Accurate wetting dynamics via a conservative Allen-Cahn based lattice Boltzmann approach for multiphase flows

Abstract

In this work we propose a local geometric wetting boundary condition for a conservative Allen--Cahn-based lattice Boltzmann framework. The prescribed contact angle is imposed through ghost phase-field values constructed from a locally reconstructed wall normal and a donor-fluid extrapolation. The ghost-node wetting update is local, geometrically consistent, and compatible with thread-safe large-scale implementations, while phase-field mass is controlled through a separate global volume correction. Validation includes static contact-angle tests, short-time droplet spreading, impact on a hydrophobic surface, and gravity-driven motion through a sharp-edged orifice. The simulations recover the imposed equilibrium angles, reproduce contact-angle-dependent spreading exponents between approximately 1/2 and 1/4, and follow the classical W e1/4 maximum-deformation scaling. The model also captures the transition between capture, release, and release with breakup. The proposed approach provides an accurate and scalable framework for wetting-controlled flows in complex geometries.