3.1. Simulations of the Particles in the CCN Chamber
 The kinetic parcel model described by Leaitch et al.  was used to attempt to reproduce the observed growth rates of the particles into cloud droplets. This model uses the Köhler equilibrium equation in a kinetic framework much as described by Pruppacher and Klett . In the original model the source term for the supersaturation is the lifting and adiabatic cooling of an air parcel using a specified updraft velocity. To apply this model to the observations in the CCNc, it is necessary to change the supersaturation source term to approximate the supersaturation development in the CCNc. For this, the observed growth curves for different size particles of (NH4)2SO4 were used as a reference to enable later separation of the effects of the chamber from those due to reduced solubility. The data are shown in Figure 4a and were collected on the same day at a supersaturation of 0.4%. The four sizes shown here 64 nm, 84 nm, 130 nm and 170 nm have the critical supersaturations of 0.3%, 0.2%, 0.09% and 0.06% respectively (calculated using Köhler theory). The detector voltage has been normalized to a number concentration of 1000 #/cc; the actual number concentrations are given in the legend. The larger particles tend to grow into larger and more visible droplets earlier than the smaller particles, and there are increasing delays associated with the smaller particles.
Figure 4. (a) Laboratory experiments: ammonium sulfate ((NH4)2SO4) of various sizes. Growth curves for nearly monodisperse distributions of (NH4)2SO4. All these experiments were performed on the same day in October 1999. The effective supersaturation in these cases was 0.4%. The legend shows the diameters for each experiment. The detector voltages were all normalized to a number concentration of 1000 #/cc. The original number concentrations can be seen in the legend for each experiment. Lines have been fitted to the data points. (b) Simulations of CCNc: ammonium sulfate ((NH4)2SO4) of various sizes. Growth curves for nearly monodisperse distributions of (NH4)2SO4. These model runs begin with a transient supersaturation that approaches a constant supersaturation of 0.4%. The total number concentration was set to 1000 #/cc. The 64 nm particles start to activate at 2 seconds but only reach a maximum of 88% activation by 3.4 seconds.
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 The model was modified to include a transient increase in the supersaturation to a constant value. The transient was represented by a linear rise in relative humidity, starting at 95%; although in the laboratory experiments the aerosol introduced to the CCNc had a relative humidity of < 20% it was assumed to rise rapidly to near saturation. The equation used for the transient supersaturation (S) is: S = 3.30831*t–5.022, where S is supersaturation in percent and t is time in seconds. The slope of the transient increase was chosen to best approximate the pattern of growth of the 170 nm (NH4)2SO4 particles laboratory case (Figure 4a). Subsequently, the other three particle sizes were simulated using the same time constants. The simulations were performed for a maximum supersaturation of 0.4% with nearly monodisperse particles. The scattering cross-sectional area of the growing particles was calculated as a surrogate for comparison with detector voltage of the CCNc. The Mie scattering efficiency of the droplet scattering was calculated but it is not included here as it introduced small oscillations in the curves. These oscillations did not affect the relative delays, and the fact that the observed curves showed no such oscillations may be explained by variability in the droplet sizes and supersaturation within the CCNc that are not accounted for in the simulations. Another plausible explanation for the absence of oscillations in the observations is the photodetector views the droplets over a range of angles, thus smoothing the curves.
 The simulated growth curves, corresponding to the measured values (Figure 4a), are shown in Figure 4b. The simulations reproduce the general pattern and approximate time of delay seen in the observations.
 The point at which all of the particles fully activate is indicated for each curve in Figure 4b, with the exception of the 64 nm case. Only a portion of the 64 nm particles activated despite the fact that their critical supersaturation is slightly lower than 0.4%. Comparing the 84 nm, 130 nm and 170 nm cases shows that the smaller particles activate before the larger ones. Thus, it is not activation of the larger particles that accounts for their faster initial growth rate.
 The delays for the different sizes of (NH4)2SO4 particles are smaller at higher supersaturations. Little delay in both the measured (laboratory) and simulated growth rates was found at 0.9% supersaturation.
 The second step in the modeling of the water growth rates in the CCN chamber was to provide for compounds of lower solubility. The model initially specifies particles that are composed of two parts: one insoluble and one soluble. The soluble part is assumed to be completely and instantaneously dissolved (i.e. has high solubility) at the starting relative humidity. This is appropriate for species like (NH4)2SO4. In order to treat species with low solubilities that will not dissolve completely until more water is present on a particle, the model was modified to make the insoluble portion of particle dissolve according to specified solubility. At each time step, part of the insoluble portion was allowed to dissolve based on water mass and compound solubility. The kinetics of the dissolution process itself is not considered, making this approach one that will tend to underestimate the delay.
 Simulations of the solubilities of the organic species measured in the laboratory were conducted for nearly monodisperse particles centered at 170 nm. The ionic dissociation factor was assumed to be 1, because these organic acids have small dissociation constants (Table 1). Solution properties, other than the solubility and the ionic dissociation factor, including the osmotic coefficient were assumed to be equivalent to those of (NH4)2SO4. The initial particles were assumed to be composed of 0.1% (NH4)2SO4 and 99.9% of the species with the solubility of interest. The small (NH4)2SO4 component was included to ensure that the particles retain water at relative humidities below saturation. The transient supersaturation was slightly different for the maximum supersaturation of 0.9% than for 0.4% as discussed earlier. The equation used for this transient supersaturation (S) is: S = 3.3683*t–5.0262, where S is supersaturation in percent and t is time in seconds.
 The results of the simulations are shown in Figure 5, with the numbers in the legend indicating the solubilities tested. The pattern of the delays is similar between the simulations and observations (Figures 1 and 2), although the observed delays for succinic and glutaric acids are larger than simulated. The comparisons with succinic and glutaric acids reflect a conservative aspect to this model, however the reason for the absence of a larger delay for these two organic acids is unknown. It is not the result of a weaker dissociation that leads to the higher critical supersaturation estimate, since the model considers this factor. It may be that differences between the osmotic and accommodation coefficients for (NH4)2SO4 and glutaric acid are responsible.
Figure 5. Simulations of CCNc: ammonium sulfate ((NH4)2SO4) plus slightly soluble compound. Growth curves for model runs with supersaturation of 0.9%. The solubility is shown in the legend. The total number concentration was set to 1000 #/cc and the mode diameter was set to 170 nm. For these runs, the (NH4)2SO4 case employed ν = 3 (number of ions from dissociation of one solute) whereas all other cases had ν = 1 (to simulate not only the solubility but the number of ions of the organics).
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 Figure 5 also shows that at approximately 100 g/L solubility and greater, there is essentially complete activation and the substance can be considered completely soluble. At approximately 10 g/L and less, the particles do not activate at all and can be considered completely insoluble. This implies that the impact of particles with solubilities in the range 10–100 g/L may be more difficult to represent in models of the indirect effect of aerosols.
 Figure 6 shows a direct comparison between laboratory results and simulations for (NH4)2SO4 and adipic acid. The model (NH4)2SO4 curve was positioned to approximate the laboratory (NH4)2SO4 curve. The resulting comparison of the simulated and observed adipic acid curves indicates that the solubility and the dissociation factor explain much of the observed delays by the organic species in the rate of water uptake.
Figure 6. Laboratory experiments CCNc voltages compared with simulations of CCNc: ammonium sulfate ((NH4)2SO4) and adipic acid. The laboratory average (NH4)2SO4 curve from Figures 1 and 2 and the adipic acid curve from Figure 1 is compared to the simulations for (NH4)2SO4 and the slightly soluble compound with solubility similar to adipic acid from Figure 5. The simulation for (NH4)2SO4 was fitted to the laboratory average case. The effective supersaturation was 0.9%. The diameter of these particles was 170 nm (nearly monodisperse aerosol) and number concentrations were approximately 1000 #/cc. Lines have been fitted to the data points.
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 According to Facchini et al. , a reduction in the surface tension of the droplets might be expected. The effect of this would be to reduce the particle’s critical supersaturation and increase its growth rate. Such an effect cannot be discounted in the present results; however, its presence is not delineated.
3.2. Simulations of the Effect of Reduced Solubility on Cloud Droplet Number Concentrations
 Here the impact of the delays in growth rates of droplets due to the solubility of the CCN on the nucleation of cloud droplets is considered. To do this, the source term for the supersaturation in the model was reverted back to the lifting and adiabatic cooling of an air parcel using a specified updraft velocity. The initial particle distribution was represented by a lognormal distribution with standard deviation of 1.5 and a mode diameter of 160 nm. The model was run for number concentrations of 100 cm−3 and 500 cm−3 and updraft velocities of 20 cm/s and 50 cm/s. Figure 7 shows the simulated cloud profiles of relative humidity for particles of low particle solubility (solubility equal to that of adipic acid and an ionic factor of 1) and particles composed of (NH4)2SO4 (ionic factor of 3). The particle number concentration and updraft velocity are 100 cm−3 and 20 cm/s for each. The point of complete dissolution of the particles is shown on the adipic acid curve; (NH4)2SO4 dissolves completely before saturation is reached.
Figure 7. Adiabatic cloud parcel model simulations: relative humidity (RH) for ammonium sulfate ((NH4)2SO4) and the solubility for adipic acid (AA). (NH4)2SO4 was fully dissolved soon after the simulation began, whereas adipic acid took quite a while to fully dissolve (see legend). The point of activation is indicated in the legend. The updraft velocity was set to 20 cm/sec. The distribution was lognormal, with one mode centered on diameter 160 nm, standard deviation of 1.5. Lines have been fitted to the data points.
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 For the droplets nucleating on the particles of lower solubility, the lower droplet growth rate results in a reduced water uptake, which in turn raises both the level and the value of the maximum supersaturation in the cloud. For the low solubility case, only the particles that have had enough water to condense on them to enable complete dissolution of the solute are activated. Despite the higher supersaturation, the delay in dissolution reduces the cloud droplet number concentrations for the low solubility case to 23 cm−3 compared with 95 cm−3 in the (NH4)2SO4 case. These droplet number concentrations are based on everything larger than and including the smallest activated particle [e.g., Nenes et al., 2001].
 Table 1 indicated that adipic acid would have a critical supersaturation of 0.13%, based on Köhler theory and complete solubility. However Figure 7 shows that the adipic acid does not activate until greater than 0.4% supersaturation. This implies that measurements in the CCNc of critical supersaturation may tend to give a higher value because the particle requires more water to be completely dissolved. This agrees with the tendency for less soluble species to have larger critical diameters, as suggested by Shulman et al. . It is also consistent with the observations of Corrigan and Novakov , who found that organic species with higher solubilities had critical diameters approaching those of the inorganics in contrast to the less soluble adipic acid.
 The simulated cloud droplet concentrations for all the model run cases are listed in Table 2. In all cases, the cloud droplet number concentrations are lower for the cases of particles of low solubility compared with particles composed only of (NH4)2SO4. There is an increase in the number of cloud droplets nucleated on particles when the updraft speed is higher. This increase is relatively larger for adipic acid than for ammonium sulfate (NH4)2SO4 particles. This is due to the peak in the supersaturation being higher above cloud base resulting in higher liquid water content and more dissolution of adipic acid particles.
Table 2. Number of Cloud Droplets Activated
|Updraft Velocity, Initial Particle Number Concentration||Ammonium Sulfate||Adipic Acid|
|20 cm/sec, 100 #/cc||95||23|
|50 cm/sec, 100 #/cc||99||41|
|20 cm/sec, 500 #/cc||340||50|
|50 cm/sec, 500 #/cc||460||97|