Kinetic theory of heterogeneous nucleation; effect of nonuniform density in the nuclei

The heterogeneous nucleation of a liquid from a vapor in contact with a planar solid surface or a solid surface with cavities is examined on the basis of the kinetic theory of nucleation developed by Nowakowski and Ruckenstein J. Phys. Chem. 96 (1992) 2313] which is extended to nonuniform fluid density distribution (FDD) in the nucleus. The latter is determined under the assumption that at each moment the FDD in the nucleus is provided by the density functional theory (DFT) for a nanodrop. As a result of this assumption, the theory does not require to consider that the contact angle which the nucleus makes with the solid surface and the density of the nucleus are independent parameters since they are provided by the DFT. For all considered cases, the nucleation rate is higher in the cavities than on a planar surface and increases with increasing strength of the fluid-solid interactions and decreasing cavity radius. The difference is small at high supersaturations (small critical nuclei), but becomes larger at low supersaturations when the critical nucleus has a size comparable with the size of the cavity. The nonuniformity of the FDD in the nucleus decreases the nucleation rate when compared to the uniform FDD.