Sharp Interface Limits of the Cahn-Hilliard Equation with Degenerate Mobility

Abstract

In this work, the sharp interface limit of the degenerate Cahn-Hilliard equation (in two space dimensions) with a polynomial double well free energy and a quadratic mobility is derived via a matched asymptotic analysis involving exponentially large and small terms and multiple inner layers. In contrast to some results found in the literature, our analysis reveals that the interface motion is driven by a combination of surface diffusion flux proportional to the surface Laplacian of the interface curvature and an additional contribution from nonlinear, porous-medium type bulk diffusion, For higher degenerate mobilities, bulk diffusion is subdominant. The sharp interface models are corroborated by comparing relaxation rates of perturbations to a radially symmetric stationary state with those obtained by the phase field model.

27 pages, 2 figures

References in corpus (4)

• Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits
• Phase Separation Kinetics in a Model with Order-Parameter Dependent Mobility
• Stationary solutions of driven fourth- and sixth-order Cahn-Hilliard type equations
• On Oscillations of Solutions of the Fourth-Order Thin Film Equation Near Heteroclinic Bifurcation Point