WIAS Preprint No. 2990, (2023)

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


  • Schmeller, Leonie
  • Peschka, Dirk
    ORCID: 0000-0002-3047-1140

2020 Mathematics Subject Classification

  • 74F10 65M60 35A15


  • Phase fields, sharp-interface limit, moving contact lines, nonlinear elasticity




We construct gradient structures for free boundary problems with moving capillary interfaces with nonlinear (hyper)elasticity and study the impact of moving contact lines. In this context, we numerically analyze how phase-field models converge to certain sharp-interface models when the interface thickness tends to zero. In particular, we study the scaling of the Cahn--Hilliard mobility with certain powers of the interfacial thickness. In the presence of interfaces, it is known that the intended sharp-interface limit holds only for a particular range of powers However, in the presence of moving contact lines we show that some scalings that are valid for interfaces produce significant errors and the effective range of valid powers of the interfacial thickness in the mobility reduces.

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