Sharp-interface limits of Cahn-Hilliard models and mechanics with moving contact lines

TL;DR

This paper investigates how phase-field models for free boundary problems with moving contact lines converge to sharp-interface limits as interface thickness diminishes, highlighting the effects of mobility scaling on accuracy.

Contribution

It introduces gradient structures for free boundary problems with elasticity and analyzes the impact of mobility scaling on sharp-interface convergence in the presence of moving contact lines.

Findings

Convergence depends on mobility scaling parameter alpha.

Errors increase when alpha is near the lower bound of valid range.

Moving contact lines significantly affect the sharp-interface limit accuracy.

Abstract

We construct gradient structures for free boundary problems with nonlinear elasticity and study the impact of moving contact lines. In this context, we numerically analyze how phase-field models converge to certain sharp-interface limits when the interface thickness tends to zero $\varepsilon\to 0$. In particular, we study the scaling of the Cahn-Hilliard mobility $m(\varepsilon)=m_0\varepsilon^\alpha$ for $0\le \alpha \le \infty$. In the presence of interfaces, it is known that the intended sharp-interface limit is only valid for $\underline{\alpha}<\alpha<\overline{\alpha}$. However, in the presence of moving contact lines we show that $\alpha$ near $\underline{\alpha}$ produces significant errors.