Oxidation of Sulphur Dioxide in Aerosol Droplets, Catalysed by Manganous Sulphate B Y PETER W. CAINSt AND MICHAEL D. CARABINE* Department of Chemical Engineering and Chemical Technology, Imperial College, London SW7 2AY Received 4th July, 1977 Experiments are described in which the changes in size distribution of water droplets in an aerosol were measured when they were exposed to humid air dosed with sulphur dioxide, such that manganese- catalysed oxidation occurred in the droplets. The size changes have been compared with calculations (a) of the growth induced by reaction and subsequent water condensation, and (6) of the changes produced by coagulation. The results are in good agreement when the most recently revised values of the rate constants of controlling steps are used.The initial rate of oxidation is related to the overall concentrations of SO2 and manganese in the aerosol. The conditions in the experiments were chosen to be similar to those a few metres from the chimney mouth in a typical industrial stack plume. Both coagulation and growth contributed significantly, and sulphuric acid production was substantially complete in 10-20 min. Light scattering size analysis was successfully applied to these rather polydisperse aerosols (cro - 0.5) of small modal diameter (UM < 0.3 pm). The object of the experiments described in this paper was to observe the rates of size change in aqueous aerosol droplets with diameters in the range 0.1 to 1 pm, as a consequence of their being exposed to humid air containing sulphur dioxide.The droplets were generated from dilute solutions of manganous sulphate and hence the oxidation of sulphur dioxide to sulphuric acid was catalytically enhanced. The results of the experiments were then compared with calculations using a model based on homogeneous liquid-phase oxidation, together with growth by condensation of water, with liquid-vapour equilibrium maintained at all stages, and with coagulation of droplets according to the theories of Smoluchowski. Conditions such as the droplet number concentrations, the initial sulphur dioxide content and humidity of the air, and the pressure and temperature, were chosen to resemble those in a stack-plume from a power-station burning sulphur-containing fuel. as a rapid route for sulphate production and for gas-to-particle conversion in such plumes ; in the present experiments the content of manganese (a particularly active catalyst) was matched to some values observed in the gases arising from ~oal-burning.~'~ Metal-catalysed oxidation in droplets is regarded 1* MODEL OF DROPLET GROWTH ARISING FROM ABSORPTION AND OXIDATION OF The possible rate-limiting processes for the growth of the droplets in this system would be (a) diffusion of SO2 to the droplets, (b) oxidation of SOz at the surface or within the droplets, (c) diffusion within the droplets of the sulphuric acid and the water and (d) diffusion of water vapour to the droplets.It has been predicted 7 Present address U.K.A.E.A., Harwell, Oxfordshire OX1 1 O M . 26892690 CATALYSED OXIDATION OF so2 I N AEROSOLS theoretically 6 s ' that the liquid and gas-phase diffusion processes (c) and (d) will reach completion in about 5 x s respectively, when droplet diameters are around 0.5 pm. Because liquid phase oxidation has been shown in experiments with bulk solutions to be complete only in times of around thirty minutes, processes (c) and (d) are considered unlikely to be rate-determining in the small droplet case.Process (a) may be eliminated by analogy and, therefore, we postulate that oxidation within the droplets is rate-limiting. There is some evidence that homogeneous reaction rate and liquid-phase diffusion are both important with droplets up to 1 mm in diameter. Proceeding with this hypothesis of rate control by the homogeneous reaction, the concentrations of all components will be uniform, at any given time, throughout the liquid phase of the aerosol, maintaining equilibrium with the gas-phase concentrations.The droplet sizes considered here are invariably too large for curvature to produce variations in equilibrium vapour pressure, and hence in concentration, from droplet to droplet. The condensed phase may, therefore, be considered as a homogeneous reaction volume for the purposes of determining the rates of increase in droplet volume (u). If this rate is denoted by dvldt, then and 2 x dv - = u l ( t ) dt where I ( t ) is a function of time only, defined by this equation. As to the distribution of sizes, discussion will be restricted to a log normal distribution function of the Z.O.L.D. type described by Espenscheid et al.,'O which has been found to be a good description of the size distributions of aerosols generated experimentally.llp l 2 The parameters of this function are aM the modal diameter, and co a measure of the spread of the distribution.Integration of eqn (1) leads to the result that the time dependence of sizes in the Z.O.L.D. distribution is given by the value of o0 remaining constant. Droplet diameter changes may be calculated from eqn (2), but first the reaction kinetics and the vapour-liquid equilibria of the system, which together determine I(t), are to be considered. KINETICS OF THE REACTION I N SOLUTION The reaction mechanism chosen for the kinetic calculations is essentially that of Bassett and Parker,8 in which there are four main stages : (1) Formation of a complex ion between Mn2+ and some anionic species derived from SO2 (e.g., SO$-, HSO; or S20g-) Mn2+ +2SOZ- + { Mn(S03)2}2-. (2) The addition to this complex ion of 02, taken to be present in some hydrated or complexed state, { Mn(S0,)2}2- + O2 + 02(Mn(S03), j2-.(3) Rearrangement, considered to be comparatively rapid, 02{ Mn(S03),j2- + {Mn(S0,)2)2-. (4) Release of the sulphate product, with sulphite ions displacing it from the complex formed in stage (3).P . W. CAINS AND M. D. CARABINE 269 1 This mechanism has been used to explain most of the qualitative features observed in experiments with bulk solutions, including the suppression, in the case of Mn2+, of the dithionate ion which is produced with some other catalytic cations.* Support for the mechanism comes mainly from the variations in the reaction rates and in the final products when various catalyst salts are used at various concentrations; as far as identification of the complex intermediates is concerned, the extraction in ether from the system of a compound of empirical formula MnS04.SO2 has been reported,13 but no evidence of application of modern analytical techniques (such as e.s.r. spectroscopy) has been found in the literature. Matteson, Stober and Luther l4 attempted to model the reaction kinetics using a scheme which is basically similar to that above, but which is expressed in terms of complexes containing neutral SO2 and SO3 molecules, as opposed to the (in our view more likely) anionic ligands of the first mechanism. The stages proposed are as follows : Mn2+ + SO2 + (MnS02}2+ (1) ki k2 k3 2(MnS02}2++02 + {(MnS02)202}2+ k4 k s ((MnS02)202}2+ + 2(MnSO3I2+ k5' k6 k7 (3) (4) (MnS03)2++H20 + Mn2++HSOi+H+.The most fundamental simplification in their analysis was the assumption that the rate limitation of the reaction is due to stages (1) and (4), and the scheme is thus equivalent kinetically to that of Bassett and Parker. For the low concentrations of SO2 considered, the concentration of oxygen is relatively high, making the rate of stage (2) unimportant. It is convenient to use the following parameters defined by Matteson et al. for their analysis. The total concentration of intermediates (moles per unit volume liquid) was expressed as the sum (XI, = (MnSO,)?' ++((MnSO2),O2)2,+ + {MnSO,);' and the relative concentration of each was assumed to remain constant as reaction proceeds.Two pseudo rate constants were defined as follows k2 (MnS O2 12' k6(MnS03)i+ i H 2 0 ) L k2. = kgf = (XI, (XI, RESULTS OF CALCULATIONS AND CHOICE OF RATE CONSTANTS In the present approach to the problem the mechanism of Matteson et al. has been adopted, and numerical solutions of their eqn (15), (35) and (36) have been evaluated giving the variation with time of the concentrations of SO2, H2S04 and intermediate X. The initial condition was (X}, = 0 ; two distinct sets of values of the rate constants were used, with contrasting results. The first set of values of k l , k2', kgP and k7 were those explicitly derived by Matte- son et al., namely k,/mol-l dm3 min-l k2 ./min-l k6./min-l k7/mol-2 dm6 m i d The results using these values are exemplified, for a given set of starting conditions, in fig.1. 2 . 4 ~ 105 10 0.22 352692 CATALYSED OXIDATION OF so2 I N AEROSOLS Secondly, a set of values was selected as follows : k6# and k7 were obtained from other theoretical work,15 kl was evaluated by fitting the data of Johnstone and Coughanowr to the equation -- d{S02'v = kl{MnS04)& dt where (SO,}, is the gas-phase concentration (moles per unit volume in gas phase), and the subscript zero denotes the value of (MnSO,), at zero time. The latter is valid for (MnSO,), < Hsoz x (S02)v,o, where Hso2 is a Henry's Law constant. Finally kzt was evaluated from eqn (21) of Matteson et al., since kl, k69, Ks and Hsoz are all known. 64 62 d d -e 60 0 .- Y E 58 Y 0 g 5 6 8 2 54 timelmin FIG.1.-Solutions to kinetics of oxidation using rate constants of Matteson et aZ.I4 and eqn (15). (35) and (36) of their paper. -- -, SOz concentration/v.p.m. ;-, H2S04concentration/mol dm-3 ; - - - -, intermediates concentration (X}L/mol dm-3. { MnZ+}L.O = 0.35 mol dm-3 ; (S0~)v.o = 63 v.p.m. ; V = 1.6 cm3 m-3: I I I I 1 I I - 2.5 60 - - 2.0 - 1.0 - 0.5 O r I I 1 I I ! I 0 4 a 12 16 20 24 28 32 t ime/min FIG. 2.-Solutions to kinetics of oxidation using rate equations and initial conditions as in fig. 1 but with revised rate constants.P . W. CAINS AND M. D. CARABINE 2693 In the same units as above, the values are kl k2 k6 ' k7 3.54x 104 6.18 2.03 1.06 x and the two sets differ most significantly in the ratio of k6' to k,, which determines the liberation rate of oxidised Svl from the complex intermediate. The results using these values, exemplified in fig.2, show all the trends observed by earlier experimenters :l6? that is to say the time scale of significant change is seen to be in tens of minutes; there is a gradual decrease in the gas-phase SO2 concentration, an increase in sulphuric acid solution concentration to values in the range 1 to 2 mol dm-3 and an initial increase in the concentration of the intermediate, followed by a slow decrease. These kinetic predictions are much more satisfactory in all respects than those illustrated in fig. 1 ; the revised values of the rate constants are evidently better. yielded kl = 2.73 x lo4 mol-1 dm3 min-l, but use of this value made no significant difference to the calculations.) (Alternative experimental data of Coughanowr and Krause CALCULATION OF DROPLET GROWTH INDUCED BY CHEMICAL REACTION Rigorous calculation of the increase in volume of the liquid phase with the accre- tion of SO2, oxygen and water vapour and with the formation of sulphuric acid requires the evaluation of the volumes of mixing of the mixtures involved.It is sufficiently accurate in the range of concentrations encountered here to consider these to be negligible and to treat the liquid as an ideal mixture. The reaction schemes for the manganese-catalysed oxidation, considered above, form the basis for the computation of growth of the exposed droplets. Initial values appropriate to those in the experiments were chosen for (a) the number concentration of aerosol droplets, (b) the concentration of MnS04 in the droplets, (c) Z.O.L.D.parameters which had been experimentally measured on the (dry) MnSO, content of sampled droplets, and (d) the gas phase concentration of SO2. From these values, the initial volume fraction V(0) of the liquid phase of the aerosol, and the initial equilibrium water vapour pressure may be calculated, giving a complete set of initial conditions. The growth was then calculated by evaluating the yield of the reaction in a time increment At (typically 0.1 min), and deriving the value of the equilibrium vapour pressure for the new liquid phase concentrations. The vapour pressure change was then converted to a change in Vfrom a total water balance on the vapour-liquid system.For convenience, this calculation of condensation and concentration was iterated.l Using the ideality assumptions stated above the increase in liquid volume fraction due to the transfer of SO2 and oxygen to the liquid was then calculated, and added to the increase due to water condensation to give a total volume increment AV in the time increment At. The growth function I(t) was then evaluated in the form of the finite difference approximation 1 AV V(t) At' I ( t ) = -- (3) The total water content of the system in both phases was used as a check during the st ep-w ise calculation. The equilibrium vapour pressures over solutions of MnSO, and H2S04 were c a l ~ u l a t e d , ~ ~ using the method of Low,2o to obtain water activities from tabulated values 21 of the mean ionic activity coefficients of the species of interest.The theory only strictly applies to solutions of single electrolytes, and the situation in this case2694 CATALYSED OXIDATION OF so2 I N AEROSOLS is further complicated by the presence of a common sulphate ion. Again, an idealised approach has been adopted, with the water activity of the solution of mixed electrolyte assumed to equal the product of the water activities that would be derived for each electrolyte individually. Although theoretically unsatisfactory, it is not anticipated that gross errors will occur as a result of this approximation. The variation with time of the droplet growth function I(t), and the volumetric increase of the droplets are illustrated in fig. 3, for a calculation using the same initial aerosol conditions as in fig.1 and 2. In table 2, column 4, are shown the mass mean diameters, Z3, at various times, resulting from further calculations using eqn (2) and the relation ii3 = aM exp (2.50;). The initial conditions were appropriate to the experiments described below, viz. aM = 0.2 pm, o0 = 0.32, (MnS04}L,0 = 0.4 mol dm-3, (SO,) v,o = 63 v.p.m., V(0) = 1.1 x cm3 m-3. 1.20 7 2x10-2 3 5 - 1.15 2 M ,./---- 0 0 4 8 12 16 20 24 28 32 time/min FIG. 3.-Function of droplet growth, I(t), (solid curve) and the fractional volumetric growth (broken curve) in the computation depicted in fig. 2. EXPERIMENTAL A block diagram of the apparatus is given in fig. 4. A stream of aqueous manganous sulphate aerosol (4.9 dm3 min-I) is mixed with an air stream (0.1 dm3 min-’) containing the required SO2 concentration, and introduced into a series of tubular reaction vessels (4 to 5 cm dim.).The aerosol-SO2 contact time before sampling and measurement could be chosen by connecting up to twenty-five 2-m long vessels in series by means of glass U-bends (radius 6 cm). The aerosol generator was of the dispersion type,lg in which a stream of humidified, filtered air atomises a bulk solution of manganous sulphate. The SOz- containing stream was prepared by introducing slugs of “ reagent grade ” SO2 into a humidi- fied, filtered air stream by means of a Wosthoff dosing valve, and dispersing to a uniform concentration by passage through ballast volumes.22 The integrity of this system was checked by SO2 absorption and titrimetric determination.The apparatus containing the aerosol and the S02/air mixture was constructed largely of glass, with greaseless cone-and-socket joints, and ball-and-socket joints sealed by PTFE-coated O-rings. Polyethylene tubing was used for flexible connections, being more suitable than plasticised PVC. S02-containing gas streams were allowed to pass through polyethylene tubing for 1 h prior to use for experimentation, to allow any adsorption/ desorption processes to eq~ilibrate.~~ Care was taken in the design of the apparatus to avoid turbulence in particle-containing streams.P . W. CAINS A N D M. D . CARABINE 2695 Measurements were made of the relative huinidity of the gas streams at the mixer outlet, with and without the S02-containing stream.The values, in excess of 96 %, exceeded the equilibrium vapour pressure over a saturated solution of manganous sulphate (94.3 %). Experiments were designed as follows : (i) to measure, in the absence of SO2, the size distribution and number concentration of the manganous sulphate residues obtained by evaporation of the solution aerosol droplets ; (ii) to measure, with and without SO2 present, the size distributions of the aerosol droplets in suspension, after a series of aerosol residence times ; (iii) to measure the changes in gas-phase SO2 concentration after a series of aerosol- SO2 contact times. The information in (i) was obtained by sampling the aerosol with a reciprocating-head thermal precipitator, and examining the dried residue by electron micrography.Samples of aerosol (60 cm3) were drawn from the stream at a rate of 7 cm3 min-l through the thermal precipitator head, the construction l9 of which closely resembles that described by Drum- m ~ n d . ~ ~ Its use ensured that a homogeneous sample could be isolated on the grid. The FIG. 4.-Schematic diagram of the flow-apparatus: G, aerosol generator; S, supply of SOZ- containing gas ; Mx, aerosol/gas mixing vessel ; TV, tubular residence vessels ; THM, temperature and humidity meter ; TP, thermal precipitator ; LS, light scattering photometer ; GS, gas sampling. The numerals denote points where connections can be made. 400 mesh copper sampling grids were coated with carbon, about 10 nm thick, by a flotation method. The samples were dried in an oven at 105°C for 1 h to ensure conversion of the residues to the monohydrate phase MnS04 .H20. The appearance of the circular deposits on the transmission electron micrographs was consistent with the formation of amorphous rn~nohydrate,~~ and no evidence of crystallinity could be detected. Additionally, some samples were shadowed with Au/Pd to determine the ratio of the thickness of the deposits to the diameter of their circular (transmission) cross-section. A value of this “shape factor” of 0.27, with a standard deviation of 0.077, was obtained from a sample of 174 particles. The residues on the micrographs obtained by the transmission method were subsequently counted and sized to give their size distribution, and the number concentration of the original droplets. The size distributions of the solution aerosol droplets, [i.e., (ii) referred to above], were obtained by the light-scattering technique of Carabine and Moore,2 using linearly polarised incident radiation with the electric vector perpendicular to the scattering plane.The size distributions encountered in this work were more polydisperse than those considered by Carabine and Moore ; early electron microscopic measurements had indicated a small modal diameter (< 0.4 pm) and a large spread parameter (ao 2 0.4). The performance of the light scattering data inversion procedure was consequently extensively tested for these conditions. The results indicate that providing (a) the light-scattering intensities obtained are not too inaccurate, ( E + 3 %), (b) sufficient angles (12 or 13) have been sampled, includ- ing some in the forward direction with the scattering angle < 40°, and (c) the “ initial guess ”2696 CATALYSED OXIDATION OF so2 I N AEROSOLS values of a M and oo supplied do not deviate grossly from the expected values, the results obtained will be acceptable.The aerosol was passed through the light scattering apparatus by containment in a nitrogen gas " sheath " in an arrangement similar to that employed by Carabine and Maddock.6 Finally, the gas phase concentration of SOz was analysed using a flame photometric detector. The results were not particularly useful owing to the relatively small quantities of SOz that would be expected to be absorbed by the aerosol, and the relatively large amounts absorbed by the liquid deposited in the tubular vessels during the course of an experiment.RESULTS FACTORS OTHER THAN so2 ABSORPTION AND OXIDATION AFFECTING AEROSOL SIZE DISTRIBUTION The technique of thermal precipitation, followed by electron micrography of the dried droplets was applied (a) to the generator outlet to assess the aerosol at source, and (b) to the (unreacted) aerosol after various residence times in the absence of the SO,-containing stream. An example of the size distribution of the residues deter- n ' I 1 I 1 1 1 diameter /pm FIG. 5.-Distribution of sizes of dried residues (MnS04. HzO) from droplets at aerosol generator outlet, counted from electron micrographs. The curve is the fitted Z.O.L.D. with aM = 0.06 pm, uo = 0.73. Aerosol flowrate = 4.0 dm min-I ; MnS04 concentration = 0.09 mol dm-3.mined from such micrographs is illustrated in fig. 5, together with the fitted Z.O.L.D. distribution function. Except in cases of high residence times where the particle number concentrations were lower (table l), the histograms were based on samples of 500-1000 particles. It is not profitable to quantify the fit of the data to the Z.O.L.D. function with such small samples,lg but the agreement typified by fig. 5 is sufficient to validate the assumption of a Z.O.L.D. in inverting the light scattering data. The confident assignment of Z.O.L.D. distribution parameters to size data as obtained above would require the deposition and sizing of very large numbers of particles (> lo4 for a standard error of % 5 %). In particular, the values of the spread parameter o0 obtained by this method were large compared with light scattering results.1g However, evaluation of the mass mean diameter from such data is more feasible and results obtained suggested that the MnSO, concentration in the aerosol droplets was in the range 0.07-0.49 mol dm-3.The data were insufficient to determine a significant variation of mass mean diameter with concentration of the generator solutions, in the range 0.09 to 0.41 mol dnr3. Experiments with a more dilute solution (0.02 mol dm-3) yielded a lower residue particle size. The light scattering technique was used to analyse the aerosol droplet size dis- tribution in the absence of the SO,-containing stream. Results, given in table 1, columns 5 to 8, showed good consistency.Over the range of residence times used,P. W. CAINS AND M. D. CARABINE 2697 particle coagulation is likely to account for significant changes in size distribution and number concentration. It is convenient to discuss size changes in terms of the particle mass mean diameter. Predictions of the changes in size and number con- centration have been made,lg based on the classical model of Brownian coagula- t i ~ n , ~ ~ ’ 2 8 using the computational method of Willis et ~ 1 . ~ ~ The values obtained from these calculations are given in table 1, columns 4 and 2. The agreement between the calculated and experimental values of the mass mean diameter is very satisfactory. The experimental number concentrations, determined by thermal precipitation and electron micrography, are relatively lower, and decline more rapidly, than the calculated values.This indicates that some removal of particles from the suspended phase was occurring, and the appearance of a “ condensate ” inside the upstream parts of the residence vessels after long periods of running tended to con- firm this. TABLE AEROSOL PROPERTIES AS A FUNCTION OF RESIDENCE TIME IN THE ABSENCE OF SOz size measurements droplet number light-scattering size measurements with S02-introduction stream in operation, concentration mass mean in the absence of the S02- /cm-3 diameter introduction stream but with zero SO2 estimated content aerosol estimated from residence from experimental, coagulation no. of Z.O.L.D. parameters mass mean no. of mass mean time coagulation by electron theory data sets from fitted function diameter data sets diameter /min theorya micrography /pm inverted &pm uo /pm inverted /pm 0.96 1.9 x 106 5.5 x 105 0.2Sb - - 2.6 1.7X106 5.1x105 0.29 4 0.22 0.32 0.29 - - 6.0 1.5x106 1.6XlO5 0.31 4 0.23 0.33 0.313 5 0.27 11.0 1.3~106 1.3xlOS 0.33 5 0.25 0.32 0.325 6 0.30 21.0 9 .o ~ 1 0 5 9.1 x 104 0.37 3 0.26 0.33 0.345 5 0.36 a Postulated initial value = 2.6X 106 cm-3. - - - - hO.01 &0.03 f0.01 rtO.01 *0.03 &0.004 *0.02 10.006 L-0.004 kO.004 *0.02 10.002 *0.005 rt0.002 rt0.02 Postulated initial value. In the last column of table 1 are the results of size analysis (light scattering) of aerosols which had been contacted with the carrier gas brought from the SO2- introduction equipment but with no SO2 present. These experiments were under- taken because the maximum relative humidity obtainable in the SO,-inducing stream was about 55-60%.This would cause a reduction in the humidity of the aerosol stream, and may have resulted in droplet shrinkage. These results are less reliable than those in column 8, being based on only 12 light scattering data points instead of the usual 14 or 15. The results at a residence time of 11.0 min are believed to be the most reliable.lg The results indicate that the size change brought about by the lower humidity in the SO2 introduction stream is less than the detection limit of the light scattering apparatus. EXPERIMENTAL OBSERVATIONS USING AEROSOLS I N THE PRESENCE OF so2 A simple, qualitative test was initially carried out to establish that the acid- producing oxidation reaction was occurring.Membrane filters (Millipore VS) were used to extract the droplets from the aerosol over a run of about 30 min (Le., from about 150 dm3 of aerosol) and after the samples had been taken into aqueous solution, the pH and response to acid BaCl, solution were compared with those of control samples. The results were positive : this incidentally confirmed that at least some of the particles present in the system were solution droplets, since solid2698 CATALYSED OXIDATION OF so2 I N AEROSOLS MnSO, cannot promote the oxidation. This was corroborated by the observed humidity values. The initial SO2 concentration (63 v.p.m.) is a value which might be expected 30 at some 10-15 m from a power-station stack exit, if an inverse square law model for dispersion 31 is assumed.The droplet mass mean diameters measured by light scattering with varying contact times are summarised in table 2. Those in column 2 were derived from scattered light intensities which had been averaged over four different experiments. TABLE 2.-LIGHT SCATTERING DETERMINATION OF PARTICLE SIZE AFTER VARIOUS RESIDENCE TIMES IN THE PRESENCE OF so2 ((MnS04)L,0 = 0.16 mol dm-3 ; (SO2)v,o = 63 v.p.m.) residence time lmin particle size (mass mean diameter) from averaged light scattering intensities lclm 0.69 0.26 0.96 0.24 2 . 6 0.25 6.0 0.27 11.0 0.27 21 .o 0.38 particle size (mass mean diameter) from selection of inversion results I m 0.26 0.24 0.25 0.30 0.37 0.39 theoretically predicted diameter I m 0.26 0.27 0.28 0.30 0.32 0.35 TABLE 3 .-TYPICAL RESULTS FROM LIGHT SCATTERING INVERSION PROCEDURE FOR AEROSOL IN THE PRESENCE OF so2 residence time = 6.0 min CZM, “‘0 values used Z.O.L.D.parameters no. of light to initiate data from fitted (inverted) mass mean scattering inversion procedure function diameter run no. angles used alr/pm “‘0 a d p m “‘0 /Pm 10.1 12 0.2 0.1 10.2 12 0 . 2 0.1 10.3 12 0.2 0.1 10.4 13 0.2 0.1 averaged 13 0.2 data 0.1 0.7 0.5 0.7 0.5 0.7 0.5 0.7 0.5 0.7 0.5 0.904* 0.050 0.051 0.050 0.064 0.065 0.140 0.140 0.111 0.111 0.139* 0.702 0.727 0.728 0.694 0.691 0.552 0.552 0.597 0.597 0.95* 0.17 0.19 0.19 0.21 0.21 0.30 0.30 0.27 0.27 Because the light scattering method can be subject to quite large and identifiable errors in data recording and in inversion, we take the view l9 that some selected results, shown in column 3, are more reliable than those based on averages.To exemplify the selection criteria used, four experiments for the 6 min contact time are detailed in table 3. The following points justify selection of 10.4 as the most reliable. The asterisked results from one inversion of run 10.1 are clearly caused by a local minimum problem in the minimisation procedure 32 ; error contours confirm this. The values of aM around 0.05 to 0.06 ,urn can be rejected because they are as low as the modal diameters of dried residues ( c . 5 fig. 5), and because the aerosol is un- questionably one composed of liquid droplets; the data in these runs 10.1 to 10.3 are intrinsically less reliable than in 10.4 because in the latter a thirteenth limiting forward angle of scatter was usable, whereas in 10.1 to 10.3 at this angle there was excessive noise originating in temporal variations in concentration of droplets at the upper extreme in size.P .W. CAINS AND M . D . CARABINE 2699 DISCUSSION The experimental analysis by light scattering has been successful in measuring the variation in size of droplets with residence time in the flow system under the conditions chosen-ambient pressure and temperature (2 1 "C), SO, concentration 63 v.p.m., relative humidity in excess of 96 %, MnS04 concentration in the range 0.07-0.49 mol dm-3 (or 0.24-1.7 mg m-3 gas phase), in droplets of 0.25 to 0.40 pm mass mean diameter, at number concentrations of lo5 to lo6 ~ m - ~ . The analysis by thermal precipitation and electron microscopy clearly indicated depletion of particulate material, particularly in the upstream parts of the apparatus (column 3, table 1).The loss by sedimentation of particulate material of the order of size dealt with in this work should be minimal; an aerosol consisting of 2.6 x lo6 ~ m - ~ of 1 pm particles should sediment out only 8 x lo3 ~ m - ~ particles in conditions analogous to those of the 21.0 min residence time e~perirnent.~,. 33 However, if regions of local supersaturation are created in the presence of particles, the latter will act as nuclei for the condensation of excess vapour present. These particles thus become enlarged and their removal by sedimentation may become marked. It was not possible to produce experimental evidence for this theory, but com- paratively small temperature fluctuations might have produced this effect.TABLE 4.-cOMPARISON OF PERCENTAGE PARTICLE GROWTHS MEASURED WITH THOSE PREDICTED FROM THEORY experimental particle growth experimental particle growth theoretical particle growth in absence of SO2 in presence of SO2 due to SO2 reaction (Le., coagulation) residence mass mean mass mean mass mean timelmin diam./pm % change diam./pm % change diam./pm % change - - 0.69 0.26 - 0.26 0.96 0.24 -7 0.27 1 2.6 0.25 - 3 0.28 6 0.29 - 6.0 0.30 16 0.30 13 0.31 7 11.0 0.37 41 0.32 21 0.33 14 21.0 0.39 50 0.35 32 0.35 21 - The results of the analysis of SO2 in the gas phase, although self-consistent, were not reliable as a measure of the uptake of SO2 in the droplets, since it appears that much more was absorbed in the liquid deposited on the walls of the apparatus.It is clear that acidity measurement on collected droplets would have been a preferable method of detecting the uptake, which is predicted only to be about 1 to 2 parts in 63. However, it can be anticipated that such analyses would be subject to well-known difficultie~.~~? 3 5 Separation of the effects on particle size distribution of SO,-induced growth and of coagulation is impossible in these experiments, since they occur on similar time scales, and has not been achieved in the theoretical predictions above. However, some progress can be made as follows in comparing the results with theory. As shown above (table l), the coagulation in the absence of SO, is consistent with the simple Brownian model.In table 4 the absolute sizes and percentage growths from the light scattering measurements are compared directly with the growth theory calculations (presented previously in table 2, column 4). Overall, there is fair agreement, and at high residence times the particle size is larger than the growth theory predicts. Also repeated here are the mass mean diameter values observed in the absence of SO,, (from table 1). It may be concluded that the effects of growth2700 CATALYSED OXIDATION OF so2 I N AEROSOLS are likely to be discriminated only at longer residence times (6 to 21 min). This is due to the limited accuracy of the light scattering technique-it is not within its scope to detect the small changes in modal diameter which would result from growth at shorter times.lg It should be noted that, since the volume fraction of particles in the experimental aerosol is 2 orders of magnitude lower than the values used to obtain fig.3, it is understandable that the growth is considerably greater than the values illustrated there. At residence times > 6 min, the margin by which the measurements (columns 2 and 3) exceed the growth theory predictions (columns 4 and 5) may be attributed to the simultaneous and coupled coagulation in the real system. RATES A N D YIELDS PREDICTED BY THE CALCULATIONS Experimental values of droplet growth in tables 2 and 4 provide evidence that the assumption of homogeneous reaction control is justified, and that the kinetics of the reaction in the situation of the experiments may be described by the rate constants given.TABLE s.-cALCULATED RATES OF so2 REACTION IN AEROSOL DROPLETS (MEASURED BY FALL IN GAS PHASE CONCENTRATION IN FIRST 3.5 min), COMPARED WITH INITIAL VALUES OF VARIOUS PARAMETERS rate volume fraction -A{SOz}v/v.p.m. min-1 V/cm3 m-3 {SO*}v/v.p.m. {Mnz+)L/mol dm-3 At {Mnz+JLx V calculation A 1.6 63 0.35 5 calculation B 0.7 63 0.35 3 calculation C 1.6 63 0.14 2.5 ratio A/C 1 1 2.5 2 ratio A/B 2.3 1 1 1.7 ratio B/C 0.43 1 2.5 1.1 (fig. 2) 0.56 0.25 0.22 2.5 2.2 1.1 It is clear that the use of the model of Matteson et al. has not lecl to realistic resulis when their rate constant values are used (fig. 1). With the revised rate constants, acid concentrations in the range 1 to 2 mol dm-3 are predicted (fig.2,3), in agreement with those quoted by other authors for the manganese-catalysed oxidation at equiva- lent sulphur dioxide concentration^.^^ 16* l 7 The revised values of kgr and k7 are also numerically consistent with the stability constant for the system 33 Mn2++SO$- + Mn SO4. In these calculations, as in those of other authors 14* l 5 no attempt was made to allow for the reduction in sulphur dioxide solubility as the acid concentration in- creased. A reduction in solubility of x 60 % has been observed for H2S04 of molality 0.09.36* 37 Calculations using different initial conditions showed the same qualitative features as those of fig. 2. In table 5 the respective rates of SO2 removal (using the rough measure of the decrement in the first 3.5 min) are compared with the various initial values of parameters V (volume fraction), (Mn2+IL, and the product (Mn2+}L x V.It is clear by inspection of the last three rows that the rate is deter- mined in part by the latter product. This enables us to emphasise that the complex reaction mechanism simplifies, as far as initial rate is concerned, to control by the first step. for The resulting simple model is one of a series described recently ransfer of a vapour to a droplet in which it reacts.P. W. CAINS AND M. 1). CARABINE 2701 For this case, if an involatile solute, B, reacts in a second order reaction with a volatile one, A, the rate law to be expected for the decrease in A per unit volume of aerosol is --- d'Ah - k(A)vHA(B),V. dt Denoting with subscript T the total concentration in both phases, then to the approxi- mation that {A}, = {AIV, and since -- - d'Ah dt - kLA)THA{B)T.The analogue in the reaction system considered here is -~ d{So21v = k{ SO,),H,,,( Mn2 + ILV. dt The total SO2 and Mn2+ concentrations per unit volume of aerosol emerge as determining the initial rate of sulphur dioxide removal. Against this background Ananth has made a useful attempt to compare results of various experiments, expressed in acid produced (m mol min-l) per mass of catalyst present (g Mn). In that review, the results of Matteson et al. are misrepresented because of an error in the time interval chosen and should be 0.476, 0.457 in these units. The results of our calculations are in the range 1 to 5 m mol min-' 8-l ; these are crude approxima- tions because rates are averaged over 5 to 30 min, and the values near 5 are subject to less error.As regards the sizes of droplets in which such acid may be located, determination of the size distribution by (a) coagulation and (b) reaction induced growth depends, as described above, on the number concentration and volume fraction of liquid: (i) with initially low values of number concentration (e.g., 2 or 3 x lo5 cm-3) and of V (e.g., cm3 m-3) growth will predominate as the process determining the size. (ii) If both have moderate values, (e.g., lo6 ~ m - ~ , cm3 m-3, as in experiments described here), both growth and coagulation will contribute. (iii) If both have initially high values (e.g., lo7 ~ m - ~ , 2 cm3 m-3 as in the calculations presented here, and in those by Willis et aZ.),29 coagulation will predominate.The authors thank the S . R. C . for a grant to P. W. C., and Prof. A. R. Ubbelohde for his interest and help. ' E. R. Gerhard and H. F. Johnstone, Ind. andEng. Chem., 1955,47,972. J. Freiberg, Atm. Em., 1975, 9, 661. K. P. Ananth, J. P. Galeski, F. I. Honea, EPA 1976, Rept. No. 600/2-76-257. P. M. Foster, Atm. Env., 1969, 3, 157. W. K. Poole and D. R. Johnston, Res. Tri. Inst. Rep., 1969, A.U. 229. M. D. Carabine and J. E. L. Maddock, Arm. Enu., 1976, 10,735. M. K. Azarniouch, A. J. Bobkowicz, N. E. Cooke and E. J. Farkas, Canad. J. Chem. Eng., 1973, 51, 590. €3. F. Johnstone and D. R. Coughanowr, Ind. and Eng. Chem., 1958, 50,1169. lo W. F. Espenscheid, M. Kerker and E. MatijeviC, J. Phys. Chem., 1964, 68, 3093. l 1 M. J. Matteson and W. Stober, J. Colloid Interface Sci., 1967, 23, 203. l 2 M. D. Carabine, J. E. L. Maddock and A. P. Moore, Nature (Phys. Sci.), 1971, 231, 18. l3 L. I. Kastanov and C . A. Guljanskaja, Zhur. obshchei Khim., 1936, 6, 227. l4 M. J. Matteson, W. Stober and H. Luther, Ind. and Eng. Chem. (Fundamentals), 1969, 8, 677. * H. Bassett and W. G. Parker, J. Chem. Soc., 1951, 1540.2702 CATALYSED OXIDATION OF so2 I N AEROSOLS R. A. Wadden, J. E. Quon and H. M. Hulbert, Atm. Em., 1974,8,1009. l6 H. F. Johnstone, Ind. and Eng. Cizem., 1931, 23, 559. l7 R. L. Copson and J. W. Payne, Ind. and Eng. Chem., 1933,25,909. '* D. R. Coughanowr and F. E. Krause, Ind. and Eng. Chem. (Fundamentals), 1965, 4, 61. 2o R. D. H. Low, J. Arm. Sci., 1969, 26, 608. 21 R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworth, London, 1959). 22 H. D. Axelrod, J. B. Pate, W. R. Barchet and J. P. Lodge, Atm. Em., 1970,4, 209. 23 R. L. Byers and J. W. Davies, J. Air. Polln Contr. Assoc., 1970, 20, 236. 24 D. G. Drummond (ed.), J. Roy. Micros. SOC., 1950, 70, chap. 4. 2 5 Inorganic and Theoretical Chemistry XII, ed. J. W. Mellor (Longmans Green, London, 26 M. D. Carabine and A. P. Moore, Faraday Symp. Chem. Sac., 1973,7, 176. 27 M. v. Smoluchowski, Phys. Z., 1916, 17, 557, 585 ; 2. phys. Chem. (Leipzig), 1918, 92, 129. 28 H. Miiller, Kolloidchem. Beih., 1928, 27, 223. 29 E. Willis, M. Kerker and E. Matijevic, J . Colloid Interface Sci., 1967, 23, 182. 30 R. J. Bibbero and I. G. Young, Systems Approach to Air Pollutioiz (Wiley, N.Y., 1974). 31 R. Scorer, Air Pollution (Pergamon Press, Oxford, 1968). 32 A. P. Moore, Ph.D. Thesis (Univ. London, 1974). 33 Aerosol Science, ed. C. N. Davies (Academic Press, N.Y., 1966). 34 R. E. Lee and J. Wagman, Amer. Ind. Hyg. Assoc. J., 1966, 27, 268. 35 J. D. Husar, R. B. Husar, E. S. Macias, W. E. Wilson, J. L. Durham, W. K. Shepherd and 36 L. G. Sillkn and A. E. Martell, Chern. SOC. Spec. Pub. (Chem. SOC., London, 1964), no. 17, p. 37 D. K. Oestreich, EPA 1976, Rept. No. 600/2-76-279. P. W. Cains, Ph.D. Thesis (Univ. London, 1975). 1932), p. 401. J. A. Anderson, Arm. Em., 1976, 10, 591. 240. (PAPER 7/1154)