An extended stochastic diffusion model for ternary mixtures

Abstract

This manuscript presents a novel approach to the simulation of anisotropic diffusion phenomena in multicomponent materials. Since all physical processes are subjected to a certain degree of random inhomogeneity, the influence of random phenomena cannot be neglected in modern physical models.Therefore, an operator-scaling anisotropic random field embedded in a multiphase version of the commonly known Cahn–Hilliard phase-field model is presented here in order to describe phase evolution in an exemplary ternary mixture subjected to random phenomena. The arising set of coupled highly non-linear diffusion equations will be solved numerically by means of a B-spline based finite element method. Since the experimental determination of material parameters characterizing the anisotropy of the specimen is cumbersome and error-prone, our approach gives rise to a completely new perspective for the simulation of anisotropic diffusion systems.