Simplified method for wetting on curved boundaries in conservative phase-field lattice-Boltzmann simulation of two-phase flows with large density ratios

Abstract

A simplified method is proposed to implement a wetting boundary condition on curved surfaces within the conservative phase-field lattice-Boltzmann (LB) simulation framework. It combines the idea of Huang et al. [“An alternative method to implement contact angle boundary condition and its application in hybrid lattice-Boltzmann finite-difference simulations of two-phase flows with immersed surfaces,” Eur. Phys. J. E 41, 17 (2018)] to find the order parameter on the other side of the wall with the conservative Allen–Cahn equation (CACE) for interface evolution solved by the LB equations. It inherits the advantage of the original method using the Cahn–Hilliard equation to avoid complicated interpolations under different geometries. By using the CACE, the boundary condition for the chemical potential is circumvented (making it more simplified), and the overshooting of the order parameter is also greatly suppressed, enabling it to simulate two-phase flows with solid objects of various shapes and wettabilities at large density and viscosity ratios. Several two-dimensional, axisymmetric, and three-dimensional problems, including some previously studied by experiments, were simulated and the capability of the proposed method is demonstrated through its good agreement with theoretical predictions and/or experimental observations.