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Simulation of formation and growth of atmospheric sulfate particles
Pergamon
J. Aerosol Sci. Vol. 28, No. 1, pp. 107-119, 1997
PIh S0021-8502(96)00063-8
Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0021-8502/96 $17.00 + 0.00
S I M U L A T I O N O F F O R M A T I O N A N D G R O W T H OF A T M O S P H E R I C S U L F A T E PARTICLES Mihalis Lazaridis** and Petros K o u t r a k i s ~ * Laboratory of Atmospheric Physics, School of Science-PhysicsDepartment, Aristotle University of Thessaloniki, Campus Box 149, Thessaloniki 54006, Greece : School of Public Health, Harvard University, 665 Huntington Ave., Boston, MA 02115, U.S.A. (First received 1 December 1995; and in final form 17 May 1996)
Abstract--This paper investigates the formation and growth of aerosol sulfate particles in the atmosphere. The evolution of the aerosol size distribution with time was modeled using the aerosol general dynamic equation. This equation was solved numerically using a discrete-nodal point method to describe the particle size distribution. For the initial size distribution we have used an average urban accumulation mode. The first step in our model considers the oxidation of SO2 by OH radicals, producing H2SO~). The next step considers the binary nucleation and condensation of the H2SO4-H20 system and its evolution due to coagulation and deposition mechanisms. A detailed description of the model is presented. The mass size distribution at different distances during the transport of the initial aerosol size distribution is also presented. The importance of different mechanisms on the evolution of the aerosol size distribution is discussed. Sensitivity analysis was performed for many model parameters where simulations were made at varying temperature, relative humidity and photo-oxidation rate conditions. Model calculations suggest that condensation growth is the dominant mechanism for the evolution of the size distribution of sulfate particles during moderate relative humidity conditions. Copyright © 1996 Elsevier Science Ltd INTRODUCTION Because of their effects on respiratory health and environment, atmospheric acid aerosols have been investigated by a large n u m b e r of researchers. Emissions of sulfur dioxide result in the formation of submicron sulfate particles (Whitby, 1978), which can be transported over long distances from their sources (Rodhe and Grandell, 1981; Eliassen, 1978). Acidic sulfate aerosols can remain mostly unneutralized during transport because of the low ambient a m m o n i a concentrations at low altitudes (Tanner et al., 1984). Sulfate particle concentrations exhibit significant seasonal and regional variations (Stevens et al., 1980; Ferek et al., 1983; K o u t r a k i s et al., 1989). Hering and Friedlander (1982) observed two distinct types of sulfate aerosols in Los Angeles with mass median diameters of 0.54 ___0.07/~m and 0.20 + 0.02 #m, respectively. The first type is consistent with an aqueous-phase episode during which sulfuric acid formation t o o k place within the droplets, whereas the second results from h o m o g e n e o u s gas-phase SO2 oxidation. J o h n et al. (1990) m e a s u r e d the particle size distributions of inorganic charged particles. The observed distributions were characterized by three modes, one at 0.2 + 0.1/~m (gasphase reaction products), one at 0.7 + 0.2/~m, and a coarse mode. G r o w t h of the first m o d e due to condensation of water and sulfate m a y have resulted in the formation of the second mode. K o u t r a k i s et al. (1989) and K o u t r a k i s and Kelly (1993) studied the equilibrium size of atmospheric aerosol sulfates at different relative humidities and observed a relationship between the mass median geometric a e r o d y n a m i c diameter of sulfate particles and b o t h particle acid content and ambient relative humidity. Sulfate particles were found to be mainly in the a c c u m u l a t i o n mode. Brosset et al. (1975) examined the nature and possible origin of acid particles at the Swedish coast. T w o types of acid particles were indentified. The first presented a size distribution between 0.5 and 1.5 ~tm, possibly generated by SO2 diffusion into water droplets. This type was associated with the transport of air-borne dark particles from the Present address: EOHSI, 681 Frelinghuysen Road, Piscataway, NJ 08855-1179, U.S.A. 107
108
M. Lazaridisand P. Koutrakis
European Continent (Brosset, 1976). The second type presented a size distribution of less than 0.4/~m and was attributed to the photochemical oxidation of SO2 and the formation of new particles. The new particles, consisting mainly of acid ammonium sulfate, were probably formed over the North Sea and transported over Sweden. Sulfate aerosol episodes were also observed by Huntzicker et al. (1984). Some of the episodes were associated with the presence of freshly generated sulfates, formed through the oxidation of SO2 by OH radicals with subsequent nucleation and condensation, while other episodes were associated with long-range transported sulfates. In addition, high concentrations of pre-existing aerosol particles in the atmosphere were found to suppress nucleation (Lin et al., 1992; Hegg et al., 1992; Whitby, 1978). Sulfate particles grow larger with increasing relative humidity (Tang et al., 1978; Winkler, 1988; Keeler et al., 1988; Koutrakis et al., 1989). Growth of hygroscopic aerosols was also studied by others (Svenningsson et al., 1992; Winkler, 1988). These studies show two different modes of hygroscopic growth, as well as effects caused by insoluble material in the aerosol droplets. In the present paper we investigate the importance of different mechanisms of sulfate particle formation and growth during a mesoscale range of transport. The aerosol general dynamic equation (Friedlander, 1977; Jokiniemi et al., 1994) is used to model the evolution of the sulfate particles. In addition, sensitivity analysis was performed for many model parameters. The sulfate formation by aqueous-phase oxidation of SO2 was not investigated, since this study does not examine cloud and fog conditions, where this mechanism appears to be important (Hering and Friedlander, 1982). MODEL CALCULATIONS General dynamic equation
Aerosol dynamics describe the evolution in space and time of the particle size distribution and the chemical composition. In the present work we investigate the aerosol dynamics using the aerosol general dynamic equation (GDE), which is solved in a one-dimensional form along the wind direction (Friedlander, 1977; Jokiniemi et al., 1994): dn k
1 j k 6 ( k _ k*) +
dx
u
+
\ dx/coag
nk,
\ dx/grow
(1)
uA V
where nk is the particle number concentration for a size class k with particle radius rk; the terms on the right-hand side of equation (I) correspond, respectively, to (1) particle formation due to binary homogeneous nucleation mechanism (* indicates nucleating embryo), (2) the coagulation mechanism, (3) growth by condensation and chemical reactions, and (4) particle removal due to deposition; Va is the particle deposition velocity, Ad is the settling area (equal to the bottom of the considered cell in the simulations) in every axial volume step (AV is the axial volume step), u is the wind velocity, Jk is the nucleation rate and 6 is a delta function. In our calculations, particle Brownian diffusive deposition and sedimentation have been modeled. The solution of the G D E is based on a discrete-nodal point method. The discrete grid can be used up to a user-specified number of coagulated molecules (k-mer), after which the nodal point grid is used (Jokiniemi et al., 1994). In the discrete scheme, in the case where only one species is nucleating and the formed aerosol particles are chemically homogeneous, the number of grid points is the number of molecules in the cluster. Therefore, the radius of an i-mer cluster is ri = (i + l)I/3ro, where ri is the radius of the i-mer and ro is the monomer radius. In the case that we have more than one chemical species we have to keep track of all particles which have different size and chemical composition and in this case we make use of the nodal point size grid. In the nodal point method the number distribution is divided into n - I nodal points distributed evenly according to the logarithm of particle radius (Jokiniemi et al., 1994).
Simulationof formationand growth of atmosphericsulfateparticles
109
The rate of molar concentration change of gas-phase species is given by the gas-phase conservation equation and the mass size distribution of different species and can be calculated by solving the condensed-phase species equation (Jokiniemi et al., 1994):
I_
d×
..]gtp L
d×
Jeoa, uAV
where Pak and Y~k are the average density of particles in the kth grid point and the composition of species j at the kth grid point respectively; the term gtp corresponds to the formation and growth of aerosol particles due to mechanisms of nucleation and condensation; the term coag refers to coagulation mechanism; and the time is related to the axial position through the wind velocity u. In these calculations several input parameters are needed. The first is the sulfuric acid production rate. Assuming that the oxidation of SO2 by OH radicals is the dominant formation mechanism of H/SO~ ) in the atmosphere, the production rate can be determined using the following equation: d[H2SO4] - k[SO2] Ion], dt
(3)
where k is the reaction rate constant, k = 1.2 x 10- xz molecules- 1 cm 3 S- 1 (Lin et al., 1992); [SO2] and [OH] are the respective concentrations of the gases; and the assumed daytime concentration of the hydroxyl radical [OH] is 5 × 106 molecules cm- 3. Other calculations were also made using a lower oxidation rate (k = 7x 10-~3molecules-lcm3s -1) and a radical concentration of [-OH] = 106 molecules cm-3 in order to examine the effect of k [OH] on the size distribution evolution. Both oxidation rates presents realistic values for atmospheric conditions. Sensitivity analysis was also performed by varying the photooxidation rate during transport. The second step in our model calculations includes the formation of H E S O 4 - H 2 0 particles due to binary nucleation. It is not yet known whether the incorporation of NH 3 into H 2 S O 4 - H 2 0 particles occurs before or after their formation. Here, it is assumed that NH3 associates with the H 2 S O 4 - H 2 0 system after particle formation. This assumption may lead to underestimation of the nucleation rate if NH3 reacts with H2SO~ ) before nucleation, since the nucleation of ammonium bisulfate is more efficient than the H E S O 4 - H 2 0 system (Raes and Van Dingenen, 1992). However, since ambient ammonia concentrations decrease with elevation, ammonia concentrations should be at sub-ppb levels at relatively high elevations (Tanner et al., 1984). The mass and number distribution for the pre-existing aerosols are needed to perform our calculations. We have used a typical aerosol distribution of continental air (Whitby, 1978; Hering and Friedlander, 1982). The relative humidity was set to 52 and 86% and the temperature to 20°C for the first simulations (see Figs 1-3). In the following simulations a sensitivity analysis was performed for the SO2 photo-oxidation rate and nucleation formation, where the temperature and relative humidity values were varying during transport. The main mechanisms considered in our calculations are described in the following sections. Binary nucleation
The binary nucleation of the H E S O 4 - H 2 0 system is calculated in a manner analogous to the one adopted by the revised classical theory (Wilemski, 1984). We have calculated the nucleating value of the free energy barrier using the equation /)bAfla = OaA~b, at the nucleation point, which determines the composition of the embryo (vi, Apl are the molar volume and the change of the chemical potentials between the gas and liquid phases of the species i). Several expressions have been presented for the kinetic part of the nucleation rate in the theory of binary nucleation leading to differences in the evaluation of the nucleation rate
110
M. Lazaridis and P. Koutrakis
(e.g. Kulmala and Laaksonen, 1990). However, differences in the pre-exponential factor of the nucleation rate had little effect on our predictions. Variations in the SO2 photooxidation rate, the relative humidity, temperature and [ O H ] were far more important. A sensitivity analysis of these parameters is presented in the next section. In order to calculate the free energy barrier AG from the classical model of binary nucleation, values for activities, densities and surface tensions as functions of temperature are necessary. The chemical potentials in the liquid phase were estimated using the method of Giauque et al. (1960). The surface tension of the mixture was estimated using the data of Sabinina and Terpugow (1935). The densities of the solutions were calculated using polynomial fitting of the data obtained from the Chemical Engineer's Handbook (1973). The saturation vapor pressure of sulfuric acid was determined using the expression derived by Kulmala and Laaksonen (1990), which is based on the experimental data from Ayers et al. (1980). The activity coefficients were calculated using a fitting of available experimental measurements. The process is based on the method by Reid et al. (1987) and the measured points can be found in the Chemical Engineers' Handbook (1973). From the saddle point conditions OAG/~?ni = 0 (ni is the number of molecules of species i in the droplet) we derive the generalized Kelvin equations, which were subsequently used to determine the mole fraction X of species at the saddle point. The nucleating radius (r*) of the binary droplet is given by (Lazaridis et al., 1992)
r* =
- 2a(Xvb + (1 - X ) / ) a ) X k T ln(Abg/Abe) + (1 -- X ) k T ln(Aag/Aat) '
(4)
where a is the surface tension of the binary droplet, k the Boltzman's constant, T the temperature, vl the molar volume and Aig and Aie are the activities in the gas phase and in the liquid phase of species i respectively. Aag = Pa/Pas, Abg = Pb/Pbs, Aa~ = P . . . . l/Pat, Ab~ = Pb,sol/Pb~(Pas and Pbs are the respective equilibrium vapor pressures of water and acid vapor over a flat surface of pure substance and Pi,sol is the partial pressure of species i over a flat surface of the solution). The nucleation rate can be determined using the following equation (Lazaridis et al., 1992):
J=RavFZexp(--
A~_),
(5)
where Rav is the average condensation rate, F is the total number of nucleating molecules, Z is the Zeldovich non-equilibrium factor, k is the Boltzmann factor, and T is the absolute temperature. The only experimental value reported for the accommodation coefficient for H2SO4 molecules was between 0.02 and 0.09 at a relative humidity of 50% (Raes and Van Dingenen, 1991). We chose this value, even though it is in contrast with the accommodation coefficient near to the one reported for the H N O 3 - H 2 0 system (Rudolf and Wagner, 1994).
Binary condensation The condensation rate of H z S O 4 onto the pre-existing aerosol particles is described by a modified Mason equation (Mason, 1971), where the transitional correction factors are included:
dm dt
4nr(S~ - S,,fl (NM/flM) + (NT/flT)'
(6)
where
RgT~ NM -- D~Mp.,(T.~)
and
NT = L ~
L(~ "~ \/~g~ ~,/ .
(7)
Simulation of formationand growth of atmospheric sulfateparticles
111
tiM and fiT are the transitional correction factors for the mass and heat transfer, ps is the saturation pressure, Rg is the ideal gas constant, D~ is the binary diffusion coefficient, M is the molecular weight of the liquid, L is the latent heat of condensation, S~o,s is the saturation ratio of the gas far from the particles, and Sr, s is the saturation ratio of gas species j at the particle surface calculated using the following equation: Sr, s = A s exp \ r R g p T , J '
(8)
where a is the surface tension, p is the density of the liquid film on the droplet, T~ is the droplet temperature, and As is the chemical activity of species j which can be expressed as a function of the mole fraction of the condensable species in the liquid droplet (x j) solution and the molal activity coefficient (~s): As = xsTs (Reid et al., 1987). In our calculations we have used background aerosol particles with a density of 1.1 g cm-3. It is assumed that the particles are wettable and the initial mole fraction of the liquid film on the particles is calculated with the use of the binary heterogeneous nucleation theory (analogous to the revised classical nucleation theory) (Lazaridis et al., 1992). Coagulation Due to the coagulation process, particles are both removed and added to size bins. In our study the processes of Brownian diffusion and turbulent gravitational coagulation are considered (Williams and Loyalka, 1991). The general equation that controls the coagulation can be written as follows: dnk _ 2 i +~'=kK ( m i ' m s ) n l n j - - n k i= ~ 1 K ( m i , mk)ni,
(9)
where i + j = k means that the summation is taken over those grid points for which ml + m s = m k (ml is the mass of particle i) ni is the number of particles in bin i, and mk includes the mass of all the particles that are in bin k (Friedlander, 1977). Settling In the present model we use the gravitational deposition and the particle diffusion settling mechanisms. The sedimentation velocity is assumed to be the terminal velocity, calculated as the product of the gravitational accelaration (g) and the particle relaxation time (/)d = gTrel) (Friedlander, 1977). The particle relaxation time (Trel) is given by the equation Zrel = (2/9)(pr 2 Cn/#), where p is the density of the particle, r is the radius of the particle, Cn is the Cunningham correction factor, and/~ is the dynamic viscosity. The particle diffusivity D was calculated using the Stokes-Einstein equation (Hinds, 1982) D = ( k T Cn/6nr#), where k is the Boltzman constant and T is the absolute temperature. In the case of particle diffusivity the deposition velocity can be defined as the deposition flux divided by the undisturbed concentration (Hinds, 1982). The evaluation of the deposition velocity is needed to calculate the losses due to settling in equations (1) and (2). RESULTS AND D I S C U S S I O N The simulation of formation and growth of sulfate aerosols was performed by numerically solving the general dynamic equation. We simulated typical conditions of sulfur episodes for continental air. Sample calculations were performed with typical aerosol distributions and SO2 oxidation rates. Particle formation was simulated by including the following mechanisms: SO2 photo-oxidation; binary nucleation; condensation of the H2SO4-H20 system; coagulation; and settling. As mentioned above, a sensitivity analysis
112
M. Lazaridis and P. K o u t r a k i s RH: 52%, SO2: 4 2 p p b
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Fig. 1. (a) M a s s size distribution (dm/d In Dp) of sulfate at different distances during the t r a n s p o r t of the initial aerosol size distribution. (b) N u m b e r size distribution of sulfate particles at different distances during the transport of the initial aerosol size distribuiton ( [ S O 2]: 42 p p b (initial conditions), RH: 52%, T = 293 K, k = 1.2 x 10-12 molecules- 1 cm 3 s 1, [ O H ] = 5 x 106 molecules cm-3).
Simulation of formation and growth of atmospheric sulfate particles
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was conducted for relative humidity, temperature and gas-phase oxidation rate parameters, because of their non-linear effect on our model calculations. The change in size distribution of the aerosol sulfate particles was examined as a function of different parameters, including SO/ oxidation rate, relative humidity, and SO2 gas concentration. We have used as an initial size distribution an average urban accumulation m o d e aerosol (around 0.1-1/~m) analogous to that of Whitby and Sverdrup (1980) and Hering and Friedlander (1982). This is a log-normal distribution with a mass median diameter of 0.32 #m. F o r the representation of the size distribution we used a nodal point size grid with 60 nodal points. The wind velocity was chosen to be 1.11 m s -1, based on wind measurements made in the N o r t h Eastern United States during a pollution episode. Input data values were chosen also for the S O / c o n c e n t r a t i o n , relative humidity, and the temperature. Figure la presents the evolution of the mass size distribution of sulfate particles. These results are based on a moderate initial SO2 atmospheric concentration ([SO2]: 42 ppb, k = 1 x 10-12 molecules- 1 cm 3 s - 1, [ O H ] = 5 x 106 molecules c m - 3). Our model calculations suggest that sulfate mass is concentrated in the accumulation region, for particle diameters between 0.5 and 1.5/~m, in agreement with the experimental results of Koutrakis and Kelly (1993). Model calculations suggest that binary nucleation is negligible. The predominant mechanism of mass transfer of sulfur onto the aerosol particles is v a p o r condensation under these conditions; thus no new particles are formed during the transport of the air masses. Figure l b shows the evolution of the number size distribution at different distances. The particle deposition mechanisms remove the particles with diameters above 1.8 #m while the accumulation mode remains unaffected.
114
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Dp) o f sulfur
at mesosca]e t r a n s p o r t o f the i n i t i a l aerosol size
distribution ([SO2]: 2 0 0 p p b (initial conditions), RH: 86%, T = 293 K, k = 7 x les-1 cm3s 1, [ O H ] = 106 moleculescm 3).
10 13 molecu-
Calculations were made to investigate the effect of the oxidation rate on sulfur condensation (see Figs 3 and 4). These results suggest that the sulfate oxidation rate is a very important factor that determines the mass size distribution of sulfate charged particles. Figure 2 presents the time evolution of particulate sulfate mass from the initial distribution for lower values of the SO2 oxidation rate and O H concentration (T = 293 K, k = 7 x 10-13 molecules-1 cm3 s-1, [ O H ] = 106 molecules cm-3). As expected, lower oxidation rates result in a lower production rate of sulfuric acid molecules and therefore in lower sulfuric acid concentrations in the accumulation mode. Again under these conditions the nucleation rate is practically zero. We also considered the effect of higher SO2 concentration (see Fig. 3)([SO2]: 200 ppb, T = 293 K, k = 7 x 10 13 molecules 1 cm 3 S 1, [-OH] = 106 moleculescm 3). Nucleation was not observed even for this high sulfur dioxide level. Another simulation was performed allowing temperature and relative humidity conditions to vary (k = 7 x 10-13 molecules-1 cm3s 1, [-OH] = 106 molecules cm 3) during aerosol transport (see Fig. 4a and b). These variations, although simple, represent changes in atmospheric conditions from morning to afternoon. The other model parameters were chosen to be the same as in the third simulation (Fig. 3), where temperature and relative humidity were set at 293 K and 86% respectively. These new calculations predict a lower mass of condensed sulfur. This is due to the fact that lower values for relative humidity and higher temperatures were used. Therefore, variations in the diurnal values of relative humidity and temperature change the mass size distribution of the sulfate charged particles. In the previous simulations nucleation was not observed. This is due to the fact that the background aerosol concentration was set to the value of about 104 c m - 3 (see Fig. 1b) and
Simulation of formation and growth of atmospheric sulfate particles
115
therefore condensation was the predominant mechanism of sulfate particle formation. Simulations were conducted using a typical aerosol distribution for continental air (Whitby, 1978; Hering and Friedlander, 1982). The starting aerosol distribution serves as the background aerosol, the growth of which competes with nucleation (Seinfeld, 1986). To determine how low the initial aerosol concentration or how high the sulfuric acid activity has to be in order to observe new particle formation, we performed the following simulations. In order to examine the importance of the nucleation mechanism we performed model calculations for high SO2 oxidation rates of 20% per hour (T = 285 K, Aa~ = 0.94, Abg = 3.8 X 10- 5) with zero background aerosol concentration. The determined nucleation rate (J = 3 x 10- 2 particles c m - a s - 1) was appropriate to lead to a new particle formation
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116
M. Lazaridis and P. Koutrakis
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117
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Fig. 5. Sensitivity study of the importance of the nucleation mechanism during mesoscale sulfur transport. (a) Sulfur mass size distribution at high acid gas-phase concentrations T = 285 K, A,g=0.94, Abg= 1.4x10 4). ( b ) N u m b e r size distribution (particles cm -3) versus aerosol diameter.
during few minutes of aerosol transport. At typical SO2 oxidation rates of about 3% per hour a time of some hours will be needed for producing a considerable number of newly formed sulfate particles. Furthermore, we performed a simulation using the background aerosol concentration that we considered above (see Fig. lb) for our calculations (T = 285K, Aag = 0.94, Abg ~- 1.4 x 10-4). Figure 5a shows the mass distribution of sulfate after a second of transport (1.11ms -~) corresponding to a nucleation burst. Although submicron particle production was observed, corresponding to the nucleation process, the sulfur condensed mass is mainly due to vapor condensation. Under these conditions we observed a high nucleation rate ( J = 2 . 2 x l 0 4 p a r t i c l e s c m - 3 s -~) resulting in a high production of new particles. In this case nucleation plays an important role in the formation of the sulfur charged particle distribution. Therefore, for very high production rates of sulfuric acid particles nucleation becomes an important process. However, under normal atmospheric conditions the sulfuric acid activity is lower and therefore nucleation is not an important mechanism for determining the size distribution of sulfur. Nucleation bursts due to high local sulfuric acid concentration may be responsible for new particle formation. Figure 5b presents the number size distribution of the aerosol particles under these conditions. A large number of newly formed particles is observed due to the homogeneous nucleation mechanism which quickly agglomerate to larger sizes.
118
M. Lazaridis and P. Koutrakis CONCLUSIONS
C o m p u t e r s i m u l a t i o n s w e r e p e r f o r m e d to i n v e s t i g a t e the f o r m a t i o n a n d g r o w t h of sulfate p a r t i c l e s at a t m o s p h e r i c c o n d i t i o n s . O u r results s u g g e s t t h a t the c o n d e n s a t i o n m e c h a n i s m is t h e d o m i n a n t p r o c e s s for sulfur g a s - p a r t i c l e c o n v e r s i o n at m o d e r a t e r e l a t i v e h u m i d i t i e s . N u c l e a t i o n d o e s n o t c o n t r i b u t e to the final sulfate p a r t i c l e size d i s t r i b u t i o n . O u r calcul a t i o n s also s h o w t h a t c o a g u l a t i o n is n o t a n i m p o r t a n t m e c h a n i s m for sulfur m a s s transfer, c o n f i r m i n g t h e c o n c l u s i o n s o f H e r i n g a n d F r i e d l a n d e r (1982). T h e s e a u t h o r s h a v e s u g g e s t e d t h a t t h e effect of this m e c h a n i s m for the size r a n g e of 1 g m is n e g l i g i b l e for t i m e i n t e r v a l s of a few days. I n a d d i t i o n , o u r c a l c u l a t i o n s s h o w t h a t t h e d e p o s i t i o n p r o c e s s is n o t an effective m e c h a n i s m for c h a n g i n g the s h a p e of the a c c u m u l a t i o n size d i s t r i b u t i o n u n d e r usual a t m o s p h e r i c c o n d i t i o n s (see also F r i e d l a n d e r , 1977). F u r t h e r m o r e , sensitivity a n a l y s i s was p e r f o r m e d for m a n y m o d e l p a r a m e t e r s to d e m o n s t r a t e t h e i r effect o n m o d e l p r e d i c t i o n s . V a r i a t i o n s in the o x i d a t i o n r a t e of S O 2 , r e l a t i v e h u m i d i t y a n d t e m p e r a t u r e a r e all i m p o r t a n t factors t h a t c a n affect the m a s s size d i s t r i b u t i o n o f t h e sulfate c h a r g e d particles. Acknowledgements--The authors would like to thank Dr Arne Semb, Dr Jozef Pacyna, Dr Yannis Drossinos,
Dr Jack M. Wolfson, Robert Burton, and Georege Allen for their comments and useful discussions. This work was funded by the Nordic Council of Ministers through a NorFa stipend, the USEPA under Cooperative Agreement No. CR816740, and by EPRI under Contract No. RP1630-59 (Project Manager, Mary Ann Allan). REFERENCES Ayers, G. P., Gillett, R. W. and Gras, J. L. (1980) On the vapor pressure of sulfuric acid. Geophys. Res. Lett. 7, 433-436. Brosset, C. (1980) Black and white episodes. Ambio 5, 157 163. Brosset, C., Andreasson, K. and Ferm, M. (1975) The nature and possible origin of acid particles observed at the Swedish West Coast. Atmos. Envir. 9, 631-642. Chemical Engineers' Handbook (1973) McGraw-Hill, New York. Eliassen, A. (1978) The OECD study of long range transport of air pollutants: long range transport modelling. Atmos. Envir. 12, 479 487. Ferek, R. J., Lazrus, A. L., Haagenson, P. L. and Winchester, J. W. (1983) Strong and weak acidity of aerosols over the northeastern United States. Environ. Sci. Technol. 17, 315 324. Friedlander, S. K. (1977) Smoke Dust and Haze. Wiley, New York. Giauque, W. F., Hornung, E. W., Kunzler, J. E. and Rubbin, T. R. (1960) The thermodynamic properties of aqueous sulfuric acid solutions and hydrates from 15 to 300 K. J. Am. Chem. Soc. 82, 62 70. Hamill, P. (1975) The time dependent growth of H20 H2SO4 aerosols by heteromolecular condensation. J. Aerosol Sci. 6, 475 482. Hegg, D. A., Covert, D. S. and Kapustin, V. N. (1992) Modeling case of particle nucleation in the marine boundary layer. J. geophys. Res. 97, 9851-9857. Hering, S. V. and Friedlander, S. K. (1982) Origins of aerosol sulfur size distribution in the Los Angeles basin. Atmos. Envir. 16, 2647 2656. Hillamo, E. M., Pacyna, J. M., Semb, A. and Hanssen, J. E. (1992) Size distributions of inorganic ions in atmospheric aerosol in Norway. Air Pollution Research Report 41, pp. 51 65. Commission of European Communities, Brussels. Hinds, W. C. (1982) Aerosol Technology. Wiley, New York. Huntzicker, J. J., Hoffman, R. S. and Cary, R. A. (1984) Aerosol sulfur episodes in St Louis, Missouri. Envir. Sci. Technol. 18, 962-972. John, W., Wall, S. T., Ondo, J. L. and Winklmayr, W. (1990) Modes in the size distribution of atmospheric inorganic aerosol. Atmos. Envir. 24A, 2349 2359. Jokiniemi, J., Lazaridis, M., Lehtinen, K. E. J. and Kauppinen, E. I. (1994) Numerical simulation of vapor-aerosol dynamics in combustion processes. J. Aerosol Sci. 25, 429--446. Keeler, G. L., Brachaczek, W. W., Gorse, R. A., Japar, S. M. and Pierson, W. R. (1988) Effect of ambient humidity on dichotomous sampler coarse and fine mass ratios. Atmos. Envir. 22, 1715 1720. Koutrakis, P. and Kelly, B. P. (1993) Equilibrium size of atmospheric aerosol sulfates as a function of particle acidity and ambient relative humidity. J. geophys. Res. 98, 7141 7147. Koutrakis, P., Wolfson, J. M. and Spengler, J. D. (1989) Equilibrium size of atmospheric aerosol sulfates as a function of the relative humidity. J. geophys. Res. 94, 6442 6448. Kreidenweis, S. M. and Seinfeld, J. H. (1988) Nucleation of sulfuric acid-water and methanesulfonic acid water s••uti•n partic•es: imp•icati•ns f•r the atm•spheric chemistry •f •rgan•su•fur spe•ies. Atm•s. Envir. 22• 283 296. Kulmala, M. and Laaksonen, A. (1990) Binary nucleation of water-sulfuric acid system: comparison of classical theories with different H2SO4 saturation vapor pressures. J. chem. Phys. 93, 696 701. Lazaridis, M., Kulmala, M. and Gorbunov, B. (1992) Binary heterogeneous nucleation at a non-uniform surface. J. Aerosol Sci. 23, 457-466. Lin, X., Chameides, W.L., Kiang, C. S., Stelson, A. W. and Berresheim, H. (1992) A model study of the formation of cloud condensation nuclei in remote marine areas. J. geophys. Res. 97, 18,161- 18,171.
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McMurry, P. H. and Wilson, J. C. (1983) Droplet phase (heterogeneous) and gas phase (homogeneous) contributions to secondary ambient formation as functions of relative humidity. J. geophys. Res. 88, 5101-5108. Mason, B. J. (1971) The Physics of Clouds, 2nd Edition. Clarendon Press, Oxford. Raes, F. and Van Dingenen, R. (1992) Simulations of condensation and cloud condensation nuclei from biogenic SO2 in the remote marine boundary layer. J. geophys. Res. 97, 12,901-12,912. Reid, R. C., Prausnitz, J. M. and Poling, B. E. (1987) The Properties of Gases and Liquids, 4th Edition McGraw-Hill, New York. Rodhe, H. and Grandell, J. (1981) Estimates of characteristic times for precipitation scavenging. J. atmos. Sci. 38, 370-386. Rudolf, R. and Wagner, P. E. (1994) Experimental study of condensational particle growth in nitric acid water vapor mixtures at nearly ambient pressures and temperatures. J. Aerosol Sci. Suppl. 25, $97-$99. Sabinina, L. and Terpugow, L. (1935) Z. Phys. Chem. A173, 237. Seinfeld, J. H. (1986) Atmospheric Chemistry and Physics of Air Pollution. Wiley, New York. Stevens, R. K., Dzubay, T. G., Shaw, R. W., McClenny, W. A., Lewis, C. W. and Wilson, W. E. (1980) Characterization of the aerosol in the great smoky mountains. Environ. Sci. Technol. 14, 1491 1498. Svenningsson, I. B., Hansson, H. C., Wiedensohler, A., Orgen, J. A., Noone, K. J. and Hallberg, A. (1992) Hygroscopic growth of aerosol partices in the Po Valley. Tellus 44B, 556 569. Tang, I. N., Munkelwitz, H. R. and Davis, J. G. (1978) Aerosol growth studies--IV. Phase transformation of mixed slat aerosols in a moist atmosphere. J. Aerosol Sci. 9, 505-511. Tanner, R. L., Kumar, R. and Johnson, S. (1984) Vertical distribution of aerosol strong acidity in the atmosphere. J. geophys. Res. 89, 7149 7157. Whitby, K. T. (1978) The physical characteristics of sulfur aerosols. Atmos. Envir. 12, 135-159. Williams, M. M. R. and Loyalka, S. K. (1991) Aerosol Science, Theorey and Practice. Pergamon Press, Oxford. Winkler, P. (1988) The growth of atmospheric aerosol particles with relative humidity. Physica Scripta 37, 223-230.
J. Aerosol Sci. Vol. 28, No. 1, pp. 107-119, 1997
PIh S0021-8502(96)00063-8
Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0021-8502/96 $17.00 + 0.00
S I M U L A T I O N O F F O R M A T I O N A N D G R O W T H OF A T M O S P H E R I C S U L F A T E PARTICLES Mihalis Lazaridis** and Petros K o u t r a k i s ~ * Laboratory of Atmospheric Physics, School of Science-PhysicsDepartment, Aristotle University of Thessaloniki, Campus Box 149, Thessaloniki 54006, Greece : School of Public Health, Harvard University, 665 Huntington Ave., Boston, MA 02115, U.S.A. (First received 1 December 1995; and in final form 17 May 1996)
Abstract--This paper investigates the formation and growth of aerosol sulfate particles in the atmosphere. The evolution of the aerosol size distribution with time was modeled using the aerosol general dynamic equation. This equation was solved numerically using a discrete-nodal point method to describe the particle size distribution. For the initial size distribution we have used an average urban accumulation mode. The first step in our model considers the oxidation of SO2 by OH radicals, producing H2SO~). The next step considers the binary nucleation and condensation of the H2SO4-H20 system and its evolution due to coagulation and deposition mechanisms. A detailed description of the model is presented. The mass size distribution at different distances during the transport of the initial aerosol size distribution is also presented. The importance of different mechanisms on the evolution of the aerosol size distribution is discussed. Sensitivity analysis was performed for many model parameters where simulations were made at varying temperature, relative humidity and photo-oxidation rate conditions. Model calculations suggest that condensation growth is the dominant mechanism for the evolution of the size distribution of sulfate particles during moderate relative humidity conditions. Copyright © 1996 Elsevier Science Ltd INTRODUCTION Because of their effects on respiratory health and environment, atmospheric acid aerosols have been investigated by a large n u m b e r of researchers. Emissions of sulfur dioxide result in the formation of submicron sulfate particles (Whitby, 1978), which can be transported over long distances from their sources (Rodhe and Grandell, 1981; Eliassen, 1978). Acidic sulfate aerosols can remain mostly unneutralized during transport because of the low ambient a m m o n i a concentrations at low altitudes (Tanner et al., 1984). Sulfate particle concentrations exhibit significant seasonal and regional variations (Stevens et al., 1980; Ferek et al., 1983; K o u t r a k i s et al., 1989). Hering and Friedlander (1982) observed two distinct types of sulfate aerosols in Los Angeles with mass median diameters of 0.54 ___0.07/~m and 0.20 + 0.02 #m, respectively. The first type is consistent with an aqueous-phase episode during which sulfuric acid formation t o o k place within the droplets, whereas the second results from h o m o g e n e o u s gas-phase SO2 oxidation. J o h n et al. (1990) m e a s u r e d the particle size distributions of inorganic charged particles. The observed distributions were characterized by three modes, one at 0.2 + 0.1/~m (gasphase reaction products), one at 0.7 + 0.2/~m, and a coarse mode. G r o w t h of the first m o d e due to condensation of water and sulfate m a y have resulted in the formation of the second mode. K o u t r a k i s et al. (1989) and K o u t r a k i s and Kelly (1993) studied the equilibrium size of atmospheric aerosol sulfates at different relative humidities and observed a relationship between the mass median geometric a e r o d y n a m i c diameter of sulfate particles and b o t h particle acid content and ambient relative humidity. Sulfate particles were found to be mainly in the a c c u m u l a t i o n mode. Brosset et al. (1975) examined the nature and possible origin of acid particles at the Swedish coast. T w o types of acid particles were indentified. The first presented a size distribution between 0.5 and 1.5 ~tm, possibly generated by SO2 diffusion into water droplets. This type was associated with the transport of air-borne dark particles from the Present address: EOHSI, 681 Frelinghuysen Road, Piscataway, NJ 08855-1179, U.S.A. 107
108
M. Lazaridisand P. Koutrakis
European Continent (Brosset, 1976). The second type presented a size distribution of less than 0.4/~m and was attributed to the photochemical oxidation of SO2 and the formation of new particles. The new particles, consisting mainly of acid ammonium sulfate, were probably formed over the North Sea and transported over Sweden. Sulfate aerosol episodes were also observed by Huntzicker et al. (1984). Some of the episodes were associated with the presence of freshly generated sulfates, formed through the oxidation of SO2 by OH radicals with subsequent nucleation and condensation, while other episodes were associated with long-range transported sulfates. In addition, high concentrations of pre-existing aerosol particles in the atmosphere were found to suppress nucleation (Lin et al., 1992; Hegg et al., 1992; Whitby, 1978). Sulfate particles grow larger with increasing relative humidity (Tang et al., 1978; Winkler, 1988; Keeler et al., 1988; Koutrakis et al., 1989). Growth of hygroscopic aerosols was also studied by others (Svenningsson et al., 1992; Winkler, 1988). These studies show two different modes of hygroscopic growth, as well as effects caused by insoluble material in the aerosol droplets. In the present paper we investigate the importance of different mechanisms of sulfate particle formation and growth during a mesoscale range of transport. The aerosol general dynamic equation (Friedlander, 1977; Jokiniemi et al., 1994) is used to model the evolution of the sulfate particles. In addition, sensitivity analysis was performed for many model parameters. The sulfate formation by aqueous-phase oxidation of SO2 was not investigated, since this study does not examine cloud and fog conditions, where this mechanism appears to be important (Hering and Friedlander, 1982). MODEL CALCULATIONS General dynamic equation
Aerosol dynamics describe the evolution in space and time of the particle size distribution and the chemical composition. In the present work we investigate the aerosol dynamics using the aerosol general dynamic equation (GDE), which is solved in a one-dimensional form along the wind direction (Friedlander, 1977; Jokiniemi et al., 1994): dn k
1 j k 6 ( k _ k*) +
dx
u
+
\ dx/coag
nk,
\ dx/grow
(1)
uA V
where nk is the particle number concentration for a size class k with particle radius rk; the terms on the right-hand side of equation (I) correspond, respectively, to (1) particle formation due to binary homogeneous nucleation mechanism (* indicates nucleating embryo), (2) the coagulation mechanism, (3) growth by condensation and chemical reactions, and (4) particle removal due to deposition; Va is the particle deposition velocity, Ad is the settling area (equal to the bottom of the considered cell in the simulations) in every axial volume step (AV is the axial volume step), u is the wind velocity, Jk is the nucleation rate and 6 is a delta function. In our calculations, particle Brownian diffusive deposition and sedimentation have been modeled. The solution of the G D E is based on a discrete-nodal point method. The discrete grid can be used up to a user-specified number of coagulated molecules (k-mer), after which the nodal point grid is used (Jokiniemi et al., 1994). In the discrete scheme, in the case where only one species is nucleating and the formed aerosol particles are chemically homogeneous, the number of grid points is the number of molecules in the cluster. Therefore, the radius of an i-mer cluster is ri = (i + l)I/3ro, where ri is the radius of the i-mer and ro is the monomer radius. In the case that we have more than one chemical species we have to keep track of all particles which have different size and chemical composition and in this case we make use of the nodal point size grid. In the nodal point method the number distribution is divided into n - I nodal points distributed evenly according to the logarithm of particle radius (Jokiniemi et al., 1994).
Simulationof formationand growth of atmosphericsulfateparticles
109
The rate of molar concentration change of gas-phase species is given by the gas-phase conservation equation and the mass size distribution of different species and can be calculated by solving the condensed-phase species equation (Jokiniemi et al., 1994):
I_
d×
..]gtp L
d×
Jeoa, uAV
where Pak and Y~k are the average density of particles in the kth grid point and the composition of species j at the kth grid point respectively; the term gtp corresponds to the formation and growth of aerosol particles due to mechanisms of nucleation and condensation; the term coag refers to coagulation mechanism; and the time is related to the axial position through the wind velocity u. In these calculations several input parameters are needed. The first is the sulfuric acid production rate. Assuming that the oxidation of SO2 by OH radicals is the dominant formation mechanism of H/SO~ ) in the atmosphere, the production rate can be determined using the following equation: d[H2SO4] - k[SO2] Ion], dt
(3)
where k is the reaction rate constant, k = 1.2 x 10- xz molecules- 1 cm 3 S- 1 (Lin et al., 1992); [SO2] and [OH] are the respective concentrations of the gases; and the assumed daytime concentration of the hydroxyl radical [OH] is 5 × 106 molecules cm- 3. Other calculations were also made using a lower oxidation rate (k = 7x 10-~3molecules-lcm3s -1) and a radical concentration of [-OH] = 106 molecules cm-3 in order to examine the effect of k [OH] on the size distribution evolution. Both oxidation rates presents realistic values for atmospheric conditions. Sensitivity analysis was also performed by varying the photooxidation rate during transport. The second step in our model calculations includes the formation of H E S O 4 - H 2 0 particles due to binary nucleation. It is not yet known whether the incorporation of NH 3 into H 2 S O 4 - H 2 0 particles occurs before or after their formation. Here, it is assumed that NH3 associates with the H 2 S O 4 - H 2 0 system after particle formation. This assumption may lead to underestimation of the nucleation rate if NH3 reacts with H2SO~ ) before nucleation, since the nucleation of ammonium bisulfate is more efficient than the H E S O 4 - H 2 0 system (Raes and Van Dingenen, 1992). However, since ambient ammonia concentrations decrease with elevation, ammonia concentrations should be at sub-ppb levels at relatively high elevations (Tanner et al., 1984). The mass and number distribution for the pre-existing aerosols are needed to perform our calculations. We have used a typical aerosol distribution of continental air (Whitby, 1978; Hering and Friedlander, 1982). The relative humidity was set to 52 and 86% and the temperature to 20°C for the first simulations (see Figs 1-3). In the following simulations a sensitivity analysis was performed for the SO2 photo-oxidation rate and nucleation formation, where the temperature and relative humidity values were varying during transport. The main mechanisms considered in our calculations are described in the following sections. Binary nucleation
The binary nucleation of the H E S O 4 - H 2 0 system is calculated in a manner analogous to the one adopted by the revised classical theory (Wilemski, 1984). We have calculated the nucleating value of the free energy barrier using the equation /)bAfla = OaA~b, at the nucleation point, which determines the composition of the embryo (vi, Apl are the molar volume and the change of the chemical potentials between the gas and liquid phases of the species i). Several expressions have been presented for the kinetic part of the nucleation rate in the theory of binary nucleation leading to differences in the evaluation of the nucleation rate
110
M. Lazaridis and P. Koutrakis
(e.g. Kulmala and Laaksonen, 1990). However, differences in the pre-exponential factor of the nucleation rate had little effect on our predictions. Variations in the SO2 photooxidation rate, the relative humidity, temperature and [ O H ] were far more important. A sensitivity analysis of these parameters is presented in the next section. In order to calculate the free energy barrier AG from the classical model of binary nucleation, values for activities, densities and surface tensions as functions of temperature are necessary. The chemical potentials in the liquid phase were estimated using the method of Giauque et al. (1960). The surface tension of the mixture was estimated using the data of Sabinina and Terpugow (1935). The densities of the solutions were calculated using polynomial fitting of the data obtained from the Chemical Engineer's Handbook (1973). The saturation vapor pressure of sulfuric acid was determined using the expression derived by Kulmala and Laaksonen (1990), which is based on the experimental data from Ayers et al. (1980). The activity coefficients were calculated using a fitting of available experimental measurements. The process is based on the method by Reid et al. (1987) and the measured points can be found in the Chemical Engineers' Handbook (1973). From the saddle point conditions OAG/~?ni = 0 (ni is the number of molecules of species i in the droplet) we derive the generalized Kelvin equations, which were subsequently used to determine the mole fraction X of species at the saddle point. The nucleating radius (r*) of the binary droplet is given by (Lazaridis et al., 1992)
r* =
- 2a(Xvb + (1 - X ) / ) a ) X k T ln(Abg/Abe) + (1 -- X ) k T ln(Aag/Aat) '
(4)
where a is the surface tension of the binary droplet, k the Boltzman's constant, T the temperature, vl the molar volume and Aig and Aie are the activities in the gas phase and in the liquid phase of species i respectively. Aag = Pa/Pas, Abg = Pb/Pbs, Aa~ = P . . . . l/Pat, Ab~ = Pb,sol/Pb~(Pas and Pbs are the respective equilibrium vapor pressures of water and acid vapor over a flat surface of pure substance and Pi,sol is the partial pressure of species i over a flat surface of the solution). The nucleation rate can be determined using the following equation (Lazaridis et al., 1992):
J=RavFZexp(--
A~_),
(5)
where Rav is the average condensation rate, F is the total number of nucleating molecules, Z is the Zeldovich non-equilibrium factor, k is the Boltzmann factor, and T is the absolute temperature. The only experimental value reported for the accommodation coefficient for H2SO4 molecules was between 0.02 and 0.09 at a relative humidity of 50% (Raes and Van Dingenen, 1991). We chose this value, even though it is in contrast with the accommodation coefficient near to the one reported for the H N O 3 - H 2 0 system (Rudolf and Wagner, 1994).
Binary condensation The condensation rate of H z S O 4 onto the pre-existing aerosol particles is described by a modified Mason equation (Mason, 1971), where the transitional correction factors are included:
dm dt
4nr(S~ - S,,fl (NM/flM) + (NT/flT)'
(6)
where
RgT~ NM -- D~Mp.,(T.~)
and
NT = L ~
L(~ "~ \/~g~ ~,/ .
(7)
Simulation of formationand growth of atmospheric sulfateparticles
111
tiM and fiT are the transitional correction factors for the mass and heat transfer, ps is the saturation pressure, Rg is the ideal gas constant, D~ is the binary diffusion coefficient, M is the molecular weight of the liquid, L is the latent heat of condensation, S~o,s is the saturation ratio of the gas far from the particles, and Sr, s is the saturation ratio of gas species j at the particle surface calculated using the following equation: Sr, s = A s exp \ r R g p T , J '
(8)
where a is the surface tension, p is the density of the liquid film on the droplet, T~ is the droplet temperature, and As is the chemical activity of species j which can be expressed as a function of the mole fraction of the condensable species in the liquid droplet (x j) solution and the molal activity coefficient (~s): As = xsTs (Reid et al., 1987). In our calculations we have used background aerosol particles with a density of 1.1 g cm-3. It is assumed that the particles are wettable and the initial mole fraction of the liquid film on the particles is calculated with the use of the binary heterogeneous nucleation theory (analogous to the revised classical nucleation theory) (Lazaridis et al., 1992). Coagulation Due to the coagulation process, particles are both removed and added to size bins. In our study the processes of Brownian diffusion and turbulent gravitational coagulation are considered (Williams and Loyalka, 1991). The general equation that controls the coagulation can be written as follows: dnk _ 2 i +~'=kK ( m i ' m s ) n l n j - - n k i= ~ 1 K ( m i , mk)ni,
(9)
where i + j = k means that the summation is taken over those grid points for which ml + m s = m k (ml is the mass of particle i) ni is the number of particles in bin i, and mk includes the mass of all the particles that are in bin k (Friedlander, 1977). Settling In the present model we use the gravitational deposition and the particle diffusion settling mechanisms. The sedimentation velocity is assumed to be the terminal velocity, calculated as the product of the gravitational accelaration (g) and the particle relaxation time (/)d = gTrel) (Friedlander, 1977). The particle relaxation time (Trel) is given by the equation Zrel = (2/9)(pr 2 Cn/#), where p is the density of the particle, r is the radius of the particle, Cn is the Cunningham correction factor, and/~ is the dynamic viscosity. The particle diffusivity D was calculated using the Stokes-Einstein equation (Hinds, 1982) D = ( k T Cn/6nr#), where k is the Boltzman constant and T is the absolute temperature. In the case of particle diffusivity the deposition velocity can be defined as the deposition flux divided by the undisturbed concentration (Hinds, 1982). The evaluation of the deposition velocity is needed to calculate the losses due to settling in equations (1) and (2). RESULTS AND D I S C U S S I O N The simulation of formation and growth of sulfate aerosols was performed by numerically solving the general dynamic equation. We simulated typical conditions of sulfur episodes for continental air. Sample calculations were performed with typical aerosol distributions and SO2 oxidation rates. Particle formation was simulated by including the following mechanisms: SO2 photo-oxidation; binary nucleation; condensation of the H2SO4-H20 system; coagulation; and settling. As mentioned above, a sensitivity analysis
112
M. Lazaridis and P. K o u t r a k i s RH: 52%, SO2: 4 2 p p b
25
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.
.
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. .
.
.
.
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.
33.2 Km ......
44.5 Km
8 10
0
'•
0.5
0
1
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1.00E+03
1.00E+02
.~, x
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112Km 21 Km 49 Km
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1.00E-02 "\ ".\ L\ "\
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0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Dp (microns)
Fig. 1. (a) M a s s size distribution (dm/d In Dp) of sulfate at different distances during the t r a n s p o r t of the initial aerosol size distribution. (b) N u m b e r size distribution of sulfate particles at different distances during the transport of the initial aerosol size distribuiton ( [ S O 2]: 42 p p b (initial conditions), RH: 52%, T = 293 K, k = 1.2 x 10-12 molecules- 1 cm 3 s 1, [ O H ] = 5 x 106 molecules cm-3).
Simulation of formation and growth of atmospheric sulfate particles
113
RH: 52%, SO2: 42ppb
3.5 m
3
; ;
:
2.5
'
i
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i
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f
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,.
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2.5
Dp (microns) Fig. 2. Mass size distribution (dm/d In Dp) of sulfur due to the evolution of the initial aerosol size distribution at different distances ([SO2]: 4 2 p p b (initial conditions), RH: 52%, T = 293 K, k = 7 x 10-13 molecules 1 cm 3 s 1, [OH] = 106 molecules cm-3).
was conducted for relative humidity, temperature and gas-phase oxidation rate parameters, because of their non-linear effect on our model calculations. The change in size distribution of the aerosol sulfate particles was examined as a function of different parameters, including SO/ oxidation rate, relative humidity, and SO2 gas concentration. We have used as an initial size distribution an average urban accumulation m o d e aerosol (around 0.1-1/~m) analogous to that of Whitby and Sverdrup (1980) and Hering and Friedlander (1982). This is a log-normal distribution with a mass median diameter of 0.32 #m. F o r the representation of the size distribution we used a nodal point size grid with 60 nodal points. The wind velocity was chosen to be 1.11 m s -1, based on wind measurements made in the N o r t h Eastern United States during a pollution episode. Input data values were chosen also for the S O / c o n c e n t r a t i o n , relative humidity, and the temperature. Figure la presents the evolution of the mass size distribution of sulfate particles. These results are based on a moderate initial SO2 atmospheric concentration ([SO2]: 42 ppb, k = 1 x 10-12 molecules- 1 cm 3 s - 1, [ O H ] = 5 x 106 molecules c m - 3). Our model calculations suggest that sulfate mass is concentrated in the accumulation region, for particle diameters between 0.5 and 1.5/~m, in agreement with the experimental results of Koutrakis and Kelly (1993). Model calculations suggest that binary nucleation is negligible. The predominant mechanism of mass transfer of sulfur onto the aerosol particles is v a p o r condensation under these conditions; thus no new particles are formed during the transport of the air masses. Figure l b shows the evolution of the number size distribution at different distances. The particle deposition mechanisms remove the particles with diameters above 1.8 #m while the accumulation mode remains unaffected.
114
M. Lazaridis and P. Koutrakis RH: 82%, SO2: 2 0 0 p p b 12
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distribution ([SO2]: 2 0 0 p p b (initial conditions), RH: 86%, T = 293 K, k = 7 x les-1 cm3s 1, [ O H ] = 106 moleculescm 3).
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Calculations were made to investigate the effect of the oxidation rate on sulfur condensation (see Figs 3 and 4). These results suggest that the sulfate oxidation rate is a very important factor that determines the mass size distribution of sulfate charged particles. Figure 2 presents the time evolution of particulate sulfate mass from the initial distribution for lower values of the SO2 oxidation rate and O H concentration (T = 293 K, k = 7 x 10-13 molecules-1 cm3 s-1, [ O H ] = 106 molecules cm-3). As expected, lower oxidation rates result in a lower production rate of sulfuric acid molecules and therefore in lower sulfuric acid concentrations in the accumulation mode. Again under these conditions the nucleation rate is practically zero. We also considered the effect of higher SO2 concentration (see Fig. 3)([SO2]: 200 ppb, T = 293 K, k = 7 x 10 13 molecules 1 cm 3 S 1, [-OH] = 106 moleculescm 3). Nucleation was not observed even for this high sulfur dioxide level. Another simulation was performed allowing temperature and relative humidity conditions to vary (k = 7 x 10-13 molecules-1 cm3s 1, [-OH] = 106 molecules cm 3) during aerosol transport (see Fig. 4a and b). These variations, although simple, represent changes in atmospheric conditions from morning to afternoon. The other model parameters were chosen to be the same as in the third simulation (Fig. 3), where temperature and relative humidity were set at 293 K and 86% respectively. These new calculations predict a lower mass of condensed sulfur. This is due to the fact that lower values for relative humidity and higher temperatures were used. Therefore, variations in the diurnal values of relative humidity and temperature change the mass size distribution of the sulfate charged particles. In the previous simulations nucleation was not observed. This is due to the fact that the background aerosol concentration was set to the value of about 104 c m - 3 (see Fig. 1b) and
Simulation of formation and growth of atmospheric sulfate particles
115
therefore condensation was the predominant mechanism of sulfate particle formation. Simulations were conducted using a typical aerosol distribution for continental air (Whitby, 1978; Hering and Friedlander, 1982). The starting aerosol distribution serves as the background aerosol, the growth of which competes with nucleation (Seinfeld, 1986). To determine how low the initial aerosol concentration or how high the sulfuric acid activity has to be in order to observe new particle formation, we performed the following simulations. In order to examine the importance of the nucleation mechanism we performed model calculations for high SO2 oxidation rates of 20% per hour (T = 285 K, Aa~ = 0.94, Abg = 3.8 X 10- 5) with zero background aerosol concentration. The determined nucleation rate (J = 3 x 10- 2 particles c m - a s - 1) was appropriate to lead to a new particle formation
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116
M. Lazaridis and P. Koutrakis
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Simulation of ~rmation and growth ofatmosphericsul~te particles
117
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Fig. 5. Sensitivity study of the importance of the nucleation mechanism during mesoscale sulfur transport. (a) Sulfur mass size distribution at high acid gas-phase concentrations T = 285 K, A,g=0.94, Abg= 1.4x10 4). ( b ) N u m b e r size distribution (particles cm -3) versus aerosol diameter.
during few minutes of aerosol transport. At typical SO2 oxidation rates of about 3% per hour a time of some hours will be needed for producing a considerable number of newly formed sulfate particles. Furthermore, we performed a simulation using the background aerosol concentration that we considered above (see Fig. lb) for our calculations (T = 285K, Aag = 0.94, Abg ~- 1.4 x 10-4). Figure 5a shows the mass distribution of sulfate after a second of transport (1.11ms -~) corresponding to a nucleation burst. Although submicron particle production was observed, corresponding to the nucleation process, the sulfur condensed mass is mainly due to vapor condensation. Under these conditions we observed a high nucleation rate ( J = 2 . 2 x l 0 4 p a r t i c l e s c m - 3 s -~) resulting in a high production of new particles. In this case nucleation plays an important role in the formation of the sulfur charged particle distribution. Therefore, for very high production rates of sulfuric acid particles nucleation becomes an important process. However, under normal atmospheric conditions the sulfuric acid activity is lower and therefore nucleation is not an important mechanism for determining the size distribution of sulfur. Nucleation bursts due to high local sulfuric acid concentration may be responsible for new particle formation. Figure 5b presents the number size distribution of the aerosol particles under these conditions. A large number of newly formed particles is observed due to the homogeneous nucleation mechanism which quickly agglomerate to larger sizes.
118
M. Lazaridis and P. Koutrakis CONCLUSIONS
C o m p u t e r s i m u l a t i o n s w e r e p e r f o r m e d to i n v e s t i g a t e the f o r m a t i o n a n d g r o w t h of sulfate p a r t i c l e s at a t m o s p h e r i c c o n d i t i o n s . O u r results s u g g e s t t h a t the c o n d e n s a t i o n m e c h a n i s m is t h e d o m i n a n t p r o c e s s for sulfur g a s - p a r t i c l e c o n v e r s i o n at m o d e r a t e r e l a t i v e h u m i d i t i e s . N u c l e a t i o n d o e s n o t c o n t r i b u t e to the final sulfate p a r t i c l e size d i s t r i b u t i o n . O u r calcul a t i o n s also s h o w t h a t c o a g u l a t i o n is n o t a n i m p o r t a n t m e c h a n i s m for sulfur m a s s transfer, c o n f i r m i n g t h e c o n c l u s i o n s o f H e r i n g a n d F r i e d l a n d e r (1982). T h e s e a u t h o r s h a v e s u g g e s t e d t h a t t h e effect of this m e c h a n i s m for the size r a n g e of 1 g m is n e g l i g i b l e for t i m e i n t e r v a l s of a few days. I n a d d i t i o n , o u r c a l c u l a t i o n s s h o w t h a t t h e d e p o s i t i o n p r o c e s s is n o t an effective m e c h a n i s m for c h a n g i n g the s h a p e of the a c c u m u l a t i o n size d i s t r i b u t i o n u n d e r usual a t m o s p h e r i c c o n d i t i o n s (see also F r i e d l a n d e r , 1977). F u r t h e r m o r e , sensitivity a n a l y s i s was p e r f o r m e d for m a n y m o d e l p a r a m e t e r s to d e m o n s t r a t e t h e i r effect o n m o d e l p r e d i c t i o n s . V a r i a t i o n s in the o x i d a t i o n r a t e of S O 2 , r e l a t i v e h u m i d i t y a n d t e m p e r a t u r e a r e all i m p o r t a n t factors t h a t c a n affect the m a s s size d i s t r i b u t i o n o f t h e sulfate c h a r g e d particles. Acknowledgements--The authors would like to thank Dr Arne Semb, Dr Jozef Pacyna, Dr Yannis Drossinos,
Dr Jack M. Wolfson, Robert Burton, and Georege Allen for their comments and useful discussions. This work was funded by the Nordic Council of Ministers through a NorFa stipend, the USEPA under Cooperative Agreement No. CR816740, and by EPRI under Contract No. RP1630-59 (Project Manager, Mary Ann Allan). REFERENCES Ayers, G. P., Gillett, R. W. and Gras, J. L. (1980) On the vapor pressure of sulfuric acid. Geophys. Res. Lett. 7, 433-436. Brosset, C. (1980) Black and white episodes. Ambio 5, 157 163. Brosset, C., Andreasson, K. and Ferm, M. (1975) The nature and possible origin of acid particles observed at the Swedish West Coast. Atmos. Envir. 9, 631-642. Chemical Engineers' Handbook (1973) McGraw-Hill, New York. Eliassen, A. (1978) The OECD study of long range transport of air pollutants: long range transport modelling. Atmos. Envir. 12, 479 487. Ferek, R. J., Lazrus, A. L., Haagenson, P. L. and Winchester, J. W. (1983) Strong and weak acidity of aerosols over the northeastern United States. Environ. Sci. Technol. 17, 315 324. Friedlander, S. K. (1977) Smoke Dust and Haze. Wiley, New York. Giauque, W. F., Hornung, E. W., Kunzler, J. E. and Rubbin, T. R. (1960) The thermodynamic properties of aqueous sulfuric acid solutions and hydrates from 15 to 300 K. J. Am. Chem. Soc. 82, 62 70. Hamill, P. (1975) The time dependent growth of H20 H2SO4 aerosols by heteromolecular condensation. J. Aerosol Sci. 6, 475 482. Hegg, D. A., Covert, D. S. and Kapustin, V. N. (1992) Modeling case of particle nucleation in the marine boundary layer. J. geophys. Res. 97, 9851-9857. Hering, S. V. and Friedlander, S. K. (1982) Origins of aerosol sulfur size distribution in the Los Angeles basin. Atmos. Envir. 16, 2647 2656. Hillamo, E. M., Pacyna, J. M., Semb, A. and Hanssen, J. E. (1992) Size distributions of inorganic ions in atmospheric aerosol in Norway. Air Pollution Research Report 41, pp. 51 65. Commission of European Communities, Brussels. Hinds, W. C. (1982) Aerosol Technology. Wiley, New York. Huntzicker, J. J., Hoffman, R. S. and Cary, R. A. (1984) Aerosol sulfur episodes in St Louis, Missouri. Envir. Sci. Technol. 18, 962-972. John, W., Wall, S. T., Ondo, J. L. and Winklmayr, W. (1990) Modes in the size distribution of atmospheric inorganic aerosol. Atmos. Envir. 24A, 2349 2359. Jokiniemi, J., Lazaridis, M., Lehtinen, K. E. J. and Kauppinen, E. I. (1994) Numerical simulation of vapor-aerosol dynamics in combustion processes. J. Aerosol Sci. 25, 429--446. Keeler, G. L., Brachaczek, W. W., Gorse, R. A., Japar, S. M. and Pierson, W. R. (1988) Effect of ambient humidity on dichotomous sampler coarse and fine mass ratios. Atmos. Envir. 22, 1715 1720. Koutrakis, P. and Kelly, B. P. (1993) Equilibrium size of atmospheric aerosol sulfates as a function of particle acidity and ambient relative humidity. J. geophys. Res. 98, 7141 7147. Koutrakis, P., Wolfson, J. M. and Spengler, J. D. (1989) Equilibrium size of atmospheric aerosol sulfates as a function of the relative humidity. J. geophys. Res. 94, 6442 6448. Kreidenweis, S. M. and Seinfeld, J. H. (1988) Nucleation of sulfuric acid-water and methanesulfonic acid water s••uti•n partic•es: imp•icati•ns f•r the atm•spheric chemistry •f •rgan•su•fur spe•ies. Atm•s. Envir. 22• 283 296. Kulmala, M. and Laaksonen, A. (1990) Binary nucleation of water-sulfuric acid system: comparison of classical theories with different H2SO4 saturation vapor pressures. J. chem. Phys. 93, 696 701. Lazaridis, M., Kulmala, M. and Gorbunov, B. (1992) Binary heterogeneous nucleation at a non-uniform surface. J. Aerosol Sci. 23, 457-466. Lin, X., Chameides, W.L., Kiang, C. S., Stelson, A. W. and Berresheim, H. (1992) A model study of the formation of cloud condensation nuclei in remote marine areas. J. geophys. Res. 97, 18,161- 18,171.
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