# Two-dimensional Cahn-Hilliard simulations for coarsening kinetics of spinodal decomposition in binary mixtures

Source: [Two-dimensional Cahn-Hilliard simulations for coarsening kinetics of spinodal decomposition in binary mixtures](<https://www.sota2.com/research/paper/68fa40941e209131ce8f492c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T02:52:42.656Z

Authors: Bj\\"orn K\\"onig, Olivier J. J. Ronsin, Jens Harting

Published: 2021-07-15T10:21:09.000Z

## Abstract

The evolution of the microstructure due to spinodal decomposition in phase separated mixtures has a strong impact on the final material properties. In the late stage of coarsening, the system is characterized by the growth of a single characteristic length scale $L\\sim C t^{\\alpha}$. To understand the structure-property relationship, the knowledge of the coarsening exponent $\\alpha$ and the coarsening rate constant $C$ is mandatory. Since the existing literature is not entirely consistent, we perform phase field simulations based on the Cahn-Hilliard equation. We restrict ourselves to binary mixtures using a symmetric Flory-Huggins free energy and a constant mobility term and show that the coarsening for off-critical mixtures is slower than the expected $t^{1/3}$-growth. Instead, we find $\\alpha$ to be dependent on the mixture composition and thus from the morphology. Finally, we propose a model to describe the complete coarsening kinetics including the rate constant $C$.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2107.07234>)

[PDF](<https://arxiv.org/pdf/2107.07234.pdf>)