Condensational Growth of Ultrafine Aerosol Particles in a New Particle Size Magnifier

Transcription

1 Aerosol Science and Technology ISSN: (Print) (Online) Journal homepage: Condensational Growth of Ultrafine Aerosol Particles in a New Particle Size Magnifier K. Okuyama, Y. Kousaka & T. Motouchi To cite this article: K. Okuyama, Y. Kousaka & T. Motouchi (1984) Condensational Growth of Ultrafine Aerosol Particles in a New Particle Size Magnifier, Aerosol Science and Technology, 3:4, , DOI: / To link to this article: Published online: 06 Jun Submit your article to this journal Article views: 409 Citing articles: 59 View citing articles Full Terms & Conditions of access and use can be found at

2 Condensational Growth of Ultrafine Aerosol Particles in a New Particle Size Magnifier K. Okuyama, Y. Kousaka, and T. Motouchi Department of Chemical Engineering, University of Osaka Prefecture, Sakai 591, Japan A new particle size magnifier (PSM) has been manufactured. In order to evaluate the performance of the PSM, the condensational growth of nltrafine aerosol particles in a supersaturated dibutyl phthalate vapor-air mixture is investigated theoretically and experimentally. First, the supersaturation ratio, the condensable DBP vapor content, and the critical size of the particle that will grow in the PSM are calculated for the mixing of hot air containing the DBP vapor with normal-temperature vapor-free air. Then the time dependence of the droplet radius during condensational growth is evaluated by numerically solving the basic equation under various conditions. From the results it is found that at higher particle number concentrations, the final droplet radii can be determined by the particle number concentration and the condensable DBP vapor content, but that at lower concentrations the particle growth can be approximated by the growth of the isolated droplet. Finally, size distributions of grown DBP droplets in the PSM are determined by sedimentational size analysis and electrical particle size analysis. Good agreement is seen between the experimental results and the previous theoretical analyses, and the overall performance of the PSM is revealed. INTRODUCTION In recent years, the study of the behavior of ultrafine aerosol particles smaller than 0.1 pm has led to a greater understanding of such diverse processes as gas-to-particle conversion in a chemical reactor, air cleaning, coal combustion, diesel particle emission, and cloud formation in air. The size analysis of ultrafine aerosol particles can usually be made with diffusion batteries or electrical aerosol analyzers. However, because of the difficulty of direct determination of the particle number concentration of aerosols in their suspended state, the particle size must be enlarged by heterogeneously condensing the vapor of some liquid on the particles, with the particles acting as nucleation centers. For this purpose, various kinds of condensation nucleus counters (CNCs) have been widely used as convenient aerosol detectors. Most of the CNCs are classified into three types: (1) expansion type CNCs, where a supersaturation is produced by the intermittent adiabatic expansion of moist air; (2) continuous flow type CNCs, where hot air saturated with vapor is cooled by a thermal cooling tube to attain supersaturation; and (3) continuous mixing type CNCs, where room-temperature aerosol is mixed with a hot vapor-air mixture. Most of these CNCs employ the vapor of water or alcohol, which have low boiling points and produce micron-order but unstable droplets which are quickly detectable. On the other hand, Kogan and Burnasheva (1960) developed a kind of continuous mixing type CNC called the particle size magnifier (PSM). In this PSM, a room-temperature aerosol is continuously mixed in a conical nozzle with high-temperature air containing the vapor of a substance (such as dibutyl phthalate (DBP) or dioctyl sebacate (DOS)) which has a rather high boiling point. Because the PSM can continuously enlarge ultrafine aerosol particles to stable droplets of around 1 pm, the PSM is considered a practically useful CNC in conjunction with an ultramicroscope or an optimal counter. Aerosol Science and Technology (1984) Elscvicr Science Publishing Co., Inc.

3 354 Okuyama, Kousaka, and Motouchi The PSM can also be a convenient aerosol generator because the size of the grown droplets can be readily controlled by adjusting the number concentration of the condensation nuclei, the temperature of the vapor-air mixture, the mixing ratio of both streams, and so on. Fuchs and his colleagues (1963, 1965, 1968, 1981) have obtained experimental results on the behavior of ultrafine aerosol particles using the PSM. However, the PSM has not come into wide use among other aerosol researchers and there still remains some uncertainty on the performance of the PSM. It is the purpose of this paper to investigate, from both theoretical and experimental points of view, which factors influence the condensational growth of ultrafine aerosol particles in the PSM using DBP vapor. First, the supersaturation ratio, the quantity of condensable DBP vapor, and the critical size of the particle to be activated are evaluated under various conditions. Then, the growth rate of monodisperse DBP droplets in the supersaturated atmosphere is calculated, taking into consideration the effect of the interactions of heat and mass transfer on the droplet growth process. In these experiments, a new PSM with a different structure from that developed by Kogan and Burnasheva (1960) is elaborated, and its performance is examined under various conditions. THEORETICAL CONSIDERATIONS Condensable DBP Vapor Content and Supersaturation Ratio In the PSM, the room-temperature air containing condensation nuclei is continuously mixed at a certain ratio with the high-temperature air saturated with DBP vapor. A strict evaluation of the consequent supersaturated atmosphere, made by solving the energy and vapor conservation equations with the velocity profile, is very difficult to obtain because it depends on the temperature and the velocity of both streams, the structure and the material of the PSM, and - 1 I I T[ Ti Tsf temperature FIGURE 1. Change in vapor content with temperature during condensation. so on. Assuming that the hot vapor-air mixture having temperature T,, is mixed very rapidly and adiabatically with the aerosol having temperature T,, the supersaturated atmosphere is produced at the point "i" on the vapor content-temperature chart in Figure 1. The changes in vapor content and temperature can be obtained from the same method described in previous papers (Yoshida et al., 1976, and Kousaka et al., 1982) concerned with the mixing of two kinds of water-vapor saturated aerosols having different temperatures. In the supersaturated atmosphere, the temperature T, and the absolute mass of DBP per kilogram of dry air Hz can be given by heat and mass balance equations: where C is the specific heat kcal/kg (dry air) OK, Q the mass flow rate kg (dry air)/sec, and H the vapor content kg DBP/kg (dry air). Here, the vapor content H can be related to the vapor pressure of DBP, p mmhg: The supersaturation ratio S, can be given as

4 Size Magnification of Aerosol 355 TABLE 1. Physical Properties of DBP-Air Mixture Molecular weight of DBP, g/mole Density of DBP, g/cm3 Surface tension of DBP, dyne/cm Latent heat of vaporization of DBP, cal/g Mean free path of DBP molecule, cm Diffusion coefficient of DBP molecule, cm2/sec Equilibrium vapor pressure of DBP, mmhg Specific heat capacity of DBP cal/g O K Specific heat capacity of air containing DBP vapor, cal/g-dry air OK Specific volume of dry air containing DBP vapor, ~ m~/~-dry air If there exists a sufficient amount of condensation nuclei in the mixture, point i in Figure 1 will change, according to the following adiabatic-saturation line, as condensation proceeds: Hf- HI = (T, - T ~)(c,/x). (4) Accordingly, after sufficient time, and if the increase in vapor pressure at the droplet surface is ignored, point i will approach point f, which is very close to the saturation curve. Therefore, the quantity of DBP vapor condensing onto the particles corresponds to the decreased vapor content AH ( = H, - HAf), as shown in Figure 1. In the calculation of S, and AH, the physical properties indicated in Table 1 were used. The temperature dependence of the latent heat and density of the DBP were not considered here because they are not very great. Figure 2 shows the calculated values of S, under various mixing conditions. Here, the FIGURE 2. Supersaturation ratio S, under varous mixing conditions.

5 Okuyama, Kousaka, and Motouchi between the vapor and the particle surface become a matter of concern and a discussion of surface chemistry is required. In the fundamental case when the condensation nuclei are spherical liquid drops, the vapor pressure at the droplet surface p, can be given by the following Kelvin equation indicating the change in vapor pressure caused by the curvature effect: FIGURE 3. Vapor content AH of condensable DBP under various mixing conditions. value of the abscissa R, (= Q,,/Q,) indicates the ratio of the flow rate of high-temperature saturated air to total flow rate after mixing. It can be seen that the values of S, greatly depend on the temperatures of both air streams and the mixing ratio R,. In addition, the values of S, are found to increase with temperature T,, and to decrease with temperature T,, indicating maximum values in the range of R, from 0.05 to 0.3. Figure 3 indicates the calculated quantities of condensable DBP vapor AH at vsrious mixing conditions. Tendencies similar to those in Figure 2 can be seen in this figure, but the dependence of AH on the temperature T, is not as great, and the value of AH has a maximum of R, = 0.6 to 0.8. Critical Size of Particles to be Activated When a supersaturated vapor condenses on a foreign condensation nuclei, the interactions For droplets suspended in the supersaturated vapor of the same substance as the droplets, the Kelvin equation can determine the threshold particle size from the supersaturation because the value of p,/p, in (5) corresponds to the value of S,. When the particles that serve as condensation nuclei are not purely spherical drops, the Kelvin effect cannot be adapted quantitatively. But recent research (Liu et al., 1980, and Porstendorfer et al., 1982) dealing with the heterogeneous nucleation of water vapor on various kinds of aerosols has considered semiquantitative or qualitative applications to be effective and reasonable as first approximations. Figure 4 shows the critical diameter of particles where condensation of vapor occurs, and was calculated by substituting the supersaturation ratio S, into the Kelvin equation. As seen from the figure, critical diameters are influenced by the temperatures T,, and T,, and the mixing ratio R,. If the PSM has a uniform supersaturated atmosphere in the mixer, the condensation nuclei larger than the critical sizes are considered to be activated and they will grow. Therefore, the theoretical minimum size of a particle that can grow in the PSM using DBP vapor is found to be about pm. The actual detection limit, of course, must be verified experimentally. Size of Grown Droplets When all the condensable vapor content AH condenses upon the condensation nuclei, the following material balance equation must be

6 Size Magnification of Aerosol satisfied: FIGURE 4. Critical size of dibutyl phthalate particles to be activated at various mixing conditions. where no is the particle number concentration in the mixed air. The particle number concentration of condensation nuclei n,, can be given by, n,, = n J(1 - R,,). From (6), the final volume mean diameter of the grown droplets can be approximated as do/= (6~~/nn,u,~)~'~, for du>> d,,. (7) When it takes a long time for droplets to grow, the size of grown droplets in the PSM cannot be evaluated by (7) because the growth time of the particles is limited to the residence time of droplets in the PSM. Although droplet growth for substances of comparatively high volatility has been investigated in the expansion type CNC by many researchers (Wagner and Pohl, 1975, Garland and Branson, 1977, and Hollander and Schumann, 1979), the research on lowvolatility liquids is limited (Davis and Ray, 1977, 1978). Accordingly, the growth rate of DBP droplets needs to be discussed. At extremely low particle number concentrations, the condensational growth process can be evaluated by the theory of isolated droplet growth. But with an increase in the particle number concentration, interactions between growing droplets must be considered. One theory for understanding the interactions between monodisperse growing droplets is based on the so-called "cellular model" (Carstens et al., 1970, Reiss and LaMer, 1950, Yoshida et al., 1976, and Zung, 1967). In this model, a droplet cloud where the droplets are distributed equidistantly from each other is assumed, and the cloud is divided into a number of identical cubic cells, each of which is supposed to contain a single DBP droplet in the center. The length of the edge of such a cubic cell is given as It is assumed that no heat-and-mass transfer takes place across the boundary of each cell, and that the change in temperature and vapor pressure surrounding the droplet, which is caused by vapor condensation, is to be

7 358 Okuyama, Kousaka, and Motouchi evaluated within each independent cell. The rate of change in the droplet radius r of the cell can be given by the following equation (Amelin, 1967, Fuchs, 1959, Mason, 1957, and Wagner, 1982), assuming the condensation coefficient to be unity: where The rise in the temperature of the growing droplet is given by the following equation, assuming the thermal accommodation coefficient to be unity: where mass transfer, but ths is negligible for the condensation of DBP vapor. Athough these correction factors depend on the thermal diffusion factor a, a reliable experimental value for a is not available for DBP. Assuming the absolute value of a to be less than 0.6, as reported by Wagner (1982), the value of F, amounts to unity, but the value of F, is difficult to evaluate accurately. In (12), however, the value of T, is almost equal to T, independent of the value of FT because DBP vapor pressure is very low. Accordingly, it may be all right to assume the values of F, and F, to be unity in (9) and (12). The rate of growth of a single DBP droplet with radius r can be determined from the above equations. In order to apply these equations to foreign condensation nuclei instead of DBP droplets, one must assume that the surface of each particle is instantaneously covered by a very thin DBP liquid film at the start of condensation. Ths assumption is reasonable because the supersaturated atmosphere is unstable enough that DBP vapor immediately condenses upon any particles serving as condensation nuclei. Assuming that the rate of supersaturation is much higher than that of condensation, the initial values for temperature and vapor pressure at the periphery of each cell can be given as In the above equatiors, p, and p, are correction factors for noncontinuum mass and heat transfers to the droplet in the transition regime, and Kn, and Kn, are the Knudsen numbers defined by Kn, = l,/r and Kn, = l,/r, respectively. Note that F, and FT are diffusional and thermal correction factors for the first-order interactions of mass and heat transfers in the vicinity of the growing droplets (Wagner, 1982). The second term in (11) for FM describes the wellknown influence of the Stefan flow on the The temperature of the particle T, can be evaluated from (12). The condensation of vapor on particles causes a decrease in the vapor concentration and a simultaneous rise in the temperature of the surrounding air. While these changes in the system are unsteady, unsteady jieields of temperature and vapor pressure are established around each condensing droplet. It is difficult, however, to calculate the change in droplet radius strictly by taking account of the unsteady fields. Hence, a quasistationary analysis was made here, where temperature and pressure fields were considered to be constant during successive steps of time. This

8 Size Magnification of Aerosol 359 quasisteady state assumption brings about an error of less than 1% (Carstens et al., 1970, and Wagner, 1975). In the quasi-stationary condition, the change in droplet radius was calculated for each step, as follows. First, (9) was numerically solved by the Runge-Kutta-Merson method. When the radius of a spherical droplet r, increases to r, during a small time step, the quantity of DBP vapor condensed onto particles can be given by According to the adiabatic-saturation line, there is a decrease in vapor and a simultaneous increase in the temperature of the air as a consequence of condensation. The relationshps among the temperature, the vapor pressure, and the supersaturation ratio during successive condensation can be given by T,, = T,, + AH 'X/C, temperature, vapor pressure, and supersaturation ratio have been evaluated as functions of time by repeating the above procedure and using a digital computer. Figure 5 shows some of the calculated results for the time-dependent changes in the sizes of growing droplets for various particle number concentrations, initial supersaturation ratios, and mixing ratios. Figure 6 indicates the decreases in supersaturation ratios during droplet growth for the same conditions considered in Figure 5. It can be seen from these graphs that the first stages of droplet growth are influenced mainly by the initial supersaturation ratio and temperature and the particle number concentration. The effect of the initial particle radius on the particle growth curve is negligible for radii smaller than 0.1 pm if the initial supersaturation ratio is high enough to activate the condensation nuclei. The decreasing - rate of the supersaturation ratio during droplet growth is dependent on particle number con- HA2=HBI -AHf, (16) centration and time. At extremely low pars2 =PR(TR,)/P,(TR~)> ticle number concentrations, it takes a long time for particles to terminate growth. At where subscript 2 denotes the value after one higher particle number concentrations, small time step. Again, computation of the droplet growth terminates much sooner. In droplet growth rate can be achieved by in- every case, these final droplet sizes are equal tegration of (9). Finally, droplet radius, to those evaluated by (7). The growth curves FIGURE 5. Increase in droplet radius by condensation. T,, = 100 C; = 20 C; r, = 0.005, 0.01, and 0.1 pm. Dashed curves: R, = 0.5, S, = 15.8; solid curves: R, =0.2, S, = 98.2.

9 Okuyama, Kousaka, and Motouchi FIGURE 6. Decrease in supersaturation L 10 ratio during condensation: T,, = 100 " C, V) T, = 20" C; r, = pm. Dashed curves: R, = 0.5, S, = 15.8; solid curves: R, = 0.2, S, = for particles with concentrations lower than lo3 particles/cm3 are considered to be approximated by the growth of an isolated droplet because the decrease in the supersaturation ratio due to droplet growth is almost negligible, as seen from Figure 6. In the case of the growth of an isolated droplet, the rate equation can be given by (Amelin, 1967, Fuchs, 1959, Mason, 1957, and Wagner, 1982): t = 0.5 sec, if the particle number concentration is lower than about lo4 particles/cm3, the radius of the droplet is independent of the particle number concentration. If the vapor condensation on the wall is small, the above results indicate that the sizes of grown droplets in the PSM are found to depend mainly on the initial particle number concentration and the growth time (whch approximately corresponds to particle residence time in the PSM). If an isolated droplet is assumed, the particle residence time t, in the PSM can be determined from its structure and the flow rate of the aerosol, and the size of the grown droplet during t, can be Since the value of the right hand side of (17) becomes constant for a very small time step, the radius of the growing droplet can be obtained by analytically integrating (17) in each time step. The total change in droplet radius can be calculated by repeating this procedure. The growth curve thus obtained agrees well with the previous numerical results for particle number concentrations less than about lo3 particles/cm3. Figure 7 shows the size of the grown droplets against particle number concentration as a function of growth time. The final droplet size for t = w completely agrees with the value obtained from (7). However, at FIGURE 7. Relation between radius and concentration of grown droplets: T,, = 100 " C, T, = 20 O C, R, = 0.5, S, = 15.8.

10 Size Magnification of Aerosol 361 evaluated from (17). On the other hand, the final size of the grown droplets can be given by (7). Accordingly, the actual size of the grown particles in the PSM can be estimated as being the smaller of these two sizes. EXPERIMENTAL APPARATUS AND METHOD Figure 8 shows the PSM designed by us. Clean air is passed at a flow rate of 0.5 to 2 L/min through a vaporizer filled with silica gel impregnated with DBP liquid. The temperature of the vaporizer is controlled by a thermostat. The obtained air containing the saturated vapor of DBP is forced through a small pipe and becomes an upward jet. The room temperature aerosol containing condensation nuclei enters at a flow rate of 0.5 to 2 L/min through a small tube and meets with the hot air saturated with vapor. Both air streams are mixed together in the narrow gap of the mixing part and flow into the lower pipe. As the volume of the narrow gap is about 0.06 cm3, the two air streams can be mixed within sec. Accordingly, the rate of formation of supersaturation is higher than that of vapor condensation onto particles. The lower pipe is reheated at almost the same temperature as the vapor-air mixture { = T,, R, + T,(l- R,)) in order to avoid the condensation of vapor on the wall. Condensational growth of particles takes place mainly in this lower pipe and the average residence time of particles in the PSM is in the region of 0.2 to 1.0 sec. This PSM is different from the one developed by Kogan and Burnasheva (1960); the main changes are as follows: (1) the path of the condensation nuclei is shorter so as to lessen the Brownian diffusive loss of particles and to prevent the aerosol from warming before mixing; (2) the surface exposed to an ultrafine aerosol is coated with an electroconductive material in order to avoid the loss of charged particles; (3) the loss of vapor on the wall is small due to the installation of the reheater. Figure 9 presents a schematic diagram of the experimental apparatus. In the experiment, ZnC1, aerosols with particle diameters from to 0.05 pm were produced by an evaporation-condensation type aerosol generator, labeled "1" in Figure 9 (Kousaka et al., 1982), and were used as condensation nuclei. Experiments were made on the following points: (1) new particle formation by homogeneous nucleation, (2) particle size of the grown DBP droplets, and (3) critical size of the particle to be activated. In experiments (1) and (2), the size distributions of grown droplets with diameters less than about 0.3 pm were determined by the combined method of the differential mobility analyser (DMA), labeled "2" in Figure 9 (Kousaka et al., 1981), with the mixing type CNC, labeled "5" in Figure 9 (Kousaka et al., 1982). Those with particle diameters larger than about 0.3 pm were made by the sedimentation method using an ultramicroscope, labeled "4" in Figure 9 (Yoshida et al., 1975). The detection of the number concentration of grown droplets with particle diameters larger than 0.3 pm was performed by observing droplets in the cell, labeled "3" in Figure 9 (Kousaka et al., 1981) using a TV camera with an He-Ne laser beam (25 mw) to illuminate individual aerosol particles. The numbers of the smaller grown droplets were counted by the mixing type CNC (Kousaka et al., 1982). Since the number of grown droplets does not change with the temperature of the vapor-air mixture, loss of particles by Brownian diffusion and thermophoresis is found to be negligible. In experiment (3), the monodisperse particles (particle radius known and geometric standard deviation less than 1.1) obtained by the electrical classification using DMA are introduced into the PSM. The numbers of grown droplets under various supersaturation ratios were observed in the cell, and the numbers of unactivated condensation nuclei were checked using another DMA and mixing type CNC. Mere, the highly sensitive TV camera was used (detection limit about 0.07

11 FIGURE 8. Particle size magnifier. Okuyama, Kousaka, and Motouchi

12 Size Magnification of Aerosol pm in diameter). Since the activated particles can grow to detectable sizes within 0.05 sec (as seen from Figure 5), they can be observed because the average residence time of the particles in the PSM is 0.2 to 1 sec. From the experimental data, the relationship between the particle number concentration of the activated condensation nuclei and the Kelvin equivalent particle size evaluated from (5) was obtained. EXPERIMENTAL RESULTS AND DISCUSSION New Particle Formation of Homogeneous Nucleation With the increase in the temperature of the hot vapor-saturated air, the supersaturation ratio in the mixing zone increases and new particles may be formed by homogeneous nucleation. However, the fresh DBP droplets were not produced by homogeneous nucleation at temperatures T,, below 120 C. In the actual use of the PSM, the effect of homogeneous nucleation can be easily checked by observing whether the number concentration of grown droplets remains constant with the increase in the temperature T,,. FIGURE 9. Schematic diagram of the experimental apparatus. Sizes of Grown DBP Droplets Figure 10 shows the representative size distributions of the grown DBP droplets by their cumulative percentage against their sizes. Under these conditions, the effect of any new particle formation by homogeneous nucleation is negligible. As seen from this figure, the ultrafine condensation nuclei grew up to become particles larger than 0.3 pm, particles which could be detected by conventional optical techniques. Ungrown condensation nuclei did not remain in these experimental results. As described before, the growth rate of droplets for number concentrations higher than lo4 particles/cm3 was so fast compared with the time scale of observation that the size distribution of the droplets at each stage of growth could not be observed. For the constants R, and T,,, the average sizes of grown droplets were found to increase with the lower particle number concentrations. Figure 11 shows the comparison of the experimental volume mean radii of grown droplets with the theoretical line formed by

13 Okuyama, Kousaka, and Motouchi FIGURE 10. Size grown droplets. distribution of (7). The good agreement seen in the figure indicates that when no is larger than about lo5 particles/cm3, the theoretical condensable quantity of DBP vapor, AH, condenses only on the condensation nuclei. This is reasonable because the droplets could terminate their growth in the PSM. In this experiment, the sizes of droplets in lower no were not determined because of the lack of appropriate apparatus. But from the direct observation of grown droplets in the observation cell, the droplet size was found to be almost constant for no < 104 particles/cm3, and, as seen in Figure 7, droplets were discharged from the PSM without completing their growth. FIGURE 11. Volume mean radii of grown droplets. Open circles: R, = 0.7; filled circles: R, = 0.5. Critical Size of Particle to be Activated Figure 12 shows the experimental results for the number ratio of the activated particles to the total particles under various supersaturation ratios. Here, the ordinate is the ratio of the number of grown droplets n to the total particle number no, and the abscissa is the Kelvin equivalent diameter evaluated from (5). It was observed that particles were not uniformly activated because the supersaturated atmosphere was not formed homogeneously at the mixer. Herc, the Kelvin equivalent diameters, where half of the par- FIGURE 12. Change in number concentration of grown droplets with the Kelvin equivalent diameter I 20.5 C - C Kelvin equivalent diameter l nml

14 Size Magnification of Aerosol ticles had grown, seem to agree with the average sizes of the condensation nuclei within the experimental error. From these results, the activation of particles in the PSM was found to depend primarily on the Kelvin effect. Figure 4 will be useful in evaluating the critical size of activated particles under various conditions. However, further experimental studies using various kinds of aerosols will be necessary in order to confirm the influences of particle material on the rate of DBP vapor condensation. CONCLUSION The new PSM was manufactured and the particle growth of ultrafine aerosol particles in the PSM was investigated theoretically and experimentally. The following results were obtained: (1) the supersaturation ratio formed in the PSM has a maximum value in the range of mixing ratio Rh from 0.05 to 0.3. The critical size of the particle to be activated can be approximately estimated by the Kelvin equation; (2) the particle size of grown droplets at particle number concentrations higher than lo5 particles/cm3 can be determined by the particle number concentration and the condensable DBP vapor content. The growth process of droplets with particle number concentrations lower than lo3 particles/cm3 can be evaluated from the theory for the isolated droplet; (3) the new PSM developed here can perform as a convenient aerosol detector of ultrafine aerosol particles by being combined with conventional optical methods. E. Mori and T. Hosokawa were very helpful in the experimental work. Part of ths work was performed under Grant-in-Aid for Scientific Research and NOMENCLATURE C CP specific heat capacity of air containing DBP vapor specific heat capacity of DBP AH' diffusion coefficient particle diameter volume mean diameter of droplets correction factors defined by Eqs. (11) and (14) DBP vapor content quantity of condensable DBP vapor content quantity of condensed DBP vapor content specific enthalpy of vapor Knudsen cumbers with respect to the vapor molecules and the air molecules mean free paths of vapor molecules and air molecules molecular weight of DBP droplet number concentration in mixed air particle number concentration of condensation nuclei number distribution function of particle with radius r vapor pressure vapor pressure at the droplet surface vapor pressure above a flat surface total pressure mass flow rate gas constant mixing ratio droplet radius length of the edge of a cubic cell supersaturation ratio temperature temperature of surrounding air far from droplet temperature at the droplet surface time residence time of droplet in the PSM molar volume of DBP specific volume of dry air containing DBP vapor

15 366 Okuyama, Kousaka, and Motouchi thermal diffusion factor correction factors defined by Eqs. (10) and (13) heat conductivity latent heat of vaporization density of DBP density of DBP vapor surface tension of DBP average far away from droplet final state of air after mixing hgh temperature initial state low temperature saturated REFERENCES Amelin, A. G. (1967). Theory of Fog Condensation, Israel Program for Scientific Translation. Carstens, J. C., Williams, A. and Zung, J. T. (1970). J. Atmos. Sci. 27:798. Davis, E. J., and Ray, A. K. (1977). J. Chem. Phys. 67:414. Davis, E. J., and Ray, A. K. (1978). J. Aerosol Sci. 9:411. Fuchs, N. A. (1959). Evaporation and Droplet Growth m Gaseous Media, Pergamon Press, Oxford, England. Fuchs, N. A., and Sutugin, A. G. (1963). J. Appl. Phys. 14:39. Fuchs, N. A., and Sutugin, A. G. (1965). J. Colloid SCI. 20:492. Garland, J. A. and Branson, J. R. (1977). J. Aerosol Sci. 70:475. Hollander, W., and Schumann, G. (1975). J. Colloid Interface Sci. 70:475. Kirsch, A. A., and Fuchs, N. A. (1968). Ann. Occup. Hyg. 11 :299. Kirsch, A. A,, and Zagnit'ko, A. V. (1981). J. Colloid Interface Sci. 80:111. Kogan, J. I., and Burnasheva, A. G. (1960). Phys. Chem. Moscow 34:2630. Kousaka, Y., Okuyarna, K., and Endo, Y. (1981). J. Aerosol Sci. 12:339. Kousaka, Y., Niida, T., Okuyama, K., and Tanaka, H. (1982). J. Aerosol Sci. 13:231. Liu, B. Y. H., Pui, D. Y. H., McKenzie, R. L., Aganval, J. K., Jaenicke. R., Pohl, F. G., Preining, O., Reischl, G., Szymanski, W., and Wagner, P. E. (1980). J. Aerosol Sci. 11:261. Mason, B. J. (1957). The Physics of Clouds, Clarendon Press, Oxford, England. Porstendorfer, J., Scheibel, H. G., Pohl, F. G., Preining, O., Reischl, G., and Wagner, P. E. (1982). Idojaras (J. Hung. Meteor. Serv.) 86:144. Reiss, H., and LaMer, V. K. (1950). J. Chem. Phys. 18:l. Wagner, P. E. (1975). J. Colloid Interface Sci. 53:439. Wagner, P. E. (1982). Aerosol Microphysics I1 (Topics in Current Physics 29, W. H. Marlow, Ed.) Springer- Verlag, New York, p Wagner, P. E. and Pohl, F. G. (1975). J. Colloid Interface Sci Yoshda, T., Kousaka, Y., and Okuyama, K. (1975). Ind. Eng. Chem. Fundam. 14:47. Yoshida, T., Kousaka, Y., and Okuyama, K. (1976). Ind. Eng. Chem. Fundum. 15:37. Zung, J. T. (1967), J. Chem. Phys. 46:2064. Received 17 January 1983; accepted 7 June 1984.