The Validity of the Spherical Cap Approximation in Heterogeneous Nucleation

Abstract

On the basis of a general formulation of the Gibbs free energy change for heterogeneously nucleating systems, the difference in the free energy change for the formation of a spherical cap embryo and a sessile drop-shaped embryo is evaluated. This difference represents the error introduced by assuming the embryo is a spherical cap in the presence of a gravitational field. Power series expressions for the volume and surface areas of the sessile drop, based on the work of Bashforth and Adams, are used to arrive at the free energy change. Ratios allowing a comparison of the error for different systems are presented along with numerical values for a hypothetical, unit system. This hypothetical system is compared to water and to mercury with the result that the maximum relative error is 10?6. Based on this value, it is concluded that the spherical cap model is an adequate and useful approximation of the shape of an embryo in heterogeneous nucleation under the action of gravity.