Interface dynamics in a mean-field lattice gas model: Solute trapping, kinetic coefficient, and interface mobility

In a recent paper we showed that we can obtain dendritic growth in a mean-field lattice gas model. The equation of motion, derived from a local master equation, is a generalized Cahn-Hilliard equation. In the present paper, we study the isothermal dynamics of planar interfaces in this model. Stationary interface states advancing with constant velocity are investigated. We present numerical results as well as a continuum approximation that gives an analytic expression for the shape correction in the limit of small interface velocities. We observe departure from local equilibrium at the interface and solute trapping. The associated kinetic coefficients are calculated. The two effects are found to be related. We finally give an expression for the interface mobility and derive a relation between this mobility and the kinetic coefficients. Furthermore, we show that there occur oscillations of the growth velocity and density waves in the two hulk phases during the advance of the interface. This is related to the discrete dynamics using the theory of area-preserving maps as proposed by Pandit and Wortis.