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

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