Sharp-Interface Limits of Cahn–Hilliard Models and Mechanics with Moving Contact Lines

Multiscale Modeling &Simulation, Volume 22, Issue 2, Page 869-890, June 2024.
Abstract. We consider the fluid-structure interaction of viscoelastic solids and Stokesian multiphase fluid flows with moving capillary interfaces and investigate the impact of moving contact lines. Thermodynamic consistency of Lagrangian diffuse and sharp-interface models is ensured even on the discrete level by providing a monolithic incremental time discretization and a finite element space discretization. We numerically analyze how phase-field models converge to sharp-interface limits when the interface thickness tends to zero, [math], and investigate scalings of the Cahn–Hilliard mobility [math] for [math]. In the presence of interfaces, certain sharp-interface limits are only valid for an interval [math], i.e., there is an upper and lower bound on the range of valid scaling exponents [math]. We show that with moving contact lines scaling is more restrictive since [math] causes significant errors due to excess diffusion. Similarly, we demonstrate that [math] leads to nonconvergence to the sharp-interface limit. We propose [math] as a range of exponents that ensure optimal convergence of the phase field dynamics towards the sharp interface dynamics as [math].