Cahn-Hilliard Equation

The Cahn-Hilliard equation describes how different substances or phases within a material separate and organize over time, such as oil and water forming distinct layers. It models the process by which a mixture naturally evolves to minimize energy, leading to the formation of regions rich in one component or another. This equation is used in materials science to understand phenomena like alloy development, phase separation, and thin film behaviors. It captures the dynamics of how materials change structure gradually, incorporating both diffusion and surface energy effects to predict the evolving patterns.