Comparison of Nucleation from Liquid to Gas and Nucleation of Rain Droplets in a Cloud

The nucleation rate for liquid to gas and rain droplets in a cloud is of the form for the nucleation rate J = M exp(N). We see that |dln(M)/dN| << 1 and in this paper is presented the expressions for N and the values for N. In Blander and Katz, 1975, page 837 they state this for liquid to gas and the same is true in Young, 1993, page 40 for rain droplets in a cloud.

Here are the expressions for J for each case: first Blander and Katz then Young.

J ≈ 3.73 (1035) [d2 σ / M3 B]1/ 2 exp [- 1.182 (105) σ3/(T (PV - PL)2)]

J = 4αc/NL(σ/2πm)1/2(e/kT)2S2exp[-16πσ3/3(kT)3(NL ln S)2]

Here for Blander and Katz J = A exp(K) and for Young it is J = C exp(D). In Blander and Katz, page 837 it is noted that the presence of σ3 in the numerator of K means that surface tension has the largest effect on temperature of nucleation. In Young, page 40 there is the comment that “it is the exponential term in the nucleation equation that is tested by these observations and not the pre-exponantial factor.” The author will produce the values for K and D, the dominating expressions, and the fact that Jennings, 2020 eliminated the prefactor in Blander and Katz.