where Lv is the latent heat of condensation, Rv is the gas constant of water vapor, Ta is air temperature, AT = Q/4nrka is the temperature rise under a BC heating rate of Q, r is the drop radius and ka is the thermal conductivity of air (= 0.0238 Wm-1 K-1 at 0°C) corrected with the gas kinetic theory. With a 50% BC content, AT is about 0.02 K for 1 ¡m aerosols and 0.1 K for 10 ¡m aerosols. Note that, as will be mentioned later, the heating rate is significantly stronger if the aerosols are wet. The heating effect may cause a change in Kohler curves because of the rise in drop surface vapor pressure, and this not only retards the condensation growth but also hinders the activation process because the critical saturation is increased. Chen and Hsieh (2004) showed that condensation growth (see Pruppacher and Klett, 1997) may be retarded by a factor (1 — B):

where m is droplet mass. dm' is mass change under BC heating,

(Sa - Sd)4nrka fhTa Sa is the saturation ratio of ambient air and fh is the heat ventilation coefficient. Note that this equation can be rearranged into a form similar to that given by Conant et al. (2002):

The overall heating from individual droplets causes two types of group effects. The first is that the reduced overall condensation [see Eq. (2)] will raise the ambient saturation Sa. So even though the critical Sd of each aerosol has been elevated, the enhanced ambient saturation Sa may increase the chance of activation, particularly for the smaller aerosols whose critical Sd is less affected. The second effect is the heating of air by energy transferred from the heated droplets. An increase in air temperature will depress Sa, thus reducing the amount of water that can be condensed. Such a "cloud-burning effect" (Ackerman et al., 2000) may have a significant influence on cloud formation and climate in polluted regions. In addition, a depressed Sa reduces the chance of aerosol activation into cloud drops, particularly for smaller aerosols which require a higher Sa to be activated. In summary, BC heating has three effects: (1) It increases the critical Sa of individual droplets, (2) it increases the ambient Sa due to retarded condensation growth on heated droplets, and (3) it decreases the ambient Sa due to heating on ambient air. How these effects combine to affect the CDNC requires a detailed cloud-microphysical model to explain.

Following the approach of Nenes et al. (2002), Chen and Hsieh (2004) applied the microphysical model of Chen and Lamb (1994) to evaluate the overall BC heating effect. The radiative heating algorithm of Toon and Ackerman (1981) was adopted to calculate BC heating. Figure 13 shows their results for three different heating scenarios, compared with the situation without BC heating (the curve NoHeat). If the heating occurs only on the droplet and the heat does not conduct to the ambient air (the curve Drop), then the peak Sa is raised due to retarded condensation growth. This led to more cloud drop activation (higher CDNC) even though the critical Sd of individual aerosols was also raised. For the externally mixed situation (the curve XM), where BC particles do not reside within the hygroscopic material, the heating is only on the air, but not the cloud drops, such that the peak Sa and CDNC are significantly reduced. If the BC and hygroscopic materials are internally mixed (the curve IM), the heating will be on both the cloud drops and the ambient air, and then the air-heating effect is mostly offset by

Figure 13. Time evolution of (a) supersaturation and (b) cloud drop number concentration in different heating scenarios. Marine aerosol distribution is applied with a BC mass content of 50%. The updraft velocity is set as 0.25 m/s. (From Hsieh, 2004.)

the drop-heating effect such that there is only a slight decrease in the peak Sa and CDNC. Note that heating of BC with a thick liquid shell is stronger than that without, a mechanism included in the above calculation.

The relative strength of saturation enhancement or reduction by the drop-heating effect and that by the air-heating effect depends on the total mass fraction of the BC and its distribution among aerosols. The changes in the peak Sa become less obvious when the aerosol distribution is of the continental type, because many more droplets are activated to quickly consume the excess water vapor. Chen and Hsieh (2004) found that the maximum Sa and CDNC can be either enhanced or depressed, depending on the types of aerosol distribution and BC distribution, a conclusion different from that of Nenes et al. (2002). Nenes et al. (2002) also indicated that soot heating may prohibit giant CCNs from reaching threshold sizes to initiate drizzle. This mechanism, most efficient at strong updrafts, tends to increase the CDNC, because there will be less accretion of cloud drops by drizzles.

Being insoluble, soot particles may also act as nuclei for heterogeneous ice nucleation. This subject is of particular interest with regard to the contrail formation from aircraft exhausts. Demott (1990) found that soot can enhance ice nucleation by the immersion-freezing mechanism, and the activity increases with particle size. For the temperature range of —5 to —20°C, Gorbunov et al. (2001) found that the ice-forming activity of soot particles increases with decreasing temperature and increasing size, as well as the degree of oxidization of the particle surface (which helps in forming hydrogen bonds with water molecules). Moohler et al. (2005) found that at temperatures below —38°C, soot particles acted as deposition nuclei at very low ice saturation ratios, between 1.1 and 1.3. At higher temperatures, ice nucleation occurred only after approaching liquid saturation. They further found that a coating of sulfuric acid elevates the ice nucleation thresholds. This result shows the importance of knowing the mixing state of soot and sulfuric acid aerosol particles. Note that freshly emitted soot is extremely hydrophobic, but during aging soot becomes less so. Decesari et al. (2002) found that the soot oxidation process causes the formation of water-soluble polycarboxylic compounds, which might cause soot to become effective CCNs.

2.2.3. Surfactants

One particular type of OC — called "surfactants" — consists of polar (hydrophilic) and nonpolar (hydrophobic) segments. Surfactants can form a monolayer surface film when exposed to water or droplets, and therefore are also known as "film-forming compounds" (FFCs). The surface film may cause a significant decrease in the water accommodation coefficient, and thus it retards the condensation or evaporation over a water surface. This phenomenon was noticed as early as in the 18th century by Benjamin Franklin, and relevant experimental work extended through the late 19th and the early 20th century until Irvin Langmuir in 1917 decisively determined many basic properties of the surface film (see La Mer, 1962).

Natural FFCs have been observed widely in the marine atmosphere (Blanchard, 1964; Goetz, 1965; Barger and Garrett, 1970). Blanchard (1963) and Garret (1967) suggested that FFCs may be injected into the atmosphere by bubble bursting over the oceans. Over the land, hydrocarbons emitted by plants may be transformed into polar species due to oxidation or polymerization by photocatalytic processes (Garrett, 1978). Seidl (2000) showed that leaf abrasion or biomass burning may produce significant fatty acids that form a dense surface film on aerosol particles. Husar and Shu (1975) found direct evidence from electron micrographs that organic coating does exist on urban haze particles, which might be related to the persistence of smog in the Los Angeles basin (Husar et al., 1976). FFCs are also common ingredients in fog, rain and snow, particularly near polluted or forested regions (Lunde et al., 1977; Meyers and Hites, 1981; Capel et al., 1990; Facchini et al., 1999b). Graedel et al. (1983) suggested that typical mass fractions of surface-active compounds in aerosol particles are on the order of 10%. This might not seem much, but if this amount is present entirely on the surface, the surface film formed may cover a large fraction of the droplet surface because it is only one molecule thick (Langmuir and Langmuir, 1927).

Derjaguin et al. (1985) considered the FFC effect using a one-dimensional model to evaluate surfactant vapor on the spectrum of cloud drops forming in the process of condensation growth. Their results indicated that as the small droplets are passivated, the number of growing droplets increases, and the growth of large droplets is accelerated. Feingold and Chuang (2002) also evaluated the potential influence of FFCs on droplet growth by using a parcel model, and provided an alternative explanation for droplet spectral broadening resulting from the presence of FFCs in CCNs. They summarized that the ability of FFCs on droplet spectral broadening is a function of both the total mass of FFCs and how it is distributed among the particles. In the following, a more detailed analysis is given to elucidate the mechanisms involved and the impacts of FFCs on cloud properties.

The basic condensation growth equation [i.e. dm/dt in Eq. (2)] can be transformed into a form commonly seen in textbooks (see Pruppacher and Klett, 1997; p. 511):

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