burning times in a flame, at 15OO0C, on respective hypotheses of diffusional and chemical reaction coiitrol (hypothetical carbon flame). Set A, physical control, eqn. (2.3); set €3, chemical control, eqn. (54.). combustion time, sec FIG. 4.-Decay of carbon concentration in a dust flame with time. Comparison of experimental values (full circles) with predicted values assuming (i) diffusional rate control (dotted line), (ii) chemical rate control (full line).R.H. ESSENHIGH AND I. FELLS 219 Microturbulence also influences the rate of ignition of the particles but this is a complex subject outside the scope of this paper. In contrast, macroturbulence has quite a different magnitude. In an enclosed jet flame, for example, the forced recirculation patterns have characteristic magnitudes approaching the combustion chamber dimensions. In dust flames such patterns, which feed back hot combustion products to the root of the jet, have a major influence on the ignition and stabilization of the flame. Thus measurements on quiescent flames 92-97 and stationary flames without recirculation 983 84 give flame speeds of the order of 1 m/sec or less in accordance generally with the simple radiation theories of flame propagation.211 259 279 281 98 In horizontal jet-flame systems, however, where the horizontal conveying speed for the dust to remain in suspension must exceed 10 m/sec, flame speeds of 1 m/sec are too low for flame stabilization. They are stabilized, however, as a consequence of the extra energy supplied by the recirculating gases which increase the flame speed by a factor of 10 or more.86s99-101 Calculations suggest that such an increase can be achieved by as little as 20 % recirculation (by volume at s.t.p.). Macroturbulence also serves to stabilize gas and oil flames though in these its influence is thought to be as a source of active centres rather than as a source of heat. The importance of turbulence has also been demonstrated in moving flames.92 Flame speeds in aluminium dust clouds, contained in tubes and ignited at the closed end, were found to be increased if the flame passed through a turbulence grating.This promotes the particularly violent form of forced convection generally character- ized as turbulent exchange and is regarded as a particularly important factor in determining the intensity and magnitude of a dust explosion; it is possibly the counterpart of recirculation in stationary flames. We are grateful to the Electricity Supply Research Council for permission to publish fig. 3 and 4. 1 Lloyd, Proc. Inst. Mech. Eng., 1948, 159, 220. 2 Khudyakov, Bull. Acad. Sci. U.R.S.S., 1949, 508.3 Godsave, Nature, 1949, 164, 708 ; 1950, 166, 1 1 1 ; 4th Int. Symp. Combustion (Cambridge, Mass., 1952) (Williams and Wilkins, Baltimore, 1953), p. 818. 4Spalding, Fuel, 1950, 29, 2 ; 1953, 32, 169; 1954, 33, 255; 4th Int. Symp. Com- bustion (Cambridge, Mass., 1952) (Williams and Wilkins, Baltimore, 1953), p. 847. 5 Goldsmith and Penner, Jet Propulsion, 1954, 24, 245. 6 Simpson, Sc.D. Thesis (Mass. Inst. Technol., 1954). 7 Hottel, Williams and Simpson, 5th Int. Symp. Combustion (Pittsburgh, 1954) 8 Kumagai and Isoda, 5th Int. Symp. Combustion (Pittsburgh, 1954) (Reinhold 9 Wise, Lorell and Wood, 5th Int. Symp. Combustion (Pittsburgh, 1954) (Reinhold 10 Kobaysi, 5th Int. Symp. Combustion (Pittsburgh, 1954) (Reinhold Publishing Corp., 11 Kumagai, 6th Int.Symp. Combustion (New Haven, Conn., 1956) (Reinhold Pub- 12 Agoston, Wise and Rosser, 6th Int. Symp. Combustion (New Haven, Conn., 1956) 13Bolt and Saad, 6th Int. Symp. Combustion (New Haven, Conn., 1956) (Reinhold 14 Kumagai and Isoda, 6th Int. Symp. Combustion (New Haven, Conn., 1956) (Reinhold 15 Miesse, 6th Int. Symp. Combustion (New Haven, Conn., 1956) (Reinhold Publishing 16 Levy, Injection and Combustion of Liquid Fuels (Ed. Thomas and Putnam) (Carpenter 17 Wise and Agoston, J. Amer. Chem. Soc., 1958, 80, 116. (Reinhold Publishing Corp., New York, 1955), p. 101. Publishing Corp., New York, 1955), p. 120. Publishing Corp., New York, 1955), p. 132. New York, 1955), p. 141. lishing Corp., New York, 1957), p. 668. (Reinhold Publishing Corp., New York, 1957), p.708. Publishing Corp., New York, 1957), p. 717. Publishing Corp., New York, 1957), p. 726. Corp., New York, 1957), p. 732. Litho. Printing Co., Springfield, 1957), chap. 18, p. 18.1.220 COMBUSTION OF AEROSOLS 18 Isoda and Kumagai, 7th Int. Symp. Combustion (Oxford, 1958) (Butterworths Scientific Publ., London, 1959), p. 523. 19 Kocker, 2nd Colloquium Flow and Combustion (Bad Kreuznach, 1960). 20 Masdin, Ph.D. Thesis (Sheffield, 1960). 21 Nusselt, Verein Deut. Ing., 1916, 60, 102; 1924, 68, 124. 22 Rosin, Proc. Int. Bituminous Coal, 1925, 1, 838 ; Braunkohle, 1925, p. 241. 23 Burke and Schumann, Ind. Eng. Chem., 1931, 23, 406 ; 1932, 24, 451. 24Tu, Davis and Hottel, Id. Eng. Chem., 1934, 26, 749. 25 Gumz, Theorie und Berechnung der Kohlenstaubfeuerungen (Springer, Berlin, 1939).26 Hottel and Stewart, Ind. Eng. Chem., 1940, 32, 719. 27 Traustell, Feuerungstechnik, 1941, 29, 1, 25, 49. 28 Ledinegg, Dampferzeugung (Springer-Verlag, Wien, 1952), p. 238. 29 Godsave, Nat. Gas Turbine Estab. Report R. 126 (1952). 30 Spalding, Proc. Inst. Mech. Eng., 1954, 168, 545. 31 Yagi and Kunii, ref. (7), p. 231. 32 Saji, ref. (7), p. 252. 33 Orning, ref. (ll), p. 559. 34 Khitrin, ref. (ll), p. 565. 35 Ghosh, Basu and Roy, ref. (ll), p. 595. 36 Khitrin, Physics of Combustion and Detonation (Moscow University Press, 1957). 37 Essenhigh, Ph.D. Thesis (Sheffield, 1959). 38 Burgoyne and Cohen, Proc. Roy. SOC. A , 1954,225, 375. 39 Hall and Diederichsen, ref. (4), p. 837. 40 Masdin and Essenhigh, Combustion and Flame, 1958, 2,443. 41 Essenhigh and Thring, Con$ Science in Use of Coal (Sheffield, 1958) (Institute of 42 Griffin, Adams and Smith, Ind.Eng. Chem., 1929, 21, 808. 43 Essenhigh, 2nd ConJ Pulverized Fuel (London, 1957) (Institute of Fuel, London, 44 Wolfhard and Parker, J. Inst. Petrol., 1949, 35, 118. 45 Burgoyne and Richardson, Fuel, 1949,28,2. 46 Gerald, D.Sc. Thesis (Mass. Inst. Technol., 1940). 47 Chang, D.Sc. Thesis (Mass. Inst. Technol., 1941). 48 Rex, Fuhs and Penner, Jet Propulsion, 1956,26, 179. 49 Lorell, Wise and Carr, J. Chem. Physics, 1956, 25, 325. 50 Factory Dept., Ministry of Labour and National Service, H.M.S.O., London, 51 Langmuir, J. h e r . Chem. SOC., 1915,37,1139; 1916,38,1145,2221,2267. 52 Arthur and Bleach, Ind. Eng. Chem., 1952,44, 1058. 53 Patai, Hoffmann and Rajbenbach, J.Appl. Chem., 1952,2, 306, 311. 54 Semechkova and Frank-Kamenetskii, Zhur. Fiz. Chim., 1940,14,231. 55 Klibanova and Frank-Kamenetskii, Acta physiochim., 1943, 18, 387. 56 Parker and Hottel, I d . Eng. Chem., 1936,28, 1334 (Analysis by Frank-Kamenet- 57 Frank-Kamenetskii, Dzrusion and Heat Exchange in Chemical Kinetics (Princeton 58 Fischbeck, Z. Elektrochem., 1933, 39, 316 ; 1934,40,517. 59 Essenhigh, current experimental work. 60 Bangham and Townend, J. Chim. physique, 1950,47, 315. 61 Crone and Bowring, J. Chim. physique, 1950, 47, 543. 62 Arthur, Trans. Faraday Sac., 1951, 47, 164. 63 Wicke, ref. (7), p. 245. 64 Blyholder and Eyring, J. Physic. Chem., 1957, 61, 682. 65 Predvoditelev and Khitrin, Combustion of Carbon (U.S.S.R. Academy of Sciences, 66 Wheeler, Advances in Catalysis (Academic Press Inc., New York, 1951), 3, 250.67 Weisz and Prater, Advances in Catalysis (Academic Press Inc., New York, 1954), 68 Walker, Rusinko and Austin, Advances in CataZysis (Academic Press Inc., New 69 Popov, Acad. Nauk U.S.S.R., 1958, 12, 90. 70 Frank-Kamenetskii and Semechkova, Acta physiochim., 1940, 12, 879. 71 Gadsby, Long, Sleightholm and Sykes, Proc. Roy. SOC. A , 1948, 193, 357. Fuel, London, 1958), p. D21. 1958), p. B1. form no. 830, Feb., 1953. skii, ref. (57)). University Press, 1955), chap. 11. 1949), chap. 3. 6, 143. York, 1959), 11, 134.R. H. ESSENHIGH AND I . FELLS 221 72 Lewis, Gilliland and McBride, Ind. Eng. Chem., 1949, 41, 1213. 73 Reif, J. Physic. Chem., 1952, 56, 785. 74 Gadsby, Hinshelwood and Sykes, Proc. Roy. SOC. A, 1946, 187, 129. 75 Long and Sykes, Proc. Roy. Soc. A , 1948,193, 377. 76 Johnstone, Chen and Scott, Ind. Eng. Chem., 1952,44, 1564. 77 Jolley and Poll, J. Inst. Fuel, 1953, 26, 33. 78 Oehley, Chem.-Ing.-Tech., 1953,25, 399. 79 Rasbash, Rogowski and Stark, Fuel, 1956, 35, 94. 80 Essenhigh, Shefield Univ. Fuel SOC. J., 1955, 6, 15. 81 Gulbransen and Andrew, Ind. Eng. Chem., 1952, 44, 1034, 1039, 1048. 82 Essenhigh and Perry, Conf. Science in the Use of Coal (Sheffield, 1958) (Institute 83 Siddall, private communication, 1960. 84 Beer, private communication, 1960. 85 Beer, Thring and Essenhigh, Combustion and Flame, 1959, 3, 557. 86 Audibert, Rev. Ind. Minerale, 1924, 4, 1. 87 Earle, Power Generation, 1948, 52, 86. 88 Porter, Chem. Eng., 1948, 55, 100. 89 Atkins, Fuel, 1950,29, 76. 90 Frossling, Gerlands Beitr. Geophys., 1938, 52, 170. 91 Katsnelson and Timofeev, Proc. Centr. Boiler-Turbine Inst. U.S.S.R., 1949, 12. 92 Caccel, das Gupta and Guruswamy, 3rd Int. Symp. Combustion (Wisconsin, 1948) (Williams and Wilkins, Baltimore, 1949), p. 185. 93 Long, Ph.D. Thesis (Imp. Coll. Sci. Tech., 1956). 94 Hattori, ref. (ll), p. 590. 95 Ghosh, Basu and Roy, ref. (ll), p. 595. 96 Burgoyne and Long, ref. (82), p. D16. 97 Essenhigh and Woodhead, Combustion and Flame, 1958, 2, 365. 98 Csaba, private communication, 1960. 99 Taffanel and Durr, 5th Series Expt. Inflammation of Dusts (Comit6 Centrale des Houillkres de France, Paris, 1911). 100 Sherman, 3rd Int. Conf. Bituminous Coal, 1931, 2, 510 ; Trans. Amer. SOC. Mech. Eng., 1934, 56, 401. 101 Int. Flame Research Foundation (Interim Report of First Performance Trial with Pulverized Coals, August, 1956). of Fuel, London, 1958), p. D1.

ISSN:0366-9033    

DOI:10.1039/DF9603000208

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

GENERAL, DISCUSSION Dr. R. D. Cade (Stanford Res. Inst.) said: In reply to Dr. Mason, we have studied the kinetics of the reaction of ammonia with sulphuric acid droplets suspended in air, both when the droplets consisted of concentrated sulphuric acid and when they consisted of dilute sulphuric acid. The reactions are extremely rapid even at the very low concentrations to be found in the smog-laden atmo- spheres of cities. Our calculations suggest that when the droplets consist of concentrated sulphuric acid, during the initial stages of the reaction about one out of every ten collisions of ammonia molecules with the sulphuric acid surfaces results in reaction. The overall reaction rate is controlled by diffusion within the droplets. On the other hand, when the sulphuric acid is dilute our results suggest that every collision results in reaction and the overall reaction rate is controlled by the rate of diffusion of ammonia in the gas phase.In the latter case the initial reaction is probably that of ammonia with water, and the sulphuric acid subsequently reacts with the ammonium hydroxide thus produced and prevents the reverse reaction from occurring to an appreciable extent. The reactions were so rapid that it was necessary to use a flow system for determining the reaction kinetics. Thus, distance from the point of mixing at which sampling was undertaken was proportional to the reaction time. The sampling was undertaken by passing the entire aerosol through a bed of molecular sieve material (artificial zeolite) which removed the ammonia but permitted the nitrogen and suspended particles to pass through unchanged. The particles were then collected with an elec tr 0s tat ic precipitator and analyzed colorime t r icall y for sulphate and for ammonia.When the droplets consisted of dilute rather than concentrated sulphuric acid, the relative humidity in the aerosol had to be main- tained at such a high level that the molecular sieve material was not effective for removing the ammonia. In this case, crystalline oxalic acid was substituted for the molecular sieve material and was found to be highly satisfactory. In reply to Dr. Elton, results obtained at Stanford Research Institute and else- where suggest that dark (thermal) reactions involving olefins at concentrations existing in smoggy atmospheres do not appear to produce aerosols.For example, the reactions of olefins with ozone at such concentrations produce only gases. However, photochemical reactions involving olefins in air, which, of course, require the presence of substances such as nitrogen dioxide and aldehydes to absorb sunlight, do produce aerosols. Recent experiments at the Institute have indicated that photochemical reactions in the system olefins + air+ NQ2+ SO2 produce highly concentrated aerosols when exposed to sunlight. Such reactions are prob- ably of great importance to the visibility-decreasing properties of smogs of the Los Angeles type. Dr. P. G. Wright (Dundee) said: Tesner 1 concludes from his results that the decomposition of acetylene at the surface of carbon particles is not diffusion- controlled.This is to be expected for even the largest of the particles (radius a ~ l O 3 A) under his conditions (SOOOK, 1 atm). In terms of Fuchs' theory 2 of evaporation and condensation, the retardation due to diffusion may be represented in the steady state (for the non-steady state the retardation is even less) by dividing by the denominator * 1 Tesner, this Discussion. 2 Fuchs, Physik. Z. Sowjet., 1934, 6, 225. * (communicated) : In its usual application (evaporation and condensation) the theory of Fuchs 2 requires that the condensable species 2 shall be rare with respect to the gaseous 1, so that single diffusion and mutual diffusion shall be indistinguishable. In the present application, though there is much acetylene as well as much hydrogen, there is true mutual diffusion because for each C2H2 molecule which decomposes, one gaseous H2 molecule is formed.Consequently, the denominator does not require further correction. 222FIG. 1 .-Linolenic acid particles; magnification 3940 x . FIG. 2.--L,inolenic acid particles; magnification 3940 X . FIG. 3 .-Silver chloride particles coated with linolenic acid; magnification 3940 X . FIG. 4.-Silver chloride particles coated with linolenic acid ; magnification 3940 x . To face p. 2231GENERAL DISCUSSION 223 a here represents the probability that an acetylene molecule decomposes on striking the surface of a carbon particle. 22 is the mean molecular velocity of acetylene (8.1 x 104 cm sec-1 at 800°K). D J ~ is the coefficient of mutual diffusion of acetylene and its decomposition product hydrogen.Its value may be taken to be approxim- ately equal to that of the (measured 1) coefficient of mutual diffusion of oxygen and hydrogen (4-8 cm2 sec-1 at 800°K and 1 atm). Taking A = 2012122 = 1.2 x 10-4 cm = 12a, even if a is as much as 1.0, the value of the correcting denominator is l + - x - X - =1*003. (; l!2 :3) Thus the retardation due to diffusion cannot exceed 0.3 %. Prof. Milton Kerker (Potsdum, N. Y.) said: We would like to report on progress in preparing " coated aerosols " since our paper was communicated. Linolenic acid has been chosen as the coating material both because of the ease with which it can be condensed on silver chloride aerosols and because by exposure to the vapours of osmium tetroxide, it can be fixed for electron microscopic observations.Fig. 1 and 2 are electron micrographs of linolenic acid aerosols. These were prepared by passing silver chloride nuclei from a hot wire through a boiler con- taining linolenic acid at 120" and 125" respectively, and subsequent cooling in an air condenser. The flow rate was 242 ml/min. Collection was effected by thermal precipitation. The particles were exposed to the osmium tetroxide for 3 h and observed in the electron microscope without further treatment. The silver chloride nuclei were sufficiently small so that they gave no visible Tyndall beam prior to entering the boiler, although the emergent linolenic acid aerosol itself was quite turbid. No aerosol was formed under the same conditions in the absence of silver chloride nuclei.Fig. 3 and 4 are electron micrographs of silver chloride aerosols coated with linolenic acid. The silver chloride nuclei were prepared in the generator de- scribed in our paper and then passed through the linolenic acid boiler at 110". The boiler of the silver chloride generator was maintained at 1010" and 1100" respectively, and the flow rate at 356 and 930ml/min respectively. The collec- tion, fixation and electron microscopy were carried out as described above. Fig. 4 is typical of coated aerosols with a thin coating. Although the coating appears somewhat as a blur this is not due to the picture being out of focus, as direct inspection on the microscope screen can easily show. By comparison, uncoated silver chloride particles give a sharp picture.It will probably be necessary to obtain densitometric traces in order to determine the thickness of the coating in such cases. We are still engaged in elucidating the relation between the conditions under which these aerosols are prepared and the type of aerosol particle obtained. We have not yet analyzed any of the light-scattering data. Prof. Milton Kerker (Potsdam, N. Y.) said: It is rather interesting that the refractive index of 1.486 used for dioctyl phthalate corresponds so closely to the value of 14821 used by us for linolenic acid aerosols. We have compared the total Mie scattering coefficients published by Penndorf for rn = 1.486 with our results. We find that the small difference in refractive index results in an average difference of 1.5 % between the two sets of scattering coefficients, and in one case the difference is as great as 5 %.This is a significant difference in view of the fact that the scattering coefficient itself oscillates with size between extrema that differ , 1 Walker and Westenberg, J. Chem. Physics, 1960, 32, 436,224 GENERAL DISCUSSION from the mean by only 20 %. Furthermore? the total scattering coefficient is frequently less sensitive to size and refractive index than the angular scattering functions themselves. This would suggest that it is probably necessary to know the refractive index of the particles to a high degree of precision. As an illustration of the vagaries that may be encountered in scattering by particles larger than the wavelength, we present some scattering data in table 1 for particles corresponding to our concentric sphere model.The refractive indexes are for a silver chloride sphere encased in a spherical shell of linolenic acid, The total size is determined by v = 2nb/i17 where b is the particle radius. The size of the inner sphere is given by a = 2na/I, where a is its radius, We have selected y = 30" (measured from the backward direction) as illustrating an extreme but not an unusual situation. TABLE l.-SCATTF,RING FUNCTION il AT y = 30" m1= 2.105 o x v 38.67 -20 x v 49.64 -40 x v 2203 -60 X v 7-43 -80 x v 1 18.48 -90 X v 26.67 a95 x v 8.01 -98 x v 32.62 a99 x v 26.68 1.00 x v 24- 67 v = 12.0 m2= 1.4821 v = 12.1 v = 12.2 21.48 22.65 26.00 25.60 7.1 1 9.13 55.68 19-96 107.47 105-44 14.1 1 12.04 41.59 55.36 25.09 16.80 21.43 7.63 11.99 -63 m3 = 1.OOO v = 12.3 v = 12.4 27-77 27.21 29.8 1 28.86 8.21 5.04 10.79 17.30 29.83 28.52 17.14 27.78 22.80 13-09 4-50 29.38 a 1 3 29.73 8.84 30.73 A particle for which a = v = 12.2 corresponds to a silver chloride sphere of about 0.8 ,u radius illuminated by blue light. A change of v by 0.1 unit, which is certainly less than the accuracy of any known method of determining the size of such particles, results in an increase of scattering by more than an order of mag- nitude.Furthermore, a coating of linolenic acid whose thickness is 1 % of the particle radius (v = 12.2, a = 0 . 9 9 ~ 12.2) causes a comparable variation in scattering. These computations have been carried out with an IBM 704 digital computer. Our programme encompasses the single sphere corresponding to the Mie theory as a degenerate case. Although the National Bureau of Standards has also programmed this problem for the same computer, we found their programme so slow that the cost of running extensive computations became excessive.From an input of a, v, ml, m2 and m3, our present programme will produce a complete set of scattering data in about 4sec. This includes angular scattering functions at 21 angles of observation. With the availability of Dr. Gucker's angular functions, this could be increased to 181 angles of observation at little or no appreciable increase in running time. The results with our programme agree precisely with those of the National Bureau of Standards for the concentric sphere case and with various values in the literature for the single sphere case as well as with various hand-computed check-points.At the present time we have com- puted the 1500 cases corresponding to v = 0.1 (0-l), 15-0 for a = (0, 0.20, 0.40, 0.60, 0.80, 0.90, 0.95, 0.98, 099)X V . Prof. Milton Kerker (Putsdam, N.Y.) said: Dr. Gucker and Dr. Rowel1 have very successfully eliminated two of the most troublesome perturbations in light- scattering work, polydispersity and secondary scattering, by making their ob- servations upon a single particle. By their very ingenious experimental work they have been able to deal with a perfectly monodisperse and infinitely dilute aerosol. In our laboratory, Dr. MatijeviC, Dr. Ottewill (on leave from Cambridge University) and I have recently been able to make light-scattering observations on another perfectly monodisperse and infinitely dilute aerosol, viz.a spider fibre.FIG. 1 .-Electron micrograph of spider fibre; magnification 6500 x . To face p. 2251GENERAL DISCUSSION 225 This system has the added advantage, that since it can be suspended from a simple frame, the spurious reflections associated with an enclosing cell are also eliminated. This work will be reported in detail elsewhere and we will only summarize our results here. The fibre studied was from a theridiid species, an electron micro- graph of which is shown in fig. 1. The fibre radius was about 112 mp although it was probably not of circular cross-section. The fibre was oriented with its axis perpendicular to the scattering plane and the intensities of the horizontal and vertical components of the scattered radiation were determined at various angles of observation.The ratio of these two intensities, the polarization ratio, was calculated for comparison with the theoretical results. Data was obtained at 436, 546 and 598 mp. We utilized amplitude functions computed by Rayleigh 1 and more recently by Larkin and Churchill 2 to calculate intensity functions, assuming the refractive index was 1.5. From theoretical curves of polarization ratio against radius for various angles of observation, it was possible to evaluate the radius corresponding to the experimentally determined polarization ratios of the spider fibre. The results are given in table 1 and agree very well with the electron microscopically determined value of 112 mp.The quantities in parenthesis are experimental values of the polarization ratio. Agreement was not obtained at angles less than 105", possibly due to the deviation of the cylinder from circularity. Apparently the 90"-scattering is less sensitive to fibre shape than that at other angles. TABLE 1 .-RADIUS OF SPIDER FIBRE CALCULATED FROM POLARIZATION RATIO 436 105 mp (-455) 107 mp (-395) 103 mp (-535) 546 111 (-145) 94 (-100) 1 20 (-235) 598 122 (-150) 109 (-120) 1 29 (-200) Attention should be drawn to a very striking phenomenon associated with scattering by infinite (long) cylinders illuminated at perpendicular incidence. The light is scattered in a disc, of thickness delineated by the incident beam, which is parallel to the scattering plane.The spider fibres were visible only when viewed along the radii of this disc, the scattered light diverging only slightly from parallelness in this plane. This divergence of the scattered light in only one direction is implicit in the theory, the scattered intensity decreasing as llr and not as l/$. Dr. W. Smith (D.S.I.R., Stevenage) said: In connection with Prof. Churchill's paper, I wonder whether he has seen the work of Vermeulen et aZ.,3 who found that their experimental results fitted the equation, wavelength, m p 0 = 900 e = 750 0 = 105' This can be obtained from eqn. (7) of the paper by expanding the hyperbolic functions, and omitting orders higher than the first. Vermeulen was concerned with much larger particles, and it is interesting to see that Prof.Churchill's ex- pression covers such a wide range. For reflection, Calderbank et aZ.4 have found that their experiments fitted where k is a constant depending upon the refractive index ratio. It should be possible to give theoretical support for this expression by obtaining it from 12 of 1 Rayleigh, Sci. Papers 434 (1919), cited by van de HuIst in Light Scattering by Small 2 Larkin and Churchill, J. Opt. SOC. Amer., 1959, 49, 188. 3 Vermeulen, Williams and Langlois, Chem. Eng. Prugr., 1955, 51, 85. 4 Calderbank, Evans and Rennie, in Rottenberg (ed.), Int. Symp. Distillation, 1960 Particles, chap. 15 (John Wiley and Sons, New York, 1957). (The Institution of Chemical Engineers, London). H226 GENERAL DISCUSSION the paper, but when I attempt to get 12 from eqn.(5) and (6) I find that no boundary condition will fit for an infinite depth of liquid-as would be required for the ideal case of reflection. Could Prof. Churchill give the solution for 121 It is noticeable that the solution (eqn. (7)) becomes trivial for the case S = 0, whereas one would expect it to converge to the ordinary solution for the condition where there is no side scatter. Dr. G. A. H. Elton (Brit. Baking Ind. lies. Assoc.) said: In the experiments described by Prof. Churchill, two approximately monodisperse samples of spheres were used, one batch had a mean diameter of 0.814 p, and the other a mean diameter of 1.171 p. I would like to ask Prof. Churchill whether, in his view, the results obtained with particles of this sort of size can be extended with confidence to much larger particles (e.g. diameters of ZOp), and to heterodisperse systems.I ask this question because in scaling down an atmospheric aerosol in the way which Prof. Churchill describes, it would be very convenient to be able to study hetero- disperse systems of larger particles of the types which occur naturally in fogs and clouds, provided that the results which Prof. Churchill found with monodisperse small particle systems can be applied to such cases. Prof. Frank T. Gucker (Indiana University) said: Did not Chandrasekhar derive an equation covering the case of multiple scattering from a semi-infinite atmosphere, and would this solution be of any assistance in treating the problem under discussion ? Prof. S. W. Churchill (University of Michigan) (communicated) : In reply to Dr.Smith the individual solutions of eqn. (5) and (6) are p cosh [y(l, - Z)] + NaS(B + S ) sinh [p(1, - l)] p cosh (pl,) + N q ( B + S ) sinh (pl,) ’ I , = and BNa, sinh [p(l, - l)] p cosh (pl,) + Na,(B + S ) sinh (pZt] I , = (9) For S = 0, corresponding to no absorption or sidewise loss, the following ex- pressions can be obtained by direct solution of eqn. (5) and (6) or by application of L‘Hospital’s rule to eqn. (8) and (9) : 1 + No,B( I, - I ) I , = l+Nas,Bl, ’ N~J3(1, - d) I , = 1 + Na$I, Eqn. (7) does not, as suggested, become trivial for S = 0. L’Hospital’s rule yields Application of which can also be obtained from eqn. (10). Eqn. (12) has the same form as the empirical equation of Vermeulen et al., indicating that their p is equivalent to our NosB.As suggested, an expression of the same form is obtained for finite absorption or sidewise loss by expanding the hyperbolic terms and retaining only the first order terms for small thickness; their p is then equivalent to our Na,(B+ 8. Eqn. (10) and (11) also yield an expression for the reflectivity which has the same form as the empirical equation of Calderbank et al., indicating that their k is equivalent to our l/BZt. The simple two-flux model thus provides theoretical support for both correlations and a physical interpretation of the coefficients.GENERAL DISCUSSION 227 In reply to Dr. Elton, we would expect our findings to be applicable semi- quantitatively to larger particle sizes and heterodisperse systems. In reply to Prof.Gucker, Chandrasekhar 1 derived exact expressions in the form of integral equations for multiple scattering by finite and semi-infinite atmo- spheres but computed numerical values only for isotropic and Rayleigh scattering. We have recently carried out numerical calculations for multiple scattering by a semi-infinite atmosphere for several realistic angular distribution functions,Z but these distributions do not correspond to the values of a used in the experiment reported herein. Dr. €3. J. Mason (ImperiaE College, London) said: I can confirm that the aggregation of ice crystals increases quite rapidly when the air temperature rises above about - 6°C. In measuring the electrification which results when impacting ice crystals rebound from the surface of an ice sphere, we find that the charging falls rapidly when the air temperature rises above -6°C because, at these tem- peratures, the crystals stick and do not bounce off.There is also radar and direct observational evidence that the aggregation of snow crystals to form snowflakes proceeds very rapidly at temperatures near the 0°C but this may be greatly assisted by the presence, in the cloud, of supercooled water droplets which may act as a cement to bind the crystals together. However, there were no supercooled droplets in our experiments nor, I believe, in those of Dr. Hosler. Although it is fashionable to attribute the adhesion between ice crystals to the presence of a liquid film on their surfaces, I find it difficult to conceive of a " liquid " layer many molecules thick at temperatures well below 0°C ; nor do I think it necessary.We have found that when a temperature difference is estab- lished across an ice crystal this is accompanied by a potential gradient, the crystal becoming, in effect, a dipole. The charge separation suddenly increases at tem- peratures above -S"C, the increase occurring mainly in the surface layers. Per- haps the adhesion of ice crystals may be attributed to these electrical forces. Dr. Hosler describes how his crystals aggregate in chain-like fashion and fold under their own weight. I have observed small ice crystals to aggregate in chains in the presence of an electric field and to behave as he describes. I wonder whether, in his apparatus, where ice crystals are striking an insulated tube, quite large electric fields might not be set up and that ice crystal aggregation may occur as a result of the charges induced in them by temperature gradients and external electric fields.I should like to see the adhesion between ice surfaces studied under very clean conditions with the adsorption of impurities eliminated or greatly reduced. Prof. C. L. Hosler (Penn. State University) said: As Dr. Mason suggests, we feel that there were no water droplets present during our experiment. This was one of the first things we looked for when we found our maximum sticking at - 11°C. Observations of individual ice crystals showed no growth over periods of many minutes indicating that no liquid phase was present. I would be interested to see whether Dr.Mason would observe sticking at temperatures lower than -6°C if he had a cloud composed of plates. I believe his experiment was carried out under conditions where only columns were pro- duced. We observed that columns did indeed stick very poorly. but at temper- atures below -10°C our experiment dealt only with plates which seemed stickier than columns. Dr. Mason's point concerning electrical effects and adsorbed impurities is an important one. We made no effort to measure the electric field in the test section and we used the air in the laboratory without special treatment. Just as the role of adsorbed materials greatly affects the activity of nucleating materials, H am sure that they must play an important role in determining the surface 1 Chandrasekhar, Radiative Transfer (Oxford Univ.Press, 1950). 2 Churchill, Chu, Leacock and Chen, DASA report IZQ. 1184 (Ann Arbor, Michigan, 1960).228 GENERAL DISCUSSION characteristics of ice. In spite of extraneous effects that adsorption might produce, however, the experiments showed a very consistent relationship between the number of ice crystals sticking to the aggregate and the temperature and crystal type. Dr. G. A. H. Elton (Brit. Baking Ind. Res. Assoc.) (communicated): The Dis- cussion has been use€ul in crystallizing a number of important physico-chemical questions which must be answered before substantial progress can be made in a number of branches of this subject. It seems to be generally agreed that the Volmer-Weber-Becker-Doring theory of nucleation is not entirely satisfactory as it does not fully describe the early stages of nucleation, nor does it account for the differing effect of positive and negative ions.It is clear that great caution must be exercised in applying thermodynamic treatments to nucleation processes in which the number of molecules involved in an aggregate is very small. The use of bulk properties such as surface tension and contact angle is likely to be par- ticularly hazardous. It is also interesting to note that, as Prof. Ubbelohde pointed out, a cluster of water molecules around a single ion can represent quite a con- centrated solution. For example, a single ion in 55 molecules of water will give a dioplet of radius 7 to 8 A, with an equivalent concentration of approximately 1 N. Turning to mechanisms of growth and shrinkage of droplets, it is established that very small (submicron droplets) in a heterodisperse aerosol change their size mainly by the evaporation-condensation mechanism, but this falls off in rate as the size increases. Coagulation becomes more important with increasing size but is not really significant in tranquil conditions until the radius exceeds about 20p. For droplets of radius of the order of 1 p, electrical double layer effects are important, especially in turbulent conditions. The forces involved are of short range, but can nevertheless be of great importance in determining coalescence efficiencies. The problem of the interaction of electrically neutral droplets containing electrical double layers presents an interesting field for theoretical work, and further experimental results covering, in particular, the effect of droplet size and electro- lyte concentration are necessary. With regard to the collision and coagulation of ice particles, there is also a need for basic physico-chemical work on the question of whether or not a liquid film exists on the surface of ice below 0°C and, if so, how thick this film is.

ISSN:0366-9033    

DOI:10.1039/DF9603000222

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

AUTHOR INDEX * hkarwv, s. F., %, 130. kmton, D. Pa, 68- Buckle, E R., 46, 59, 65, 66, 146, 153. Buff, P. P., 52. Cadle, R. D., 154,195, 222, Cllarnberlaia, A. C., 162. Churchill, s. W., 192, 226. Chrk, G . C , 192. Ihvies, C. N., 144, Ihnnis, W. L,, 78, 144. Dcrja.guhT B. V., 96, iW, Dunning, Wp J., 9, 59, 63, Egglekm, A . E. .J., 162, Rimer, H. S., 86, 147. Elton, G. A. H., 63, 140, 142,22.6, 228. Essenha, R. H., 143,245, 248. Fdls, I[,, 203. Fletcher, N. IN., 39, 61. Fuchs, N., 139. GuckerD F. T., 135,226. Hdlgrcn, R. k,, 200. Hartky, G- S., 141, 144. Hmler, C+ L., 200, 227. Kerker, ha., 178,223, 224, *wy, 3*, 113. Kurghh, 1. s,, %, h e , W. R., 64. L ~ o Y , L. Pa, 124, 153. Lessisrg, a., 7, Mason, B. J., 20, 59, 62, €4- 65, 140, 142, 153, 227. Matijevii* E., 178, Matthew, H. I., 113. M e w , W. J., 162. Morris, J, B., 162, Picknett, R G., 139, 147. Prokhmv, P. S., 124, 153. Quince, B. W., 86, Kobbh, R. C.,. 155. Rowell, R. L, 185. Ryky, D. J., 142. %hotland, R. M., 72, 142. W u h K. F., 178. Shack, C., 86. Slicpcevicb, C. M., 192. Smith, W,, 143, 225. Te~ner, P, A., €70, Wilman, H., 61, 66, 113. Wright, P, G., 100, 147, 148, 222. 229

ISSN:0366-9033    

DOI:10.1039/DF9603000229

出版商:RSC    

年代:1960

数据来源: RSC