Fluctuation effects on pattern selection in the hyperbolic model of phase decomposition

Abstract

Phase separation processes in the hyperbolic model of spinodal decomposition are considered. The model is addressed to description of earlier and later stages of phase separation in binary systems deeply undercooled into spinodal region of phase diagram. In addition to deterministic local equilibrium contribution and deterministic pure nonequilibrium contribution into spinodal decomposition, we have introduced the noise induced fluctuations which are defined as multiplicative fluctuations. With introducing fluctuations of the diffusion flux the hyperbolic model has been analyzed for earlier and later stages of spinodal decomposition. The effective Fokker-Planck equation for the hyperbolic model describing phase separation with fluctuations is derived. Using the exact stationary distribution functional for the concentration field the pattern selection processes at late stages of spinodal decomposition are analyzed.