Cloud critical radius

Calculate the critical radius /y and critical supersaturation Sc. for activation into a cloud droplet of a 10-l5-g NaCl particle. Assume the surface tension is 72 dyn cm-1 and the liquid density is that of water. 

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. 

As a particular example, one can consider the homogeneous nucleation in the pure water vapor at 25° C. The surface tension coefficient of water is a = 71.96 N/m at this temperature. Table 5.1 shows some characteristics of the new phase. When the oversaturation is p/p =8.1, the critical nucleus of 0.5 nm radius is seen to comprise 18 water molecules. The equihbrium pressure of such nuclei is not high (approximately 10 bar). Since the water vapor pressure in real clouds is usually no more than 0.1% over that of the saturated vapor, it is unrealistic to expect in the rea sonable time scale the homogeneous formation of water drops in Earth s atmosphere. 

Thus, for a given if the actual cloud radius (Rc/Bp) is less than the predicted critical value Rc/Rp), then all of the particles in a quasi-stationary burning could will be able to bum individually. 

Fig. 7-8. Influence on cloud nuclei formation of the mass fraction e (water-soluble material/particle dry mass). Left Critical supersaturation of aerosol particles as a function of particle dry radius. Right Cloud nuclei spectra calculated for e = 0.1 and 1 on the basis of two size distributions each for continental and maritime aerosols (solid and dashed curves, respectively). [Adapted from Junge and McLaren (1971).] The curves for the maritime cloud nuclei spectra are displaced downward from the original data to normalize the total number density to 300 cm-3 instead of 600 cm-3 used originally. The curves for e = 1 give qualitatively the cumulative aerosol size distributions starting from larger toward smaller particles (sk = 10 4 corresponds to r0 0.26 p.m, sk = 3 x 10 3 to rs 0.025 Atn). Similar results were subsequently obtained by Fitzgerald (1973, 1974). The hatched areas indicate the ranges of cloud nuclei concentrations observed in cloud diffusion chambers with material sampled mainly by aircraft [see the summary of data by Junge and McLaren (1971)] the bar represents the maximum number density of cloud nuclei observed by Twomey (1963) in Australia.

In this spirit we investigated models where the dust density n fell off as r°, r, or r . The grain emission (and absorption) efficiency was taken as a three part power law in X. a for X < lOOoX e a X for lOOOA < X < 20y and e a X" for X > 20y. This crude form is consistent with expectations for H2O and silicate grains (Irvine and Pollack 1968 and Knacke and Thomson 1973). Once the dependence of dust opacity on radius from the star and on wavelength have been adopted, the only remaining critical parameter is the absolute value of the optical depth at lOOy, T] ooy measured from the outer radius of the dust shell through to the star. The adopted inner and outer radii at which one truncates the dust shell are easily seen to be unimportant provided the cloud is not optically thin (T] QQy O.l) and provided the outer layers do not contribute substantial optical depth respectively. 

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