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Sharp-interface limits of Cahn-Hilliard models and mechanics with moving contact lines (2301.04968v1)
Published 12 Jan 2023 in math.AP, cond-mat.soft, and physics.flu-dyn
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.