Modeling of contact angle hysteresis for rigid mobile particles: A phase-field lattice Boltzmann approach

We introduce a scheme for contact angle hysteresis in the presence of moving curved solid boundaries for a class of two-phase fluid models, where the interface between fluid phases is diffuse, while the ones involving solid phases are sharp. The scheme essentially reconstructs a ghost-node phase-field profile based on an Allen-Cahn equation along the solid surface. After validating the combined phase-field lattice Boltzmann approach with benchmarks in constant contact angle mode, we systematically investigate the hysteresis behavior with three benchmarks: (1) a cylinder rotating at a fluid-fluid interface, (2) a capillary bridge between two parallel plates that is stretched by separating the plates at a constant velocity, and (3) a cylinder equilibrating in a liquid pool under gravity. In all cases, contact line pinning is reproduced accurately, including the transition between the pinned and depinned states. The force and torque measured on the solid surface agree well with analytical solutions.