Interface Growth Driven by Surface Kinetics and Convection

A moving, solidifying interface that grows by the instantaneous adsorption of a diffusing solute is described by the classic one-sided “Stefan problem” [15, 19]. More generally, the behavior of precipitate growth can depend on both surface kinetics and bulk drift of the depositing species. We generalize the Stefan problem and its interface boundary condition to explicitly account for both surface kinetics and particle convection. A surface layer, within which the surface adsorption and desorption kinetics occurs, is introduced. We find that surface kinetics regularizes the divergent interface velocity at short times, while a finite surface layer thickness further regularizes an otherwise divergent initial acceleration. At long times, we find the behavior of the interface position to be governed by the particle drift. The different asymptotic regimes and the cross-over among them are found from numerical solutions of the partial differential equations, as well as from analysis of a nonlinear integro-differential equation.