Simulation of coarsening in two-phase systems with dissimilar mobilities

TL;DR

This study uses phase field simulations to explore how two-phase microstructures with highly different mobilities coarsen, revealing morphological transitions and kinetic behaviors that depend on dimensionality and mobility contrast.

Contribution

It demonstrates the impact of dissimilar mobilities on coarsening morphology and kinetics in two- and three-dimensional systems, including a new model linking coarsening rate to curvature variance.

Findings

Morphological transition to nearly-circular particles in 2D with dissimilar mobilities.

3D bicontinuous microstructures evolve self-similarly, following the $t^{1/3}$ law.

Coarsening rate constant correlates linearly with curvature variance during transient.

Abstract

In this work, we apply phase field simulations to examine the coarsening behavior of morphologically complex two-phase microstructures in which the phases have highly dissimilar mobilities, a condition approaching that found in experimental solid-liquid systems. Specifically, we consider a two-phase system at the critical composition ($50\%$ volume fraction) in which the mobilities of the two phases differ by a factor of 100. This system is simulated in two and three dimensions using the Cahn-Hilliard model with a concentration-dependent mobility, and results are compared to simulations with a constant mobility. A morphological transition occurs during coarsening of the two-dimensional system (corresponding to a thin film geometry) with dissimilar mobilities, resulting in a system of nearly-circular particles of high-mobility phase embedded in a low-mobility matrix. This morphological transition causes the coarsening rate constant to decrease over time, which explains why a previous study found lack of agreement with the theoretical $t^{1/3}$ power law. Three-dimensional systems with dissimilar mobilities resulted in bicontinuous microstructures that evolve self-similarly, as determined by quantitative analysis of the interfacial shape distribution. Coarsening kinetics in three dimensions agreed closely with the $t^{1/3}$ power law after the initial transient stage. A model is derived to explain a nearly-linear relationship between the coarsening rate constant and the variance of scaled mean curvature that is observed during this transient stage.