Kohler curve

These plots are called Kohler curves after their originator (Kohler, 1936). His assumptions that... 

Fig. 7-10 Kohler curves calculated for the saturation ratio Phjo/PhjO of a water droplet as a function of droplet radius r. The quantity im/M is given as a parameter for each line, where m = mass of dissolved salt, M = molecular mass of the salt, i = number of ions created by each salt molecule in the droplet.

When a droplet reaches the peak of its appropriate curve, due to being in a region of RH greater than the RH for that critical size, it will continue to grow in an uncontrolled fashion. As it gets larger, the curvature effect decreases its vapor pressure and it enters a region of increased supersaturation relative to that at the peak of the Kohler curve. A particle that turns into a droplet and passes the critical size is said to be an activated CCN. 

There are several basic physical-chemical principles involved in the ability of aerosol particles to act as CCN and hence lead to cloud formation. These are the Kelvin effect (increased vapor pressure over a curved surface) and the lowering of vapor pressure of a solvent by a nonvolatile solute (one of the colligative properties). In Box 14.2, we briefly review these and then apply them to the development of the well-known Kohler curves that determine which particles will grow into cloud droplets by condensation of water vapor and which will not. 

KELVIN EFFECT, VAPOR PRESSURE LOWERING, AND THE KOHLER CURVES... 

As we have seen in Chapter 9, there are a variety of dissolved solutes in atmospheric particles, which will lower the vapor pressure of droplets compared to that of pure water. As a result, there is great interest in the nature and fraction of water-soluble material in atmospheric particles and their size distribution (e.g., Eichel el al., 1996 Novakov and Corrigan, 1996 Hoffmann et al., 1997). This vapor pressure lowering effect, then, works in the opposite direction to the Kelvin effect, which increases the vapor pressure over the droplet. The two effects are combined in what are known as the Kohler curves, which describe whether an aerosol particle in the atmosphere will grow into a cloud droplet or not under various conditions. 

Kohler curves. Calculation of the mole fraction of dissolved solute, xB, in a water droplet requires knowing the number of moles of water and of dissolved solute. Take a two-component solution such as NaCl in water, where the solute dissociates into i ions (i = 2 for NaCl). Assume mB grams of salt of molecular weight MWU are dissolved in water to form a solution of density ps. The number of moles of dissolved ions is imB/MWU. The number of moles of water for a drop of volume V = (4/3)7rr3 is [psV—mB]/MWa, where MWA is the molecular weight of water. The mole fraction of dissolved... 

Plots of S against radius are known as Kohler curves. Figure 14.38a shows a schematic diagram of such a curve. A more detailed thermodynamic treatment of Kohler curves is given by Reiss and Koper (1995). 

As we have already seen, the critical supersaturation Sc. corresponding to the peak of the Kohler curve depends on a number of parameters unique to the aerosol particle. Thus, at a given supersaturation some particles will form cloud droplets and some will not. As a result, the total number of CCN will vary with the supersaturation used in the CCN measurement. This is illustrated in Fig. 14.39, which shows the concentration of CCN measured in Antarctica as a function of the percentage supersaturation for CCN that grow into droplets larger than 0.3 and 0.5 gm, respectively (Saxena, 1996). This particular set of measurements... 

As expected from the earlier discussion of the Kohler curves, not all particles act as CCN. For example, only about 15-20% of the Aiken nuclei (see Chapter 9.A.2) in a marine air mass off the coast of Washington state acted as CCN at 1% supersaturation (Hegg et al., 1991b). Similarly, in a marine air mass in Puerto Rico, between 24 and 70% of the particles measured at 0.5% supersaturation before cloud formation led to cloud droplet formation (Novakov et al., 1994). 

Close examination of various equations which have been proposed for predicting saturation ratios over solution droplets reveals that they differ only in detail and all give essentially the same results. Figure 14.7 is a plot of versus d for NaCl masses of various sizes with water as the solvent, computed from Eq. 14.19. Curves similar to these are very often referred to as Kohler curves. 

These plots are called Kohler curves after their originator (Kohler, 1936). His assumptions that cloud condensation nuclei (CCN) are water-soluble materials is now widely accepted. In the past, it was often thought that NaCl particles from the ocean were the main CCN however, more recent studies have demonstrated the frequent dominance of sulfate particles with composition between H2SO4 and (NH4)2S04-... 

Junge and McLaren (1971) have studied the effect that the presence of insoluble material has on the capacity of aerosol particles to serve as cloud condensation nuclei. Using Eq. (7-25) they calculated the supersaturation needed for an aerosol particle to grow to the critical radius at the peak of the Kohler curve, from where spontaneous formation of cloud drops becomes feasible. The results are shown in Fig. 7-8. They indicate that the difference is less than a factor of two in radius for particles whose soluble fraction is greater than e =0.1. The majority of particles can be assumed to meet this condition (see Fig. 7-19). By assuming particle size distributions similar to those of Fig. 7-1 for continental and maritime background aerosols, Junge and McLaren also calculated cloud nuclei spectra as a function of critical supersaturation and compared them with observational data. These results are shown in Fig. 7-8b. We shall not discuss the data in detail. The results make clear, however, that the presence of insoluble matter in aerosol particles does not seriously reduce their capacity to act as cloud condensation nuclei. 

FIGURE 17.5 Kohler curves for NaCl and (NH4)2S04 particles with dry diameters 0.05,0.1, and 0.5 pm at 293 K (assuming spherical dry particles). The supersaturation is defined as the saturation minus one. For example, a supersaturation of 1% corresponds to a relative humidity of 101%. 

The steeply rising portion of the Kohler curves represents a region where solute effects dominate. As the droplet diameter increases, the relative importance of the Kelvin effect... 

The Kohler curves also represent the equilibrium size of a droplet for different ambient water vapor concentrations (or relative humidity values). If the water vapor partial pressure in the atmosphere is pw, a droplet containing ns moles of solute and having a diameter Dp satisfying the Kohler equations should be at equilibrium with its surroundings. Realizing that the Kohler curves can be viewed as size-RH equilibrium curves poses a number of interesting questions ... 

This equation gives the critical saturation for a dry particle of diameter ds. Note that the smaller the particle, the higher its critical saturation. When a fixed saturation S exists, all particles whose critical saturation Sc exceeds S come to a stable equilibrium size at the appropriate point on their Kohler curve. All particles whose Sc is below S become activated and grow indefinitely as long as S > Sc. 

Figure 17.7 presents the Kohler curves for (NH4)2S04 for complete dissociation and no dissociation. Note that dissociation lowers the critical saturation ratio of the particle (the particle is activated more easily) and increases the drop critical diameter (the particle absorbs more water). 

FIGURE 17.7 Kohler curves for (NH4)2S04 assuming complete dissociation and no dissociation of the salt in solution for dry radii of 0.02, 0.04, and 0.1 pm. 

Kohler curves for a particle consisting of various combinations of (NH SCU and insoluble material are given in Figure 17.8. We see that the smaller the water-soluble fraction the higher the supersaturation needed for activation of the same particle, and the lower the critical diameter. Critical supersaturation as a function of the dry particle diameter is given in Figure 17.9. 

FIGURE 17.A.3 Kohler curves for particles consisting of a 0.1 pm adipic acid core coated with an equivalent of 0.05 pm ammonium sulfate with 0, 5, and 10 ppb of HN03 at 20°C and 1 atm. For adipic acid, a slightly soluble C6 dicarboxylic acid, the following parameters are used I , = 1 ions molecule-1, Mss = 0.146kgmol-1, p . = 1360kgm-3 (Cruz and Pandis 2000), and T = 0.018 kg kg water-1 (Raymond and Pandis 2002). Surface tension is taken as that of water. 

The steeply rising portion of the Kohler curves represents a region where solute effects dominate. As the droplet diameter increases, the relative importance of the Kelvin effect over the solute effect increases, and finally beyond the critical diameter the domination of the Kelvin effect is evident. In this range all Kohler curves approach the Kelvin equation, represented by the equilibrium of a pure water droplet. Physically, the solute concentration is so small in this range (recall that each Kohler curve refers to fixed solute amount) that the droplet becomes similar to pure water. 

---