Mobility inference of the Cahn–Hilliard equation from a model experiment

A challenge in phase field modeling of phase-separating binary systems using the Cahn–Hilliard equation (CHE) is the determination of the mobility coefficient, which controls the kinetics of order parameter evolution. This work presents numerical simulations to assess the feasibility of determining mobility in the CHE from a notional, model experiment. The qualitative behavior of these simulations differentiates between a mobility that is uniform throughout the system and one that is restricted only to phase interfaces. Moreover, quantitative analysis of the proposed model experiment permits inference of the product of mobility and the coefficient of the uniform-free energy term as well the characteristic length of the CHE. If the free energy coefficient is determined by other means (e.g., form thermodynamic or atomistic models), then the mobility may be calculated, as well. Graphic abstract