Stochastic generalization for a hyperbolic model of spinodal decomposition

A model for diffusion and phase separation which takes into account exponential relaxation of the solute diffusion flux and its fluctuations is developed. The model describes a system undergoing phase separation governed by a partial differential equation of hyperbolic type. The analysis is done for the evolution of patterns in spinodal decomposition for the system supercooled below critical temperature. Analytical results show that relaxation processes of the solute diffusion flux lead to the selection of patterns with different wavenumbers. Considering spatial–temporal correlations of the flux fluctuations, we have found that the temporal correlations promote selecting large-period patterns, whereas the corresponding spatial correlations accelerate such processes.