SHARP-INTERFACE LIMITS OF CAHN–HILLIARD MODELS AND MECHANICS WITH MOVING CONTACT LINES

SHARP-INTERFACE LIMITS OF CAHN-HILLIARD MODELS AND MECHANICS WITH MOVING CONTACT LINES

This code/repository supplements the mathematical results of the paper by Leonie Schmeller and Dirk Peschka from the Weierstrass Institute for Applied Analysis and Stochastics in Berlin published in the SIAM Journal Multiscale Modeling and Simulation (MMS) in 2024 with the DOI https://doi.org/10.1137/23M1546592.

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. In particular, we study the scaling of the Cahn-Hilliard mobility m for variable exponents of the small thickness. In the presence of interfaces, it is known that the intended sharp-interface limit is only valid for for a certain range of exponents. However, in the presence of moving contact lines we show that certain choices of "feasible" exponents produce significant errors.

Funding. We acknowledge the funding by the German Research Foundation (DFG) within the DFG Priority Program SPP 2171 Dynamic Wetting of Flexible, Adaptive, and Switchable Substrates through the projects 422786086 and 422792530 and thank the Berlin Mathematics Research Center MATH+ for funding and support through project AA2-9.