Application of operator-scaling anisotropic random fields to binary mixtures

Abstract

In modern technical applications various multiphase mixtures are used to meet demanding mechanical, chemical and electrical requirements. To understand their structural properties as continuous macroscopic materials, it is important to capture the microstructure of these mixtures. Due to their vast range of applications multicomponent systems are subjected to microstructural changes such as phase separation and coarsening. Therefore the ultimate microstructural arrangement depends on the system's configuration and on exterior driving forces. In addition to this, random physical imperfections within the material and random noise in the exterior thermodynamic fields influence in essence the microstructural evolution. Since all physical processes are subjected to a certain degree of random inhomogeneity under realistic conditions, the influence of random phenomena cannot be neglected in modern physical models. An advanced mathematical description and an implementation of these stochastic processes are required to adapt simulation results based on deterministic mathematical models to experimental observations. In our contribution we will present an operator-scaling anisotropic random field embedded in the Cahn–Hilliard phase-field model to describe the phase evolution in a binary mixture. The arising nonlinear diffusion equation will be solved numerically in the innovative framework of the isogeometric finite element method. To illustrate the flexibility and versatility of our approach, numerical and experimental results for a eutectic Sn-Pb alloy are contraposed. This is the first time that the microstructural evolution in a multicomponent system has been associated with operator-scaling anisotropic random fields. Due to its enormous potential as an essential ingredient in stochastic mathematical and physical modeling it is only a matter of time until these processes will become prevalent in engineering applications.