Evaporation Rates of Monodisperse Organic Aerosols in the to 0.2-µm-Diameter Range

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1 Aerosol Science and Technology ISSN: (Print) (Online) Journal homepage: Evaporation Rates of Monodisperse Organic Aerosols in the to 0.2-µm-Diameter Range D. J. Rader, P. H. McMurry & S. Smith To cite this article: D. J. Rader, P. H. McMurry & S. Smith (1987) Evaporation Rates of Monodisperse Organic Aerosols in the to 0.2-µm-Diameter Range, Aerosol Science and Technology, 6:3, , DOI: / To link to this article: Published online: 29 May Submit your article to this journal Article views: 531 Citing articles: 40 View citing articles Full Terms & Conditions of access and use can be found at

2 Evaporation Rates of Monodisperse Organic Aerosols in the to 0.2-pm-Diameter Range D. J. Rader," P. H. McMurry, and S. Smith Particle Technology Laboratory, Department of Mechanical Engineering, University of Minnesota, 11 1 Church St. SE, Minneapolis, MN The tandem differential mobility analyzer (TDMA) iechnique was used to measure evaporation rates of monodisperse organic aerosol droplets in the to 0.2-pmdiameter range. The species investigated include dioctyl phthalate (DOP), diocytl sebacate (DOS), and oleic acid, all of which are frequently used to produce monodisperse aerosol standards for instrument calibration. Transition regime mass transfer expressions were used to determine vapor pressutes from measured evaporation rates. The vapor pressure of DOP at 25.7O C was found to be in good agreement with reported values (2.36 X 10-4 dynes /cm2). Vapor pressures at 25" C for oleic acid and DOS were 2.2 X 10-4 dynes/cm2 and 2.6 X 10 -' dynes/cm2, respectively. The data provide direct evidence for the validity of the Kelvin equation for these species. Also, these results suggest that because of its lower vapor pressure, DOS is more stable than the other species, and is therefore more suitable for use as a material for monodisperse aerosol standards. INTRODUCTION Evaporation rates of organic aerosol droplets have recently been used to study the mass transfer from transition regime aerosol droplets (Davis and Ray, 1978; Davis et al., 1978, 1980; Davis, 1983), and to measure ultra-low vapor pressures (Ray et al., 1979). In these previous studies, individual droplets were trapped for extended time periods in an electrodynamic balance, and evaporation rates were determined with light scattering techniques. The effects of gas composition, gas pressure, temperature, and aerosol species on evaporation rates have been investigated. Measurements have been restricted to particles larger than about 0.3 pm, because light scattering intensities for smaller particles are weak and therefore difficult to measure. In addition to providing information about mass transfer fundamentals and vapor * D. J. Rader is now at the Fluid and Thermal Sciences Department, Sandia National Laboratories, Albuquerque, NM pressures, evaporation rate measurements are useful in evaluating effects of curvature on vapor pressure. The classical relationship between curvature and vapor pressure is given by the Kelvin equation (Thomson, 1870, 1871; Defay et al., 1966): -- pv s - exp - 4%~ p," prtd, ' where Pv, = the vapor pressure immediately above the droplet surface; P," = the vapor pressure over a flat surface; Mv = molecular weight of droplet material; y = surface tension of droplet material; p = droplet density; R = ideal gas constant; T = absolute temperature; and d, = droplet diameter. Previous experimental investigations of the Kelvin effect have been reviewed by Skinner and Samples (1972). This previous Aerosol Science and Technology 6: (1987) Elsevier Science Publishing Co., Inc.

3 248 Rader, McMurry, and Smith work includes microscopic investigations of metal droplet evaporation rates (Blackman et al. 1968; Sambles et al., 1970; Sambles, 1971) and studies of droplet evaporation in a Millikan-like oil drop apparatus (Woodland and Mack, 1933; Shereshefsky and Steckler, 1936). The Kelvin effect has also been studied with droplets consisting of two components, one volatile and the second nonvolatile (Gudris and Kulikova, 1924a, b; LaMer and Gruen, 1952). These previous studies, as well as more recent work (e.g., Fisher and Israelachvili, 1981), have generally found good agreement between data and predictions of the Kelvin equation. Most of these curvature-effect studies have focused on metals or relatively simple organics. Organics that are typically important in aerosol systems (such as in secondary atmospheric aerosols, or in laboratory-generated calibration aerosols) are likely to have higher molecular weights than previously studied species, and may also be present in complex multicomponent mixtures. Furthermore, recent work (Heisler and Friedlander, 1977; McMurry and Grosjean, 1985) has shown that the Kelvin effect probably plays a key role in the growth of secondary atmospheric organics. Therefore, there is a need to study curvature effects for such species. Because curvature effects only become significant for particles smaller than about 0.3 pm, such research can best be done with particles smaller than have been studied to date. Rader and McMurry (1986) recently developed a technique for measuring size changes (either growth or shrinkage) of monodisperse aerosols with the tandem differential mobility analyzer (TDMA). Diameter changes are determined by precisely measuring the change in the electrical mobility of singly charged particles that results from growth or shrinkage. They showed that diameter changes of about 0.3% can be resolved with this instrumentation. The TDMA technique is ideally suited for studies with particles in the sub-0.3-pm-diameter range, where it is relatively easy to produce singly charged, monodisperse aerosols. Therefore, thls technique complements light scattering techniques, which work best with particles larger than 0.3 pm. Furthermore, because the method works well for sub-0.3-pm particles, it is well suited for studies of curvature effects. In the present study, evaporation rates of dioctyl phthalate (DOP), dioctyl sebacate (DOS), and oleic acid droplets in the to 0.2-ym-diameter range were measured with the TDMA technique. These species were selected because they are often used to produce monodisperse aerosol standards for instrument calibration; we anticipated that evaporation rate data would provide useful information about the stability of such aerosols as well as interesting fundamental information about mass transfer, vapor pressures, and curvature effects. The vapor pressure of DOP was found to be within 15% of the value reported by Davis et al. (1980). Vapor pressures of the other two species at room temperature have not been reported previously. Also, it was found that curvature effects were consistent with predictions of the Kelvin equation, and that DOS is less volatile and, therefore, preferable to the other two species as a laboratory aerosol for instrument calibration. EXPERIMENTAL Evaporation rates of organic droplets in the to 0.2-ym-diameter range were measured using the tandem differential mobility analyzer shown schematically in Figure 1. The TDMA consists of a monodisperse aerosol generator, an aerosol conditioner (in this study a laminar flow evaporator), and a mobility detector. Differential mobility analyzers (DMAs) (Liu and Pui, 1974; Knutson and Whitby, 1975) similar to the commercially available DMA (TSI Model 3071) are used in both the aerosol generator and the mobility detector. A detailed analysis of aerosol transport through a TDMA

4 - MAKE- UP AIR AC -ACTIVATED CARBON PACKED BAD FILTER DMA-DIFFERENTIAL MOBILITY ANALYZER Dd FLOW REGULATING CA -COLLISON ATOMIZER HV -HIGH VOLTAGE SUPPLY VALVE CNC-TSI MODEL 3020 CONDENSATION NL -Kr-85 NEUTRALIZER X FLOWMETER NUCLEUS COUNTER PC -IBM PERSONAL COMPUTER [XI ABSOLUTE PARTICLE CO -CRITICAL ORIFICE TH -THERMOMETER FILTER DAS-KEITHLEY/DAS SERIES 500 MEASUREMENT AND CONTROL SYSTEM FIGURE 1. Schematic diagram of TDMA apparatus used for droplet evaporation studies.

5 250 Rader, McMurry, and Smith system, as well as a suggested procedure for using the TDMA to measure size changes, is discussed by Rader and McMuny (1986). The monodisperse aerosol generator is functionally identical to that of Liu and Pui (1974). Dried, filtered, and carefully regulated compressed air was expanded in a Collison atomizer, entraining a liquid solution of 0.05 wt% solution of DOP (dioctyl phthalate), DOS (dioctyle sebacate), or oleic acid in alcohol. A TSI 85Kr neutralizer brought the aerosol to a stationary state charge distribution with a cloud of biopolar ions. The aerosol was then diluted in order to evaporate the alcohol from the droplets and to reduce the background vapor pressure of the organic compound of interest. Dilution was achieved by directing part of the aerosol flow through an absolute filter and an activated carbonpacked-bed filter. The scrubbed fraction was then recombined with the remaining, aerosol-laden flow. The aerosol flow was next introduced, along with dry, particle-free sheath air, into DMA-1. Laminar flow elements were used to measure the inlet and the outlet aerosol flow rates for the DMAs, and sheath air flow rates were measured with a TSI mass flow meter. The inlet and outlet aerosol flow rates were set equal for any given experiment, and varied between 0.5 and 2.0 lpm during the experiments reported here. The sheath air flow rate was held fixed at 30 lpm. The electric mobility of the aerosols that penetrate through the exit slit on the DMA center rod depends solely on the aerosol and sheath air flow rates and on the voltage between the center rod and the outer, cylindrical housing (Knutson and Whitby, 1975). Because the electric mobility of a spherical aerosol particle depends both on particle diameter and on charge, particles with a given mobility may consist of several discrete sizes corresponding to singly charged, doubly charged, etc., particles. In the present study, experiments were restricted to particles smaller than about 0.2 pm, where effects of multiple charging could be kept insignificant. Therefore, in the remainder of ths discussion, the aerosols leaving DMA-1 are referred to as being monodisperse. After classification, the aerosol exiting via the sample flow was directed to a laminar flow evaporator. The evaporator consists of a 3.66-m length of cm-i.d. stainlesssteel tubing and associated connectors. Complete details of the evaporator are given by McMurry et al. (1983). Due to the development of a parabolic velocity profile, the residence time of a given particle withm the evaporator will depend on its radial location. To minimize the nonuniforrnity in residence times, only a fraction of the total flow is sampled at the exit from the evaporator, while the remainder of the flow is discarded. In the present work, one-fifth of the total flow is extracted from the central core of the laminar flow. Even so, some spread in residence times is expected. This spread is discussed below, where a determination of an appropriate mean residence time is defined. The mobility characteristics of the aerosol exiting the evaporator are measured with DMA-2 and a TSI Model 3020 Condensation Nuclei Counter (CNC) (Agarwal and Sem, 1980). The sheath air flow rate into DMA-2 was held fixed at 6 lpm, and the DMA-2 aerosol flow rate was set equal to one-fifth of the flow through the evaporator (equivalently, one-fifth of the DMA-1 aerosol flow). This ensured that the ratio of sheath air to aerosol flow rates in DMA-1 and DMA-2 were equal. This is a necessary constraint for the applicability of the method that is used to determine the size at the exit from DMA-2 (Rader and McMurry, 1986). For a fixed center rod voltage on DMA-1 (i.e., at a constant initial mobility), an experimental response function is obtained by measuring the concentration exiting DMA-2, N,, versus the value of the voltage applied to its center rod, V,. Data acquisition is automated; an IBM Personal Computer interfaced with a Keithley/DAS Series 500 Measurement and Control System permits

6 Evaporation Rates of Monodisperse Organic Aerosols 251 programmable control of the DMA and monitoring of the CNC. Since particle concentrations did not exceed 1000/cm3, the CNC is strictly operated in the single-particle counting mode. Software corrects for particle coincidence in the sensing volume. The preset, factory counting times are used to reduce low-concentration counting errors to acceptable levels. Variations in counting efficiencies with size are not likely to be significant and are neglected (Aganval and Sem, 1980; Bartz et al., 1985). Evaporation Times As mentioned above, the development of a parabolic velocity profile introduces a radial dependency to the residence time of particles moving through the evaporator. Particles suspended in fluid parcels traveling along the tube center line (r = 0) move with the maximum velocity u,; fluid velocities diminish quadratically toward the wall, meeting the no-slip condition at the wall itself (r = R). The extraction of a sample from the core of the evaporator flow reduces the nonuniformity in residence times, but does not eliminate them. In the present work, it is convenient to relate the residence time to that for a fluid parcel traveling along the center line, to = L/uo = rr2 L/2Qt, where L, R, and Q, are the evaporator length, internal radius, and total flow rate. The ratio of the mean residence time, t,, to the rninimum transit time, to, is given by where Qs is the sample flow rate. In the present work, Q,/Q, = 1/5, and the mean exceeds the minimum residence time by the factor Also of interest is the longest travel time t, of any particle included in the sample flow Qs: For Q,/Qt = 1/5, this ratio equals Thus, the maximum predicted spread in residence times is only 11.8%, and the longest and shortest transit times differ by about 6% from the mean, t,. Several experimental tests were conducted to investigate the accuracy of Eqs. (2) and (3). In these tests, DMA-1 was set to a particular voltage V,, and the voltage V2 at DMA-2 yielding the highest particle penetration at its exit was found. With DMA-1 held at V,, the voltage at DMA-2 was switched from 0 to V2, and the time that elapsed until the CNC first detected particles was recorded.' The time until steady state (taken when the concentration attained 0.90 of its eventual value) was also noted. These elapsed times measure the transit time of particles between the mobility tube and the CNC detector. Next, the voltage at DMA-2 was held at V,, and the voltage at DMA-1 was switched from 0 to V,. Again, the elapsed times until the first CNC count and until steady state were recorded. The difference between these sets of elapsed times gives a good value for the minimum transit time (or evaporation time) between the mobility tubes of DMA-1 and DMA-2. Also, a good estimate for the maximum observed transit time can be found. The experiments outlined above were performed for an evaporator total flow rate of 0.5 lpm and DMA-2 sample flow rate of 0.1 lpm. The minimum predicted residence time in the evaporator was 90.6 s; the minimum observed residence time between DMAs ranged between 95 and 108 s. Longer observed residence times can be explained by the additional plumbing used to connect the DMAs to the evaporator and by the plumbing internal to the DMAs. The indicated variation in the minimum transit time was observed in typical day-to-day operations. 'The fast-response CNC described by Stolzenburg and McMurry (1986) was used in these measurements. This instrument is a modified version of the TSI 3030 CNC and has a response time of less than 1 s.

7 Rader, McMurry, and Smith Inaccuracies in flow settings may account for some of these variations. In order to overcome these uncertainties, direct measurements of to using the above method were made during many of the experimental runs. Experimental estimates of t,, also exceeded the predicted value. Equation (3) predicts that the difference between the maximum and the minimum residence times is 10.7 s, whle experimental values ranged from 15 to 24 s. Ths increase can again be explained by the connecting plumbing, since in these sections the aerosol flow is not sheathed and particles moving near to tube walls will be retarded relative to the central flow. Some difficulty in the measurement of t,, was encountered, and it is felt that values toward the lower end of the stated range are more reliable. In consideration of the above results, the effective mean residence time is taken as 1.1 times the experimentally observed value of to for the given run. When to was not directly measured, estimates of it from runs made at similar flow rates were used. Accuracies of about 5% are expected for ths choice for t,. RESULTS AND DISCUSSION The results of studies of the evaporation rates of small droplets (particle diameters between 0.2 and 0.02 pm) of oleic acid, DOP, and DOS are presented in this section. A nearly monodisperse aerosol is generated, using the DMA method described above, and is then introduced into the laminar flow evaporator. Typical residence times are about 2 min. At the exit of the evaporator, the mobility distribution is analyzed using the least-squares method described in Rader and McMurry (1986). From this analysis, the diameter of the aerosol at the exit of the evaporator, d,,, is found. The extent of evaporation as a function of the initial size, dpi, can then be determined. The experimental observations are compared with theory. Theoretical expressions for single particle mass transfer in the transition regime and the Kelvin equation are required in the analysis. Extent of Evaporation The diameter reduction ratio d,!dpi is plotted against the initial particle diameter, d,,, for DOP and DOS in Figure 2. The results for oleic acid are presented in Figure 3. The temperature, total pressure, and residence time are recorded in the figures for each set of data. The evaporation rates for DOP and oleic acid were found to be approximately equal, whereas DOS droplets evaporated at a significantly reduced rate. For each liquid tested, a sharp increase in the evaporation rate was observed at smaller diameters. This is consistent with the exponential dependence on diameter of the Kelvin effect, as will be considered below. Several points regarding the quality of the experimental data need to be discussed. Two key assumptions that will be made when comparing data with theory are that (1) the free stream saturation ratio of the evaporating vapor is zero, and (2) the evaporating droplets consist of pure DOS, DOP, or oleic acid. Rader (1985) has considered these assumptions in detail, and his conclusions are summarized below. Because the aerosol particles are borne by vapor-free sheath air at the entrance to the evaporator, the vapor pressure (and therefore saturation ratio) at the evaporator inlet is close to zero. As particles evaporate during transport through the evaporator, however, the saturation ratio of the vapor builds up. Rader (1985) estimated saturation ratios at the exit from the evaporator by performing mass balance calculations. Rader found that for the DOP and DOS data the saturation ratio at the evaporator exit should be less than 0.05, and he concluded that it is reasonable to assume a free stream saturation ratio of zero throughout the evaporation process. For the oleic acid experiments, aerosol particle concentrations were suffi-

8 Evaporation Rates of Monodisperse Organic Aerosols

9 Rader, McMurry, and Smith

10 Evaporation Rates of Monodisperse Organic Aerosols ciently high such that aerosol evaporation may have produced nonneghgible saturation ratios at the evaporator exit. Although this is not expected to have a significant effect on calculated vapor pressures, this effect does tend to increase uncertainties in the oleic acid data. The assumption that particles consisted of pure DOS, DOP, or oleic acid is also suspect. Aerosols were produced by atomizing 0.05 wt% DOS, DOP, or oleic acid solutions in alcohol. Concentrations of total dissolved solids in the alcohol are likely to be equal to or less than 10 ppm, and these solids will remain in the organic aerosol droplets after the alcohol evaporates. It follows that concentrations of nonvolatile contaminants in the unevaporated droplets are likely to be 2% or less. As evaporation proceeds, the relative concentration of nonvolatiles is expected to increase by a factor equal to the cube of the ratio of initial to final diameter. For the DOS data, the largest value for this factor was 3.7. If an ideal liquid and Raoult's law are assumed, the maximum decrease in vapor pressure over the drop due to nonvolatile contaminants should be between 5 and 10%. For DOP and oleic acid, much larger values of diameter ratios were investigated. Nevertheless, for DOP and oleic acid data with final to initial diameter ratios exceeding 0.4 (the majority of the data), the maximum vapor pressure lowering due to dissolved solids (assuming Raoult's law) would be less than 15%. We conclude, therefore, that dissolved solids are unlikely to contribute substantial uncertainties to measured evaporation rates. Another source of error in the present work is an observed discrepancy between the DMAs in sizing aerosol of essentially the same size. For example, one experiment with DOS was performed with large diameter aerosols at short evaporator residence times. Particles diameters were varied between 0.11 and 0.15 pm, and the residence time was varied by over a factor of 4. From results shown in Figure 2, the influence of evapora- tion on diameter should have been negligible; that is, the initial and final particle diameters should be essentially the same. In fact, the value of d,, was 2% greater than expected, and this observed discrepancy was a constant over the diameter and residence time ranges given above. It is concluded, therefore, that this is a systematic error. Day-to-day variations in the magnitude of this systematic error of 0 to 2.5% were also observed. Such discrepancies could result from several sources; flow measurement error and the assumption of a uniform inlet mobility distribution in the data analysis (see Rader, 1985; Rader and McMurry, 1986) certainly contribute to this error but don't completely explain it. The magnitude of this systematic error was determined for DOS, and data in Figure 2 were corrected accordingly. Uncertainties in reported diameter ratios should, therefore, be less than about 0.5% for these data. For the more volatile species, DOP and oleic acid, accurate correction factors could not be determined; in these cases the data are not corrected for this effect, and uncertainties in the diameter ratio as large as 2% are possible. Liquid and Vapor Properties In order to compare data with theory for evaporative mass transfer rates, several liquid and vapor phase properties of the organic aerosol species must be known. These include molecular weight, density, surface tension, and diffusivity in air. In this section the methods that were used in evaluating these properties are summarized. The evaporation rates of three substances were investigated: DOP (dioctyl phthalate or di-[2-ethylhexyl] phthalate), DOS (dioctyl sebacate or di-[2-ethylhexyl] sebacate), and oleic acid (9,lO-octadecenoic acid cis). Values from the literature for molecular weight, liquid density, and the liquid-vapor surface tension are given in Table 1A. Experimental values for density and surface tension that were obtained for the present study are also

11 256 Rader, McMurry, and Smith TABLE 1A. Physical Properties of Liquid Density Surface tension m (g/cm3) (dyne/cm) (g/mol) Ref. Exp. (25 O C) Ref. (20 O C) Ekp. (22O C) DOP " ' 30.9 DOS ' ' 30.9 Oleic acid ' ' 31.9 TABLE 1B. Le~ard-Jones Parameter DOP = 1300d 10.12' 600' 622 DOS = 1512~ = 11.07f - 6OOg = 690' Oleic acid = 1035~ = 9.51f 634h = 729' "Condensed Chemical Dictionary (1971). 'CRC ( ). 'Jaspar (1972). d~stimated by Lydersen's method (1955). eray et al. (1979). 'Estimated using u, and Eq. (6). gappropriate value not available, estimated result h~aye and Laby (1973). 'Estmated using Tb and Eq. (5). presented. For the density measurements, a Mettler/Paar DMA 40 Digital Density Meter was used. The reported and experimental values for density agreed within 0.5% for all three substances. A Du Nouy Ring and balance was used for the surface tension measurements. Good agreement between the literature and measured values was found for surface tension as well. The measured values were each lower, but at most by 2%. In later calculations involving these physical variables, the values obtained from the literature will be used. In the present study, the Chapman- Enskog (Chapman and Cowling, 1970) result for the binary diffusion coefficient will be used. where Q,*, = dimensionless collision integral; M, = molecular weight air; rn, = mass of vapor molecule; P = total pressure; k = Boltzmann's constant. Thls requires the calculation of the Lennard-Jones parameters for the vapor-gas collision diameter a,, and interaction parameter~,,. These parameters are generally calculated from the pure component parameters by the following combining rules cvg - (Cw. egg)+; %, = 2(% + a,,). (4) For the carrier gas (air) these pure component values are available from Hirschfelder et al. (1954): u, = A and c,$k = 90.7 OK. Ray et al. (1979) studied the continuum regime evaporation of DOP and similar species and found the correlations of Hirschfelder et al. (1954), ~,/k = 1.15Tb, (5)

12 Evaporation Rates of Monodisperse Organic Aerosols 257 and of Chen and Othmer (1962), a, = ~,0.~OO~, (6) to be in better agreement with their experimental work than numerous other correlations. Here T,, is the normal boiling point, and u, is the critical volume [estimated according to the group contribution method of Lydersen (1955)l. A summary of the Lennard-Jones parameters is presented in Table 1B. The values reported by Ray et al. (1979) have been used for DOP, with the values for DOS and oleic acid estimated using Eqs. (5) and (6). Comparison with Theory The experimental data consist of measurements of final droplet size, after droplets of a known initial size have been allowed to evaporate for a known time period. In order to compare these data with theoretical predictions, it is necessary to integrate the theoretical transition regime mass flux equation for evaporative mass transfer. The equation for the mass flux, J (g/cm2. s), can be expressed as: where p is particle density. The integral equation relating the final and initial sizes is: where J, is Maxwell's result for evaporative mass flux from a continuum regime particle given by and where M, = molecular weight of evaporating species; Dvg = diffusivity of evaporating vapor in carrier gas (air); R = ideal gas constant; T = absolute temperature; Pv, = partial pressure at the droplet surface; Pv,, = partial pressure far from the droplet surface [= 0.0 in y = surface tension of aerosol material. Note that in evaluating the partial pressure at the droplet surface, P,,,, it is necessary to account for vapor pressure enhancement due to droplet curvature. Thls effect is included in the exponential expression on the left hand side of Eq. (8). The integral is specified by an appropriate transition regime expression for J and is evaluated by numerical quadrature. Evaporative mass transfer from transition regime aerosol droplets has been investigated theoretically by numerous investigators. This work has recently been reviewed by Davis (1983) and Rader (1985). Based on these reviews it was concluded that the theories of Bademosi and Liu (1971), Fuchs and Sutugin (1970) [based on work of Sahni (1966)], and Sitarski and Nowakowski (1979) [as modified by Davis et al. (1980)l were most likely to represent accurately the evaporation mass flux, J, of these heavy molecular weight organics. Therefore, each of these approaches was used in evaluating our data. Vapor mean free paths for these three theoretical expressions were calculated as recommended in the original papers. Methods that were used to determine diffusivities of the vapors in air were discussed above. Only the vapor pressure remains to be accounted for in Eq. (8). Davis et al. (1980) have provided the following correlation for the vapor pressure of DOP near room temperature: log,, ( P,?) = , (10) where P," is in mm Hg. This result is consistent with the earlier work of Small et al.

13 258 Rader, McMurry, and Smith (1948), who measured the vapor pressure of DOP at temperatures above 100 "C. For DOP, all variables are known, and the experimental results can be compared directly with theoretical predictions. This provides an approach for investigating the consistency of data acquired with this new experimental technique with related work from previous studies. For DOS and oleic acid, the vapor pressure at room temperature remains as the unknown that is found from the integration of Eq. (8). Values for the vapor pressure of DOS at high temperatures (> 100" C) are available in the literature (Perry and Weber, 1949; Small et al., 1948). Room temperature vapor pressures for DOS can be estimated by extrapolation of the following high temperature result (Small et al., 1948): Vapor pressure data for oleic acid was not found. Data for evaporation of DOP aerosols are compared with theory in Figure 2. Values recommended by Davis (1983) for vapor pressure and the Lennard-Jones parameters (hence their experimental result fu>r D,,) were used in calculating theoretical diameter reduction factors with Eq. (8). The modified Sitarski-Nowakowski theory was used to model the transition regime mass transfer. This theoretical result is shown for DOP as the solid line in Figure 2. In general, the agreement between theory and experiment is good, particularly at smaller diameters. The deviation at higher diameters is partially accounted for by the diameter discrepancy discussed above (since the DOP data has not been corrected to account for this systematic error); this effect will be most noticeable for small diameter differences. Slightly better agreement with the data is obtained with the Bademosi-Liu transition expression, although noticeable differences are still present. This result is also shown in Figure 2. Another method of comparing the DOP data with theoretical predictions is to com- pare vapor pressure predicted by Eq. (8) with the actual value of 2.36 X lop4 dynes/ cm2 from Eq. (10) at 25.7 " C. It was found that for particles with initial diameters exceeding 0.09 pm, calculated vapor pressures were size dependent and increased with increasing size. This is, no doubt, due to the systematic sizing error discussed earlier. For particles smaller than 0.09 pm, however, there was no systematic dependence of calculated vapor pressure on particle size. The average vapor pressure for all data points in this sub-0.09-pm-size range was 2.1 x dynes/cm2 using the Sitarski- Nowakowski-Davis and Fuchs-Sutugin expressions, and 2.2 X lop4 dynes/cm2 using the Bademosi-Liu expression, in good agreement with Eq. (10). The standard deviations in these average values is less than 5%. The calculated vapor pressure is not very sensitive to the particular transition expression used, as all of the transition theories investigated yielded vapor pressures within 10% of the Bademosi-Liu result (Rader, 1985). The calculated values for the vapor pressure at small diameters do not show any tendency to decrease, as might be expected if nonvolatile contamination became significant. Thus, the effect of contamination is thought to be small. The success of Eq. (8) in analyzing small particle evaporation rates provides a direct verification of the Kelvin equation. This can be most easily seen by removing the Kelvin expression from Eq. (8). The results of such calculations are shown in Figure 2 as the broken curve. The absence of the exponential is particularly evident at small diameters. For a 0.02-pm DOP droplet, vapor pressure enhancements predicted by the Kelvin equation are about a factor of three times that over a flat surface. Removing the Kelvin exponential from Eq. (8) results in.a strong diameter dependence in the vapor pressures calculated from the size-change data. Calculated vapor pressures then differ by a factor of two over the diameter range that was investigated.

14 Evaporation Rates of Monodisperse Organic Aerosols 259 The same approach was used to estimate the vapor pressures for oleic acid and DOS. Using the same three transition expressions from above, the vapor pressure for oleic acid at 25 " C was found to vary from 2.1 x to 2.4 X dyne/cm2, depending on the mass transfer model. For DOS at 25 O C, the predicted vapor pressures were nearly an order of magnitude less, falling between 2.5 x and 2.7 X dyne/cm2. This is in good agreement with the extrapolated value of 2.9 X dyne/cm2 from Eq. (11). The vapor pressure of DOS predicted by Perry and Weber (1949) is 50% greater than these values, reflecting the uncertainty in earlier measurements. Using the Davis-Sitarski- Nowakowski transition expression, and the predicted vapor pressure, results in the solid curves for DOS and oleic acid shown in Figure 2 and 3. Agreement with data is seen to be excellent. Since experimental values for the diffusion coefficients for DOS and oleic acid were not available in the literature, they were estimated using the approximations to the Lennard-Jones parameters given in Eqs. (4-6). Thus, the calculated vapor pressures should reflect any uncertainty in the estimation of these parameters. Since each of the mean free paths are either calculated directly from the Lennard-Jones parameters, or indirectly through their dependence on the diffusion coefficient, errors in the parameters will also affect the mean free path calculation. To test the sensitivity of the predicted vapor pressures to these uncertainties, the data analysis for DOP was repeated using several different values of the Lennard-Jones parameters. Collision diameters, a, of 10 and 12 A (11.07 A had been assumed) and interaction parameters, c,,, of 600 and 800 " K (690 " K had been assumed) were tried in various combinations with the Davis-Sitarski-Nowakowski transition regime expression. Variations of less than 3% in the predicted vapor pressure were observed for the entire data set. The independence of the predicted vapor pressure from the diffusion coefficient (the Lennard-Jones parameters) and the mean free path is a result that would be expected only in pure free molecular evaporation. SUMMARY The evaporation rates of small (0.02- to 0.2- pm-diameter) organic liquid droplets have been investigated using the TDMA technique (Rader and McMurry, 1986). Direct evidence supporting the Kelvin effect in organic aerosols is offered at smaller particle diameters than have been previously reported. When the vapor pressure and diffusion coefficient are available, the agreement between evaporation theory and measured evaporation rates is good. When the diffusion coefficient and the vapor pressure are not known, the former is estimated using the Chapman-Enskog result and the latter is calculated from the evaporation data. Predictions for the vapor pressure using several of the available transition regme mass transfer expressions did not vary significantly. Also, the sensitivity of the predicted vapor pressure to errors in estimating the diffusion coefficient was less than 3%. Thus, the TDMA technique provides a convenient and yet fairly accurate method for determining very low vapor pressures. The vapor pressure predicted for DOP was within about 15% of the previously reported value. Oleic acid was found to have a vapor pressure approximately equal to that of DOP. Calculations for DOS revealed a vapor pressure nearly an order of magnitude less than that of the other two organics. The implications of the present results to the generation of liquid aerosol standards is that the use of DOS is preferred to DOP or oleic acid. Even with DOS aerosols, however, the enhancement of evaporation rates resulting from the Kelvin effect can produce measurable reductions in diameter for sub-0.1-pm particles in time scales on the order of several minutes.

15 Rader, McMurry, and Smith This research was supported by Grant No. ATM from the U.S. National Science Foundation, Division of Atmospheric Chemistry, and by the Coordinating Research Council, CAPA project group. REFERENCES Agarwal, J. K., and Sem, G. J. (1980). Aerosol Sci. 11: Bademosi, F., and Liu, B. Y. H. (1971). Particle Technology Laboratory Publication No. 157, University of Minnesota, Particle Technology Laboratory. Bartz, H., Fissan, H., Helsper, C. Kousaka, Y., Okuyarna, K., Fukushima, N., Keady, P. B., Kerrigan, S., Fruin, S. A,, McMurry, P. H., Pui, D. Y. H,, and Stolzenburg, M. R., (1985). J. Aerosol Sci. 16: Blackman, M., Lisgarten, N. D., and Skinner, L. M. (1968). Nature 217: Chapman, S., and Cowling, T. G. (1970). The Mathematical Theory of Nonuniform Gases. Cambridge University Press, Cambridge, England. Chen, N. H., and Othmer, D. F. (1962). J. Chem. Eng. Data 7: Condensed Chemical Dictionary (8th ed.) (1971). Van Nostrand, New York. CRC ( ) Handbook of Chemistry and Physics, 53rd ed. Chemical Rubber Co., Cleveland, OH. Davis, E. J. (1983). Aerosol Sci. Technol. 2: Davis, E. J., and Ray, A. K. (1978). J. Aerosol Sci. 9: Davis, E. J., Ray, A. K., and Chang, R. (1978). A.I.Ch.E. Symp. Ser. 74(175): Davis, E. J., Ravindran, P., and Ray, A. K. (1980). Chem. Eng. Commun. 5: Defay, R., Prigogine, I., Bellemans, A,, and Everett, D. H. (1966). Surface Tension Adsorp. John Wiley, New York. Fisher, L. R., and Israelachvili, J. N. (1981). J. Colloid Interface Sci. 80: Fuchs, N. A., and Sutugin, A. G. (1970). Highly Dispersed Aerosols, Chap. 3. Ann Arbor Science, Ann Arbor, MI. Gudris, N., and Kulikova, L. (1924a). J. Rurs. Phys. Chem. Soc. 56:167. Gudris, N., and Kulikova, L. (1924b). Z. Phys. 24:121. Heisler, S. L., and Friedlander, S. K. (1977). Atmos. Enuiron. 11: Hirschfelder, J. O., Curtiss, C. F., and Bird, R. B. (1954). Molecular Theory of Gases and Liquids. John Wiley, New York. Jaspar, J. J. (1972). J. Phys. Chem. Ref. Data 1:841. Kaye, G. W. C., and Laby, T. H. (1973). Table of Physical and Chemical Constants, 14th ed. Longman, New York, p Knutson, E. O., and Whitby, K. T. (1975). J. Aerosol Sci. 6: LaMer, V. K., and Gruen, R. (1952). Trans. Faraday Soc. 48: Liu, B. Y. H., and Pui, D. Y. H. (1974). J. Colloid Interface Sci. 47: Lydersen, A. L. (1955). University of Wisconsin Engineering Experiment Sta. (SP) Report 3, Madison, Wisconsin. McMurry, P. H., and Grosjean, D. (1985). Atmos. Enuiron. 19: McMurry, P. H., Takano, H., and Anderson, G. R. (1983). Enuiron. Sci. Technol. 17: Perry, E. S., and Weber, W. H. (1949). J. Am. Chem. Soc. 71: Rader, D. J. (1985). Ph.D. Thesis, Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN. Rader, D. J., and McMurry, P. H. (1986). Aerosol Sci., 17: Ray, A. K., Davis, E. J., and Ravindran, P. (1979). J. Chem. Phys. 71(2): Sahni, D. C. (1966). J. Nuclear Energy 20: Sambles, J. R. (1971). Proc. R. Soc. Lond. Ser. A 324: Sambles, J. R., Skinner, L. M., and Lisgarten, N. D. (1970). Proc. R. Soc. Lond. Ser. A 318: Shereshefsky, J. L., and Steckler, S. (1936). J. Chem. Phys. 4: Sitarski, M., and Nowakowski, B. (1979). J. Colloid Interface Sci. 72(1): Skinner, L. M., and Sambles, J. R. (1972). J. Aerosol Sci. 3: Small, P. A,, K. W. Small, and Cowley, P. (1948). Trans. Faraday Soc. (Lond.) 44: Stolzenburg, M. R., and McMurry, P. H. (1986) in Aerosols: Formation and Reactiviq, Proceedings of the Second International Aerosol Conference, West Berlin, September, pp Thomson, W. (1870). Proc. R. Soc. (Edin.) 7: Thomson, W. (1871). Phil. Mag. (IV) 42: Woodland, D. J., and Mack, E., Jr. (1933). J. Am. Chem. Soc. 55: Received 26 November 1985; accepted 9 July 1986