solute ions (B) is then given by Eq. (DD): ifflB/MWB

Using Eq. (CC), the vapor pressure lowering due to mB grams of dissolved salt that forms i ions per dissolved molecule is therefore given by

Thus, if a nonvolatile solute is dissolved in water, the vapor pressure of water is lowered by an amount proportional to the mole fraction of dissolved solute, taking into account any dissociation that occurs (vide infra). It should be noted that this assumes ideal solution behavior.

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 et 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 Köhler curves, which describe whether an aerosol particle in the atmosphere will grow into a cloud droplet or not under various conditions.

3. Köhler curves. Calculation of the mole fraction of dissolved solute, xn, 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 raB grams of salt of molecular weight MWB are dissolved in water to form a solution of density ps. The number of moles of dissolved ions is /mB/MWB. 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


For dilute solutions, where raB is small, this reduces to



RmWb P

This vapor pressure lowering by the solute acts simultaneously with, and counteracts, the vapor pressure increase due to the Kelvin effect [Eq. (BB)]. Multiplying the two, the net result for the vapor pressure above a solution containing a dissolved solute is given by



Applying the approximation

= 1 + x x /2!+ ••• and using only the first two terms, Eq. (GG) becomes

where a = 2-yMWA/psi?T and the r~4 term has been omitted since it is small compared to the other three terms for radii of atmospheric interest.

The term supersaturation, S, defined as (PA/PA - f) is often expressed in the form of percent supersaturation, i.e., as 100{PA/P°A - f), where PA and PA are defined in Box 14.2. The relationship between the equilibrium vapor pressure over the droplet and that over the bulk liquid [Eq. (HH)] is often expressed in a simplified form using the supersaturation:

Plots of S against radius are known as Köhler curves. Figure f4.38a shows a schematic diagram of such a curve. A more detailed thermodynamic treatment of Köhler curves is given by Reiss and Koper (1995).

Typical values of supersaturation found in clouds are between about 0.2 and up to 2%. For fogs, the values are lower by about an order of magnitude, typically between about 0.02 and 0.2% (Pruppacher and Klett, 1997).

FIGURE 14.38 (a) Schematic diagram of traditional Köhler curve, where S = PA/PX - 1 is the supersaturation and r is the radius of the droplet, (b) Köhler curves for 30-nm dry particle of (NH4)2S04: (1) traditional curve; (2) for a 500-nm CaS04 particle (slightly soluble) and (NH4)2S04 as for curve 1; (3) as for curve 2 but in the presence of 1 ppb HNO, which is taken up by the particle (adapted from Kulmala et al., 1997).

FIGURE 14.38 (a) Schematic diagram of traditional Köhler curve, where S = PA/PX - 1 is the supersaturation and r is the radius of the droplet, (b) Köhler curves for 30-nm dry particle of (NH4)2S04: (1) traditional curve; (2) for a 500-nm CaS04 particle (slightly soluble) and (NH4)2S04 as for curve 1; (3) as for curve 2 but in the presence of 1 ppb HNO, which is taken up by the particle (adapted from Kulmala et al., 1997).

The dependence of S on the radius r is such that at small radii, the second term due to the vapor pressure lowering dominates and S is negative. In this region, air with RH below 100% is in equilibrium with the particle; such diagrams are often plotted as a function of RH in this region, instead of S. At large radii, the first term due to the Kelvin effect dominates, and S becomes positive and ultimately reaches a maximum before decreasing again. The region to the left of the peak is known as the haze region for reasons that will become apparent shortly, whereas that to the right is known as the cloud droplet region.

Take as an example, a small dry particle of NaCl of a given mass (mu) that is introduced into air at a water vapor pressure corresponding to SA in Fig. 14.38a. Assuming that the RH is above the deliquescence point of NaCl, ~75% at 25°C, the particle will take up water, dissolve, and form a stable droplet of radius rA. Similarly, if the air saturation ratio increases to Su, the particle will, under equilibrium conditions, take up water and grow to radius ru.

These particles are then in stable equilibrium with water in the air. Say the particle at point B loses some water molecules and starts to shrink. The equilibrium supersaturation for the smaller particle is lower than for the original particle. However, the supersaturation of the surrounding air remains higher, so that water will condense back out on the particle to bring it back to its original size. Similarly, if the particle at B gains some water molecules and the radius starts to increase, the value of S required to maintain this new size would be larger than that of the surrounding air and water would evaporate to restore the equilibrium size.

In short, particles to the left of the peak in Fig. 14.38a do not tend to shrink or grow. Because they are generally in the 0.1- to l-/j,m size range which scatters light efficiently (see Chapter 9.A.4), these particles are known as haze particles or droplets. These often occur at relative humidities below 100%.

Consider, however, a particle at point D in Fig. 14.38a. If it gains some water molecules and the radius starts to increase, the surrounding air will have a larger supersaturation than the required equilibrium value of S for this larger particle. As a result, water will condense out on the droplet, causing it to grow further. Particles that lie to the right of the peak are thus in an unstable equilibrium (e.g., see Reiss and Koper, 1995) and can therefore activate into cloud droplets from the condensation of water.

There are two questions with respect to potential indirect effects of aerosol particles on properties of clouds: (1) What are the sources of new particles? (2) How do these new particles grow to sufficient size (>50 nm) to act as CCN?

The first issue is that of formation of new particles. As discussed in Chapter 9.B, nucleation of gases to form new particles in the atmosphere is not well understood. The observed rates of nucleation of H2S04, for example, greatly exceed the calculated rates. An important contributor to the formation of new particles in the boundary layer (BL) under some conditions appears to be exchange between the BL and the free troposphere (e.g., Davison et al., 1996; Raes et al., 1997; Clarke et al., 1997). For example, some of the DMS from the oceans can be carried to the free troposphere, where it is oxidized to sulfate, generating new CCN. Mixing of the air mass back into the BL may then quench the formation of new CCN in that region by scavenging the low-volatility species such as H2S04 before they can nucleate to form new particles (e.g., see Slinn, 1992; and Raes, 1995).

The second issue is how these new particles grow into a sufficient size that they can act as CCN. The size to which the particles must grow to act as CCN is determined under equilibrium conditions by the Köhler curves. The peak values of S and r on the Köhler curves (Fig. 14.38) are known as the critical values, Sc. and rK (see Problem 6). Whenever the supersaturation of the air mass is greater than Sc, condensation occurs to form cloud and fog droplets. However, if it is less than Sc, particles with radii less than the critical radius rc. will maintain an equilibrium size (e.g., point B in Fig. 14.38a) and not form clouds or fogs. Of course, in the real atmosphere, there are a variety of initial particle sizes containing varying amounts of dissolved solutes, and the supersaturation of the air mass also changes with time. However, the Köhler curves provide a basis for understanding which particles can grow into clouds and fogs and which will not.

It is important to note that the Köhler relationship assumes equilibrium. However, under real atmospheric conditions, the system may not be at equilibrium. P. Y. Chuang et al. (1997) and Hallberg et al. (1998) point out that if the time scale for growth of cloud droplets is larger than that for the particle to reach equilibrium, the growth of CCN into cloud droplets may be controlled by kinetics, rather than equilibrium. They suggest that ignoring this potential kinetic limitation may lead to overestimating the number of cloud droplets that will form from a given number of CCN. In addition, measurement techniques for CCN using cloud chambers may not give an accurate assessment of CCN under ambient conditions since the range of time scales encounted in air is much larger than that used in the measurements. At present, it is not clear how much of a problem such kinetic limitations present in the atmosphere. [Some parameterizations in use, however, do take into account the kinetic limitations (e.g., C. C. Chuang et al., 1997).]

In addition, these traditional Köhler curves do not take into account the effects of slightly soluble solutes or gases that can dissolve in the particles. Figure 14.38b compares the traditional Köhler curves for a 30-nm dry particle of (NH4)2S04 at 298 K with that for the same particle but containing a 500-nm core of slightly soluble CaS04 (Kulmala et al., 1997). The increased particle size reduces the Kelvin effect contribution and a minimum in the curve reflects the point at which all of the CaS04 dissolves. Also shown is a Köhler curve for the case where 1 ppb of gaseous HN03 is present and is taken up by the particles. It can be seen that the equilibrium supersaturation is less than 1 for sizes up to ~ f 0 /¿m; i.e., for this more complex (but realistic) case, cloud droplets can form at RH below 100%.

Possible mechanisms of growth for small particles into a sufficient size that they are on the right side of the Köhler curve include uptake of small particles into existing cloud droplets where in-cloud oxidation of gaseous species such as S02 to sulfate occurs. Evaporation of the cloud then leaves a larger particle containing the additional oxidation products (e.g., see Hoppel and Frick, 1990; Hegg, 1990; Van Dingenen et al., 1995; and Hoppel et al., 1996). Other possible mechanisms of particle growth include coagulation of fine particles or the growth of existing particles by condensation of low-volatility products (e.g., see Lin et al., 1992, 1993a, 1993b; Hegg, 1990,1993). However, coagulation is not expected to be important in remote areas since the number concentration of particles is much smaller than in polluted areas where coagulation can be important (Lin et al., 1992).

As we have already seen, the critical supersaturation Sc. corresponding to the peak of the Köhler 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 /¿m, respectively (Saxena, 1996). This particular set of measurements

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