Physical mechanisms governing the dynamics of Los Angeles smog aerosol

Physical Mechanisms Governing the Dynamics of Los Angeles Smog Aerosol R. B. HUSAR, 1 K. T. W H I T B Y , AND B. Y. I-I. LIU Particle Technology Laboratory, University of Minnesota, Minneapolis, Minnesota 55455 Received August 6, 1971; accepted August 13, 1971 T h e aerosol size d i s t r i b u t i o n s m e a s u r e d during t h e 1969 Pasadena Smog S t u d y and those obtained later in laboratory smog-simulation experiments are analyzed. Emphasis is on the identification of physical mechanisms and parameters which are responsible for the daily aerosol concentration changes. The role of relative humidity, solar radiation intensity, coagulation, and condensation is discussed. Data from field measurements and artificial humidification experiments indicate that by changing the relative humidity, the submieron aerosol volume concentration, as well as the total light scattering, may be changed by at least a factor of two. The effect of solar radiation on the photochemical gas-particle conversion rate was investigated by inflating a plastic bag with particulate-free ambient air and exposing it to solar radiation. The observed nuclei-generation rates in Pasadena were on the order of 105 nuclei/sec. The solar radiation was found to be necessary for the nuclei production. Laboratory experiments performed in Minnesota suggest that the growth of photochemical nuclei after formation is governed by simultaneous coagulation and condensation. During late night hours, the aerosol was found to decay according to the laws of coagulation. The size distributions were observed to approach a universal form which could be simulated by laboratory aging experiments and by numerical (Monte Carlo) simulation. The mean coagulation coefficient for the smog decay was between 2 X 10 -9 and 10 -s cm~/sec. During the daytime, coagulation was found to limit the total number concentration to 2 X 105/cm 3 by rapid removal of small particles (0.01/~m) by the larger ones (0.I ~m). It appears that the important particle diameter range 0.I < Dp < 1.0#m, which on the average contains about 60% of the total aerosol mass fraction, was not affected significantly by coagulation. A comparison of field data with laboratory experiments and numerical calculations suggests that the noontime accumulation of aerosol mass in the 0.1 < Dp < 1.0 ~m subrange is primarily due to condensation of photochemically produced supersaturated vapors on the existing particles. INTRODUCTION

This is the third in a series of three papers on the Los Angeles smog aerosol, as measured by the University of Minnesota group during the 1969 Pasadena Smog Experiment. The Minnesota Aerosol Analyzing System, MAAS, is described in the first paper [Whitby et al. (1)]. The main experimental data on the smog aerosol size distriP r e s e n t address : K e c k L a b o r a t o r y of E n v i r o n m e n t a l H e a l t h Engineering, California I n s t i t u t e of Technology, P a s a d e n a , CA 91109. Copyright Q 1972by Academic Press, Inc.

butions are presented in the second paper [Whitby et aI. (2)]. In it the aerosol is characterized in terms of physical parameters such as aerosol number distributions, volume distributions, etc., as well as in terms of statistical parameters, such as means, standard deviations, etc. This paper is devoted to the discussion of selected physical processes and parameters which were found or suggested to be of importance in determining the smog aerosol size distributions. During the experimental period of about Journal of Colloid and Interface Science, Vel. 39, No. 1, April 1972

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3 weeks (August and September 1969), the aerosol size distribution, along with other physical, chemical, and meteorological parameters were measured in six intensive experimental periods; the duration of each intensive period was about 1 day [see Fig. 1 in t~ef. (2)]. The smog size distribution data, discussed by Whitby et al. (2), were measured and recorded by the Minnesota Aerosol Analyzing System (MAAS) in time intervals of 20 rain so that a total of 349 size distributions were obtained. Favorable meteorological as well as other environmental conditions during the intensive experimental periods permitted the sampling of a fairly representative variety of smog conditions. It is, therefore, believed that the available data are sufficient to identify some of the physical mechanisms that govern the dynamics of smog aerosol at the Pasadena sampling station. It was described previously (2) that the physical parameters of smog aerosol are generally subject to diurnal cycles: particle growth from morning until about noon, followed by a decay during the afternoon and night hours. The observed daily aerosol changes are attributed to the dynamic interaction of the following processes and parameters: I. Aerosol sources: automobile and indnstrial emissions, natural aerosol production, etc. 2. Meterological parameters: inversion height, wind speed and direction, relative humidity, solar radiation intensity, etc. 3. Chemical and physical rate processes: gas-gas reactions, gas-particle reactions, nucleation, condensation, coagulation, growth by adsorption, absorption, etc. The object of this paper is to report the observed diurnal aerosol cycle in detail and to discuss the role of solar radiation, relative humidity, nucleation, condensation, and coagulation on the daily aerosol cycle. The understanding of such a complex system requires a versatile methodology of investigation, starting with field experiments, detailed data analysis, complemented with laboratory and numerical simulation experiFor the definition of the nomenclature see Table II in Ref. (2). Journal of Colloid and Interface ~cience, Vol. 89, :Rio. 1, April 1972

ments. Our present understanding of the dynamics of the LA smog aerosol was gained through field measurements in Pasadena which were complemented by laboratory and numerical-simulation experiments at the University of Minnesota since 1969. This latter work is still in progress. In the first part of this paper, the role of sun radiation and relative humidity is discussed, followed by a comparison of laboratory and numerical smog-simulation experiments with actual smog aerosol data. In the following, our interest is focused on the changes in the volume fraction V 3 - , below 1 ~m which was found to be closely related to visibility (3, 4). The aerosol volume fraction above 1 ~m, which is believed to be subject of mechanisms other than those influencing the size distribution below 1 ~, are not discussed here. THE EFFECT OF RELATIVE HUMIDITY The variations of relative humidity, solar radiation intensity, and several other aerosol parameters during a 30-hr run are shown in Fig. 1. It shows the total number (NT top line), the total volume (VT), then V 3 - , the volume fraction below 1 ~m, and the broad band scattering measured by the nephelometer (3, 4). The variation of relative humidity (RH) and that of the sun radiation intensity (SR) is shown on the bottom of the graph. The two distinct maxima of the volume fraction at the beginning and at the end of the run demonstrate the effect of sun radiation, which sets the pattern for the diurnal cycle. Superimposed on the daily solar cycle is the effect of relative humidity. Short-term changes in R H extending over 1 hr between 18:00 and 19:00 or slow changes continuing over the entire night are reflected by a response in both volume fraction below 1 um (V3--) and total scattering. The increase of RH around midnight of August 21/22 for instance, is accompanied by an unusually high night mass concentration, which then slowly decays following the decrease in relative humidity. In the morning hours upon onset of solar radiation, a growth of V3-- is observed in spite of the decrease in relative humidity. The above data suggest

DYNAMICS OF SMOG AEP~OSOL that the two meteorological parameters, the relative humidity (RIq) and solar radiation intensity (S1%), do influence the submicron mass fraction ( V 3 - ) and the turbidity. Further evidence on the influence of RH and SR may be gathered from a statistical analysis of all the Pasadena runs: the linear correlation coefficient between V 3 - and RH is 0.40 and the linear correlation coefficient between V 3 - and SR is 0.36. Thus, individually R H and SR correlate with V 3 rather poorly. However, a multivariate 2°i

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correlation between V 3 - and the linear combination of the solar radiation intensity (SR) and relative humidity (RH) results in a correlation coefficient of 0.71. The corresponding regression equation is: V 3 - [#ma/cma] = - 2 . 1 7 q- 1.18.RH [%] q- 18.06 "SR [gin, cal/cm 2, min] Though it is certain that other independent variables, such as inversion height, wind speed and direction, traffic intensity, etc., do influence the aerosol volume fraction V 3 - , the relatively high correlation coefficient of 0.71 suggests that the relative humidity and solar radiation intensity are two major meterological parameters. It is also of interest to observe the changes of the volume distribution during a period of rapid change in relative humidity as observed between 18:00 and 19:00 hr on Aug. 21. Figure 2 shows the volume distributions at 14 % RH and then at 38 % RH measured 20 rain later. The change of the volume distributions at different humidities is manifested by a 3-fold increase of V3-and by a shift of the mode from D~ = 0.35 #m to Dp = 0.25 #m. It is likely that the rapid increase of RH between 18:00 and 19:00 was caused by the passing of different air masses over the sampling station. It is

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PHOTOCHEMICAL NUCLEATION AND GROWTH RATES

Photochemical nucleation rates and the subsequent evolution of aerosol size distribution were studied through further field and laboratory experiments. The first experiments were performed during the main sampling period in Pasadena. The experimental setup [top of Fig. 1 in Ref. (1)] consisted of a 5-m3 poly0.01 O,l 1.0 ethylene balloon (located on the roof of the Dp, ~m Keek Laboratory, at the California Institute Fro. 3. The volume distribution before (25% of Technology), a two-stage absolute filter RH) and after (86% RH) artificial humidification. arrangement, and a General Electric condensation nuclei counter. The spectral probable therefore that the volume distri- transmissivity of the 0.018-mm-thick balloon butions in Fig. 2 represent two different material was measured as 77 % at 700 m~ types of aerosols at different humidities. wavelength, decreasing monotonically to The measurement of the aerosol size distri- 45 % at 250 m~. Thus, on the average about butions, without the knowledge of the 55 % of the solar radiation was transmitted. aerosol history is, therefore, inconclusive The balloon was continuously exposed to with respect to the effect of RH. solar radiation. More conclusive data on the effect of The first experiments revealed that aprelative humidity were obtained by a proximately 3 min after the inflation of the special experiment performed during the bag with filtered air was stopped, the number main experimental period in Pasadena. The of nuclei, as monitored by the GE counter, purpose of the experiment was to increase started to increase. The initial strong inartificially the relative humidity and to ob- crease, which reached its maximum at 105serve the resulting changes in the aerosol 107 particles/cm3 depending on the day and size distribution. In this humidification hour of the measurement, was followed by experiment the smog aerosol was passed a slow decay. This phenomenon has been through a 10-fiter wet-walled vessel and observed by several investigators (5, 6) and subsequently introduced to the Minnesota it is attributed to the nucleation of photoAerosol Analyzing System [see Fig. 1 in Ref. chemically produced supersaturated vapors. (1)]. The aerosol volume distributions before A comparison of the LA smog data with (25 % RH) and after artificial humidification similar data of Bricard et al. (5) (their Fig. 2) (86 % RH) are shown in Fig. 3. reveals that both the nuclei production rate The result of the artificial humidification and the attained maximum concentrations is an approximately 60 % increase in V 3 were significantly higher for the LA air such that the shape of the volume distribu- then for the Paris air (see Fig. 4). On a tion for D~ < 1 um is essentially the same moderately smoggy day the nuclei producas at 25 % RH. The reduction of the volume tion rate during the initial 5 min was about distribution for D~ > 1 ~m in Fig. 3 is due 105 nuclei/em3 sec. to impaction losses in the mixing type The observed day-to-day variation of the humidifier. These experimental data have nucleation rates (Fig. 4) suggest that the lead us to conclude that a considerable frac- attained maximum concentrations are assotion of smog aerosols in the submieron range ciated with the rate of photochemical gasare hygroscopic. The relative humidity is, particle conversion. In order to investigate therefore, a major meterological parameter this hypothesis the daily variation of the

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Journal of Colloid and Inter'face Science, Vol. 39, No. 1, April 1972

DYNAMICS OF SMOG AEROSOL

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NUCLEATION M E A S U R E M E N T SEPT. 13, 1969

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experiments, a 15-liter Pyrex flask was used instead of the baloon. Figure 5 shows the maximum attained concentrations at different hours of the day on Sept. 13. There is a rise of the production rate until 10:00, a relatively constant production rate until about 17:00, and a sharp drop to zero at 17: 30. The drop in the nuclei production rate coincides with the diminishing solar radiation intensity. The following auxiliary experiments performed in Pasadena provide further support for the hypothesis that the nuclei production rates are directly associated with solar radiation: 1. Atmospheric, partieulatedree air sampled at midnight, but exposed to solar radiation at noon, indicated a similar produetion rate as the irradiated noontime air. 2. Particulate-free atmospheric air sampled at noontime, but confined in a dark room did not produce condensation nuclei. Although these experiments provided information on the nucleation rates, they reveal no details about the particle size-time evolution of the photoehemically formed aerosols. Results of other investigators (5, 6) have shown that the photochemieally formed nuclei tend to grow in size after formation. However, the diffusion battery method (5) and the total light-scattering measurement (6) used by these investigators could not provide sufficiently accurate data to conclude what mechanism is responsible for growth. Complete size distributions of aging photochemical aerosols were only recently obtained in our laboratory at the University of Minnesota (7). Photochemical aerosols were produced spontaneously in a polyethylene bag initially filled with particle-free laboratory air and irradiated by diffuse solar radiation penetrating the wide, north-facing window of the laboratory. Parameters other than the aerosol size distribution were not measured. It was found that during the initial stages of growth, when Dp < 0.01 tim, the aerosol size distribution is rather narrow, with an equivalent logarithmic standard deviation of ~g = 1.35. With further growth, the size distribution becomes broader, reaching Journal of Colloid and Interface Science, VoI. 39, No. 1, April 1972

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HUSAR, WHITBY~ AND LUI

a~ = 1.5 at Dp = 0.03 tim. The shape of the measured size distributions was found to be somewhat similar to the spectra of decaying aerosols due to Brownian coagulation (8). Significant differences between the evolution of photochemical aerosols and aerosols undergoing Brownian coagulation were observed by comparing higher moments of the number distribution such as the total aerosol surface area and the total volume fraction. While for pure Brownian coagulation (i.e., absence of aerosol sources) the total volume fraction is conserved, in the case of photochemical aerosol formation the volume fraction was found to increase continously with time in spite of the decrease of the total number concentration as shown in Fig. 6. During the growth of photochemical aerosols, only the total surface area S is ~pproximately conserved. Based on the experimental data shown in Fig. 6 and further results (7), we propose that the chronological evolution of a photochemically formed aerosol in an initially particle-free chamber may be characterized in the following manner: 1. The initial strong increase of a to{al number concentration is a manifestation of photochemical nucleation. The nucleation is

heterogeneous, since new particles are generated, while the existing ones continue to grow by condensation. This is evident from the observation that the nucleation continues over an extended period of time ranging from several minutes to hours; and second, from the eontinously increasing characteristic diameter D~ = (6 VT/TrN) 1/a. 2. When the aerosol concentration reaches a sufficiently high value, the particles start to interact by coagulation. The maximum concentration is attained when the production rate Q (particles/see) is equal to the coagulation rate K p N 2 where K~ is an average coagulation constant of the polydisperse system and N is the total number of particles. 3. With further growth, the aerosol surface area approaches a value which is sufficient to accommodate all the supersaturated vapor. The supersaturation drops and the nucleation rate diminishes. The decay of the number concentration is then entirely due to coagulation, while the increase of the volume fraction is determined by the condensation rate. The above process of photochemical nucleation and growth may be expressed by the following simplified rate equation: dN/dt = -K~

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During period 1, the nuclei production rate Q is considerably higher than the coagulation rate. In period 2, the two right 300 v_ side terms are approximately equal and the rate of change in the number concentration I0 is small. In the final period 3, the source term Q is zero and Eq. [1] reduces to the % 2oc well-known coagulation equation. The invariance of the dimensionless parameter ST/VTmN m in Fig. 7 derived by Pich et al. (9) indicates that the subseIOC -~ ~ ST quent size distributions during the decay period (3) are similar in shape, i.e., they are self-preserving. o I I I I I I ~ A further observation, derived from i200 2400 3600 4800 6 0 0 0 7200 8400 several spontaneous photochemical growth TIME, SEC FIG. 6. The chronologicalevolution of the total experiments, is that due to the simultaneous number (NT), total surface area (ST), and totat nucleation and condensation, the volumevolume fraction (VT) for a photochemically mean diameter 13~ during period 2 is ~pformed aerosol. Note the continuous increase of proximately 0.005 tim regardless of the photochemical conversion rate. If this ohVT, probably due to condensation. NT

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Journal of Colloid and Interface Science, Vol. 39, No. 1, April 1972

DYNAMICS OF SMOG AEROSOL servation may be extended to the photochemical nucleation experiments shown in Fig. 4, then the particle-number generation rate may be transformed to volume (or mass) using the average diameter /)p and the generation rate. We reconsider such estimates in the following section. THE ROLE OF COAGULATION AND CONDENSATION A consideration of the physical mechanisms and parameters which may alter the submicron aerosol size distribution reveals that, on a time scale of several hours, substantial changes in the size distribution may be caused only by the following factors: the rate of aerosol production by sources, condensation, coagulation rate, and convective transport. The removal of submicron particles by impaction and sedimentation may be neglected. The largescale aerosol transport by Brownian diffusion is also insig~aificant. The investigation of aerosol production rates by sources and of the nature of the convective transport, was beyond the scope of the 1969 Pasadena smog experiments. such data could only be obtained by spatial (vertical and horizontal) size-distribution measurements and by sampling in the vicinity and downstream of sources. The simplest model for an urban basin atmosphere is one in which it is assumed that air masses in the entire urban area are perfectly mixed horizontally and vertically. The urban basin may then be regarded as a well-mixed reactor bounded horizontally by geography and vertically by the inversion height. In such a model, no consideration needs to be given to the sampling position. Such a model is a rather rough approximation, but it seems to be the logieM first step before developing more comprehensive models. Furthermore, this perfectly mixed atmospheric model permits a convenient laboratory simulation. From the available data, there is some evidence that, for certain periods of the diurnal aerosol cycle, both convective transport and aerosol sources tend to play a minor role, i.e., a well-mixed vessel model is a fair approximation. During the late night hours, coagulation is believed to be the

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governing mechanism, whereas the condensation on the existing particles is thought to be mainly responsible for the aerosol growth during the early noon hours. In the following section, these two processes, coagulation and condensation, are discussed in more detail. The emphasis is plaeed on physieaI principles and on comparisons of field and laboratory experiments, rather than on the mathematical details. Coagulatwn

The relative motion of submicron particles which leads to interparticle collisions, i.e., coagulation, may be caused by the following forces: thermal force (which leads to Browman motion and Brownian coagulation) ; inertial forces (turbulent coagulation) ; electrostatic force; and gravitational force. An order of magnitude estimate of these forces suggest that, for submicron particles suspended in the atmosphere, the prevailing coagulation mechanism is the thermal or Brownian coagulation (12). Therefore, in the numerical studies on coagulation discussed in this section, only Brownian coagulation was considered. The theory of coagulation rates of submicron particles in Brownian motion was recently reviewed by Fuchs and Sutugin (11); Hidy and Brock (12) and Husar (8). Though the available coagulation theories for the submicron (or Knudsen) range are approximate, it is believed that the coagulation constant of monodisperse particles Km in the size range 0.002 ~m < Dp < 1.0 ~m may be predicted within a factor of 2 which is considered to be sufficient for our atmospheric aerosol studies. For monodisperse systems, K~ is a weak function of particle size: Km ~ 10-9 cm3/sec [Fuchs (10), p. 294] for 0.006 ~m < Dp < 0.05 ~m, decreases monotonically to K~ ~ 3.10 -~° em3/sec for Dp = 1.0 ~m. For our present consideration, however, it is more important to consider the coagulation rate of highly polydisperse systems, such as those encountered in the atmosphere. In a polydisperse system, the coagulation constant K~ is defined by Eq. [1] with the source term Q equal to zero. The minimum value of Kp corresponds to the coagulation Journal of Colloid and Interface Science, VoL 39, No. 1, April 1972

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HUSAR, WtIITBY, AND LUI

discrepancy between the experimental and theoretical size distributions (17) and characteristic coagulation times (18) was noted. It seems that the Pasadena smog data, L.AI,AUG, 2 8 / 2 9 , 196 along with laboratory and numerical simula106 tion experiments, offer an opportunity to 1500 elucidate some of these discrepancies. Figure 7 shows three typical size distributions measured on Aug. 28 at 15:00 and at ~ 105 -01:00 and 04:00 on Aug. 29. At 15:00, the 'oE or_a, number distribution is dominated by parti6 4:00 z i cles below 0.05 ~m. At 01:00, the total number of particles is considerably reduced 10 4 and also there is a reduction of the number concentration in the 0.1 ~m < Dp < 1.0 ~m size range, where a large fraction of the mass is located. At 04:00, the lower end of the number distribution decreased further, but no significant change is observed for D~ > 0.1 t~m. This suggests that, between 01:00 and 04:00, the size distribution j ,001 d 2 ~.I .0[ changes are essentially due to coagulation. Dp, pLm The experimentally observed decay of Fro. 7. Aerosol number distributions at 15:00 smog aerosol in the late night hours was on Aug. 28; at 01:00, Aug. 29; and 04:00, Aug. 29: further investigated by laboratory and Note the decay of the lower end of the distribution. numerical simulation experiments (8). In a 75-m3 coagulation vessel, an initial distribuconstant of monodisperse particles K ~ . tion was produced which approximated a The increase of Kp with increasing poly- noontime smog aerosol (Fig. 8, t = 600 see). dispersity is due to the preferential collisions Such size distribution was produced by between particles with large size difference continuously reinforcing an aging aerosol, (10). which was produced by heating a nichrome The average coagulation coefficient of a wire. The absolute concentration for the polydisperse system K~ is obtMned by laboratory simulation experiments was about integration of the product of two number 10 times higher than the corresponding distribution functions, weighted by the atmospheric concentration. This was necescollision-frequency factor. (Fuchs (10), Eq. sary in order to reduce the wall losses. 49.28). For narrow size distributions (say The main characteristics of the initial with logarithmic standard deviation ~g -< spectrum showa in Fig. 8 is that it consists 1.4), the value of Kp is, at most, 15 % higher of two relatively distinct subranges, one than K ~ . For highly polydisperse atmos- below and one above D~ = 0.05 ~m. The pheric or combustion aerosols, K~ may subrange below 0.05 pm contains 93.0 % of attain values one to two orders of magnitude the total number, NT, but only 1.3 % of the larger then the corresponding K ~ . totM volume fraction, VT. The surface area It has been recognized by many investiga- is divided such that 90 % is in the upper tors that coagulation is one of the major subrange and 10 % in the lower. mechanisms responsible for the growth of All estimate of the collision rates readily atmospheric aerosols below 0.1 ~m in size reveals that the collision frequency between [Junge (13), Friedlander (14), Clark and the particles in the larger subrange for Whitby (15), Carnuth (16)] but the available atmospheric aerosol size-distribution data dimensionless time ~ = NoK# of the order were not sufficient for experimental verifica- of unity, is negligible compared to the tion of its importance. Furthermore, a collisions between the subranges. No is the

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Journal of Colloid and Interface Science, V o l . 39, N o . 1, A p r i l 1972

DYNAMICS OF SMOG AEROSOL I0 3

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number concentration at the beginning of the measurement. Initially, collisions within the lower subrange are substantial but, with increasing dimensionless time r this type of collision also becomes negligible and the coagulation transfer of matter is predominantly governed by collisions between particles belonging to different subranges. Since the amount of mass transferred is negligible compared to the total mass, no significant changes are expected to occur in the upper end while the number in the lower subrange is likely to decrease strongly with increasing t. The experimentM data shown in Fig. 8 agree with the above qualitative arguments eoncerning the decay of a "bimodal" spectrum. At t = 2700 see, the lower subrange has virtually disappeared, while the concentration of particles in the smaller size range of the upper subrange has decayed only a little. In a numerical experiment, the decay was simulated by a Monte Carlo run (8) with an initial distribution approximating the experimentally measured initial distribution.

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As shown in Fig. 8, the approximation is not unbiased. The numerically obtained size distributions corresponding to t = 2700 see indicate a close agreement between the experimentally obtained data and the Monte Carlo simulation. Stronger deviations are detectable at t = 1200 see which is, at least partly, attributed to the experimental difficulties of measuring a low concentration of small particles in the presence of a high concentration of larger ones. For the numerical simulation, Fuch's (10) limiting sphere method was used to calculate the collision frequencies. The numerical simulation experiments also showed that, due to the preferential collisions between particles belonging to different subranges the value of K~ corresponding to t = 600 see is 55 X 10-l° cm3/sec while Km at the same mass mean diameter of Dp = 0.12 ~m is 7 X 10-l°, i.e., eight times less. With increasing time, however, the value of K~ rapidly approaches Krn.

It is of interest to compare the volume distribution of the laboratory-simulated aerosol to the well-aged atmospheric aerosols measured in the Los Angeles basin (2). The comparison of normalized volume spectra and the 19 subsequent well-aged atmospheric spectra agree closely, thus further substantiating the validity of the laboratory simulation of the night aerosol decay. We shall now discuss the role of coagulation in the daytime period of the diurnal aerosol cycle. One of the findings of the Pasadena smog study was that the total number of particles during smoggy periods was on the order of 105/em 3 and exceeded this number for only short periods as shown in Fig. 9. On the basis of tile previous discussion of the coagulation of polydisperse system and other physical considerations, we suggest that the instantaneous nuclei concentrations, shown in Fig. 9 may be interpreted as follows: The ambient aerosol sampled at the Pasadena sampling station consists of: 1. a well-mixed "background" air mass, carrying weIl-aged aerosols produced relatively long time before sampling; and 2. individual eddies containing aged as Journal of Colloid and Interface Science, Vol. 89, No. 1, April 1972

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FIG. 9. The instantaneous readings of the total nuclei concentration: The "base line" indicates the concentration of the aged aerosol passing over Pasadena and the spikes are the manifestation of local sources. well as fresh aerosols produced near the sampling point. For the well-aged aerosol (for which r = N o K p t >> 1) the total concentration N T at time t is independent of the initial concentration N o , and is given b y N T "~ 1/K~,t. Thus, the background number concentration, which sets the base line for the nuclei concentration fluctuations in Fig. 11 is a measure of the general age of the aerosol and not necessarily of the aerosol volume concentration. Simple estimates suggest t h a t the role of coagulation in the noontime growth of the volume fraction in the range 0.1 ~m < Dp < 1.0 ~m is minimal: Assuming extreme high values for the urban concentration (106/cm 3 at 0.01 ~ m ; 5 X 103/cm 3 at 0.2 ~ m ; K p = 10-7 cm3/sec), the maximum amount of m a t t e r transferred from the range Dp < 0.05 ~m is 0.9 #m~/cm 3, hr. This amount is negligible compared to the measured growth rates of 10-40 ~m3/cm 3 hr in the 0.1-1 ~m range. Condensation

T h e early noon period of the diurnal aerosol cycle between 10:00 and 12:30 hr is characterized b y an increase of the submicron aerosol mass concentration, an increase in turbidity, and b y a relatively stable total number concentration (2). Since, during this period, the mass concentration approaches its peak at about t2: 30, an understanding of the mechanism and parameters which Journal of Colloid and Interface Science, Vol. 39, No. 1, April 1972

determine the rate of mass accumulation is of considerable importance. I t was pointed out previously (2) that the increase of the aerosol mass concentration in the early noon hours is most pronounced in the 0.1 gm < Dp < 1.0 gm range, subrange 3. Around noontime this subrange may contain over 70 % of the total aerosol mass. I t was also shown [Fig. 12, in Ref. (2)] t h a t the accumulated aerosol volume (or mass) in subrange 3 is such t h a t successive volume distributions AV/A log Dv are similar in shape and their form could be approximated b y a logarithmic normal distribution. The mode of the volume distribution in V3 was found to be at about Dp = 0.25 gm and it is nearly invariant with time and absolute volume concentration. T h e standard deviation of the best fit log-normal distribution showed a slight decrease from zg = 1.70 at 10:00 to zo = 1.65 at 12:00. Using the available field data and the data from laboratory experiments it is attempted to identify the mechanisms responsible for the increase of the aerosol mass concentration in the early noon hours. In general, the ~ o w t h of the aerosol mass concentration in subrange 3 (0.1 gm < Dp < 1 gin) may be attributed to three potential mechanisms: 1. aerosol emission from ground level sources directly into size range 3; 2. aerosol growth by accumulation of photochemically produced vapors; and

DYNAMICS OF SMOG AEROSOL 3. coagulation transfer of matter into size range 3. In the previous section it was shown, t h a t for the measured size distributions, the amount of m a t t e r that could be transferred into size range 3 by coagulation is at most 1.0 t~m3/em3 hr. Compared to the measured growth rates of 10 to 40 ~m3/cm 3 hr, the eoagulative transfer, listed as mechanism 3, may be neglected. Due to the lack of data on the size distribution and intensity of sources, no direct estimate could be made on the role of mechanism 1. I t was indicated previously t h a t we attribute a large fraction of the growth rate during 10:00 and 12:30 to condensation. Unfortunately, our arguments are based on indirect, laboratory simulation, numerical simulation, and speculative arguments rather than on convincing field measurements. First, as a result of the photochemical nucleation experiments (shown in Fig. 4), it was found t h a t the nucleation rate at noontime reached 105 nuclei/era ~ see. Subsequent laboratory experiments showed that, while nuclei are still produced, there is simultaneous growth by condensation. The volume mean diameter of such a "continuously reinforced" condensation aerosol was found to be about /)p -- 0.005 tim at the maximum number concentration. The nuclei production rate of 105/era 3 see at a size of /)~ = 0.005 ~m yields an aerosol volume growth of 24 um3/cm ~ hr, which is on the order of the observed growth rates. The laboratory photochemical experiments (7), mentioned previously, also revealed t h a t the growth rates d V / d t for a given run were uniquely associated with a given surface area S (Fig. 10). The experimental data indicate that, with increasing growth rate, the "equilibrium" surface area also increase. T h e range of the measured surface area S and d ( V 3 - ) / d t during 10:00-12:30 in the Los Angeles smog is shown in Fig. 10 as a shaded area. An extrapolation of the laboratory results, broken line, suggest t h a t in the morning hours in LA, there is more than sufficient aerosol surface area present for the aeeomodation of the photoehemieally produced vapors. This implies that, in general, the supersaturation of the photoehemieally pro-

221

r. -

o

LABORATORY

LA

SMOG

DATA

"

t

L

ioo~ ~ 001

O[

[0

dr/dr,

I0

I00

#-mS/cm3, hr

Fro. 10. The experimental values for the "equilibrium surface area" (see Fig. 6) at various aerosol formation rate dV/dt: The size distribution of the Los Angeles smog aerosol in the morning hours is such that the surface area available for condensation is more then sufficient to aecomodate the supersaturated vapors. duced vapors does not build up to a high value and also that the production of new nuclei b y photochemical processes in the smog is expected to be minimal. A further implication of the low supersaturation is that the condensation growth of particles is restricted to particle sizes larger than a critical diameter. With this tentative conclusion in mind, we may now consider a numerical experiment in which we follow the growth of a morning aerosol, subjected to a weak supersaturation. Our primary interest is the evolution of subsequent volume distributions, d V / d log D z as a result of the condensation. T h e volumetric growth rate, d V / d t of a submieron particle b y condensation may be expressed as follows r11): dV dt-

lr dD z 2 D'~ dt -

aD z 1 -t- b(2X/Dz) ' [2]

where a depends on the molecular weight and supersaturation of the condensing vapor; b is a constant approximately unity; and X, the mean free path of the condensing vapor. For the following calculation, X was chosen to be that of the air: X -- 0.066 ~m; b = 1, and a = const. Integrating Eq. [2] from Dp = D~0 at t = 0 to D~ at time t, we obtain the following relationship : D , 2 -t- 4XD, = D~0 = 4XD~0 -V 4at.

[3]

7r

Journal of Colloid and Interface Science, Vol. 39, No. 1, April 1972

222

HUSAR, WtIITBY, AND LUI

The positive root of Eq. [3] yields the size D~ of a particle growing from initial size D~o during the time interval at. The value of the constant a may only be determined from the supersaturation and substance of the condensing vapor. This information is not available. For the following qualitative considerations, however, it is sufficient use at as a characteristic time parameter. It is of interest to note that, in a dilute, polydisperse system, i.e., when particles do not interact by coagulation and for a = eonst, the size change of any particle is given by Eq. [3]. Thus, in principle, by tracing the growth of individual size ranges, the changes in the entire size distribution may be followed. An equivalent, but numerically more elegant and more convenient procedure of determining the size distribution changes, is the transformation of distribution functions. The number distribution function n(Dp) is defined as the number of particles dN in the size interval D~ and D~ + dDp, i.e., dN AN n(D~) - dDp - - AD~

[4]

Due to the finite value of the measurable size increases, experimental data are generally presented in terms of the approximate distribution function AN/AD~. Since in the process of condensation, no new particles are produced and the growth of each particle is given by Eq. [3], one can readily calculate the number distribution function at any time at by transformation from the independent variable D~9 to D~. Denoting the initial number distribution function by n(Dpo) one obtains for the distribution function n(D~) at time at the following expression:

by the following relationship: dV ~r d ]og D~ - 6 logs I O . D ~ n ( D ~ ) .

[6]

Using Eqs. [4] and [5], the evolution of the volume-distribution function may be calculated for different values of the characteristic time at. For the initial size distribution, in the numerical experiment, the measured smog data on Sept. 3, 10:00, Run 275 was taken. The critical size, i.e., size above which nuclei grow by condensation, was set at D, = 0.09 ttm.

The results of the calculation are shown in Fig. 11 for different values at at. The broken lines are the calculated growth "trajectories" of experimental points using the aerosol size distribution existing at 10: 00. As expected, the rate of change of the particle diameter is the largest at the lower end of the distribution. Inspection of Fig. 11 leads to the interesting observation that the subsequent volume distributions have their peak at approximately the same diameter and that the remaining points of the distribution at any time are similar in shape. We now recall that this growth pattern is 200

I

t I I 1

t~

a? : 0.032

150

c0 I 0 0

o

50

n(D~) = n(D~o) dD~o dDp =

n(D~o)

F1 + L

/1 /

10:00

[5]

lu2 (D~0 + 2x)~J " 4at

Furthermore, it can be shown that the volume-distribution function dV/d log Dp is related to the number-distribution function Journal of Colloid and Interface Science, ¥ol. 39, No. 1, April 1972

I

0 0,1

I

I

I

I

I

II

Op , p.m

Fro. 11. The calculated condensational growth pattern of the aerosol size distribution measured at 10:00 Aug. 28 (at = 0).

DYNAMICS OF SMOG AEROSOL similar to the measured growth pattern in LA smog, shown in Fig. 12 in Ref. (2). Thus we believe to have found a further evidence that the growth in the early noon hours is due to condensation. Figure 11 shows t h a t the aerosol particles with D~ = 0.09 tim at at = 0 grow to Dp = 0.17 #m at at = 0.032. If there were no new particles introduced into the range D~ > 0.09 ~m, then, at at = 0.032, the volume distribution would be sharply cut off at Dp = 0.17 ~m. T h e experimental data indicate, however, t h a t the lower end of the volume distribution is continuous, i.e., in the process of condensational growth, new particles are introduced in the range D~ > 0.09 ~m presumably by coagulation or from sources. The upper end of the calculated volume distribution in Fig. 11 is not changed sig:aificantly. This is in contrast to the measured atmospheric data [Fig. 12, Ref. (2)]. A fascinating but again, highly speculative explanation for this observation may be derived from the available data on the chemical composition of the smog aerosol, reported b y Mueller (19). I t was found that the aerosol below 0.5 ~m contains much carbon, while in the size range 0.5 < Dp < 2.0 ~m contains a large amount of sulfur. This finding hints on the possibility of two (or more) component vapor condensation: (i) a vapor with relatively high supersaturation activating particles larger then 0.09 ~m and producing aerosol with high carbon content, and (ii) a less supersaturated sulfur-associated vapor which activates particles larger then Dp > 0.5 ~m. In the context of these considerations on the role of condensation, it seems appropriate to mention the atmospheric aerosol measurements of Kocmond and Mack (20) performed downstream of an industrial area near Buffalo, NY. From an airplane they conducted soundings of the horizontal and vertical distribution of the total nuclei concentration and also of the cloud nuclei measured b y the Cornell Aeronautical L a b o r a t o r y cloud nuclei counter. The soundings, performed on 8 different days have yielded some rather interesting results: T h e cloud nuclei counts in the vicinity of the source (less then 10 k m downstream) was found to decay approximately in accordance

223

with the concentration decay of a turbulent plume. At a distance of about 20 kin, however, a secondary peak of cloud nuclei count was observed with no significant change in the totaI nuclei concentration. Since, on some of the days, the downstream soundings were made over Lake Erie, it is unlikely that the observed increase of the cloud nuclei counts was due to the presence of ground sources. The authors, therefore, suggest t h a t the secondary peak could be due to the growth of particles by condensation of photochemieaily produced vapors on the existing particles. I t is known that cloud nuclei counters tend to indicate the number of aerosol particles larger than a critical size. For Koemond and Mack's measurements, the critical diameter is estimated to be approximately 0.1 pm. Accordingly, the obs~:rved secondary peak downstream of the source is probably associated with a considerable growth in the mass-concentration in subrange 3, much like the growth of smog aerosol in the Los Angeles basin. 2O

,, ~ , , ~ , i ~

i , ~ , l

L

~ COAGULATION I TOTAL R

~

__~~

i

i

~

8O

6O

•

TOTAL

VOLUME

s

I

i

I VOLUME,Dp< l~rn V3-

-

I I

I r

VOLUME ,Dp > rffm V4+

--

% o

4o

>.2O I i

r

f 4

/,

If...'l,

IIX,./,SOLAR RADIATION

x

I 8

I

I

h

)x [

i2 ;6 20 HOUR OF THE DAY

i

[ 0

I

I

;

4

FIG. 12. Comparison of the grand average total ntamber concentration (GE condensation nuclei counter) NT-CNC, VT, V3--, V4+ for each hour of the day with solar radiation. Note that, while the total volume peaks at the same time as the solar radiation, the condensation nuclei concentration does not. Also note that decay in NT-CNC during the early morning hours from 00:00 to 04:00 can be fitted quite well by a simple coagulation curve assuming a coagulation constant of 1.8 X 10-9 cm3/see. Journal of Colloid and Interface Science, VoI. 39, No. 1, April 1972

224

HUSAR, WHITBY, AND LUI SUMMARY

Based on the previous discussion on the individual processes and parameters, we now summarize our major findings and tentative explanations concerning the dynamics of the Los Angeles smog aerosol. For this purpose, it seems most appropriate to observe the "average" daily cycle of several characteristic aerosol parameters shown is Fig. 12. The selected parameters are the total number of particles measured by the General Electric nuclei counter, top line; the total volume fraction (VT) measured by the MAAS and its two subranges: below 1.05#m (V3-) and above 1.05 ~m, V4-b. The sun radiation intensity is plotted on the bottom line. The averaging was performed in two steps, first averaging three runs to obtain an hourly average and then the values for a given hour of a day were averaged over the 7 days of experiments. The daily growth period begins at about 05:30 in the morning somewhat before sunrise. It is manifested by a sharp rise of the total number concentration and by a less pronounced increase of the aerosol volume fraction. This initial rise continues until about 08:30. It is attributed primarily to the morning rush hour. The initial rapid growth is followed by a period of decreasing concentration between 08:30 and 10:30 which is presumably due to ~he decline of the automobile traffic intensity and due to the slow photochemical conversion rates. At 11:00 with the sun approaching the zenith, a strong increase of the volume below 1 ~m (V3-) is observed which may be attributed to photochemical reactions and subsequent gas particle conversion in form of condensation, reaching its peak at about 12:30. The sharp rise of V 3 - is (Fig. 12) immediately followed by a decay that continues until 16:30. As at present, no explanation is offered for the observed decay of V 3 - between 12:30 and 16:30. Possible explanations may include dilution due to the lifting of the inversion height or it may be evaporation. Simple estimate suggests that the decay cannot be attributed to removal by impaction or sedimentation. At about 15:30 a secondary peak is observed for the vohime fraction of particles larger than 1 ~m which is believed to be associated with the second rush hour. Starting at 16:30 the volume fraction in both subranges remains essentially constant until the new daily cycle starts at about 05:30. The total number concentration has its peak at about 17:00 and it decays at a slow rate until about 23:00. Evidently various sources, such as automobile traffic, provide sufficient nuclei during the early night hours (17:00-23:00) to compensate for the decay b y coagulation. The contribution of these nuclei sources to the aerosol mass fraction, Journal of Colloid and Interface Science, Vol. 39, No. 1. April 1972

however, is negligible. The nuclei sources apparently diminish at about 23:00 and the dynamics of the smog aerosol size distribution is then essentialIy governed by pure Brownian coagulation. The broken line, in the top right corner of Fig. 12, indicates the theoretical decay curve for the total number concentration as a result of pure Brownian coagulation (Kp = 1.8 X I0-s cm3/see). REFERENCES 1. WHITBY, K. T., LIu, B. Y. H., HVsAR, R. B., AND BARSIC, N. J., J. Colloid Interface Sci. 39, 136 (1972). 2. WHITBY, K. T., HVSAR, 1%. B., AND Lltr, B. Y. H., Colloid Interface Sei. 39, 177 (1972). 3. ENSOR, D. S., CttARLSON, R. J., AHLQUIST, N. C., WtIITBY, K. T., HUSAR, R. B., AN]) LIu, B. Y. H., J. Colloid Interface Sci. 39, 242 (1972). 4. TItlELKE, J. ~., CHARLSON, R. J., WINTER, J. W., AHLQUIST, N. C., WmTBY, K. T., ItusAn, R. B., .~ND MY, B. Y. H., J. Colloid Interface Sci. 39,252 (1972). 5. BRICARE, J., BILLARD, F., AND MADELAINE, G., J. Geophys. Res. 73,342-355 (1968). 6. GOETZ,A., ANn PUESC~EL, R., Atmos. Environ. 1,287-306 (1967). 7. HVSAR,R. B., ANOWHIMSY,K. T., unpublished data. 8. HvsAn, R. B., Phi) thesis, Univ. of Minn, 1971. 9. PICH, J., FRIEDLANDER, S. I~., AND LAI, F. S., Aerol Sci 1, 115-126 (1970). 10. Fvc~s, N. A., "The Mechanics of Aerosols." Pergamon Press, New York, 1964. 11. Focus, N. A., AND SVTUGIN,A. G., "Visokodyspersny Aerosoly" (Highly Dispersed Aerosols). Soy. Acad. Sci. Publ. House, Moscow, 1969. 12. Hmv, G. M., AND BI~OCK, J. R., "The Dynamics of Aerocolloidal Systems," Pergamon Press, New York, 1971. 13. JUNGE, C. E., "Air Chemistry and Radioactivity." Academic Press, New York, 1963. 14. ]?I¢IEDLANDER, S. I4~., or. Meteorol. 17, 373

(1960). 15. CLARK,W. E., AND WttlTBY, K. T., or. Atmos. Sei. 24, 677 (1967). 16. CARNVT~, W., Proc. Int. Conf. Condensation Ice Nuclei, 7th, 1069, 677 (1969). 17. FRIEDLANDER, S. K., AND HIEY, G. M., Proc. Int Conf. Condensation Ice Nuclei 7th, 1969, 21 (1969). 18. JUNGE, C. E., or. A t m o s . ,%i. 26,603-608 (1969). 19. MVnLLER, P. K., unpublished data. 20. KOCMOND, W. C., AND MACK, E. J., Cornell Aeronautical Lab. Rep. VC-2730-P-1, Buffalo, New York, 1971.