Wetting boundary schemes in modified phase-field lattice Boltzmann method for binary fluids with large density ratios

In this work, wetting boundary schemes in a modified phase-field lattice Boltzmann (LB) method are developed to simulate the contact-line motion and contact angle hysteresis of binary fluids with large density ratios. In the modified phase-field LB method, two multiple-relaxation-time (MRT) LB equations are utilized, one with a nondiagonal relaxation matrix used to solve the conserved Allen-Cahn (A-C) equation and the other with a modified discrete source term used to solve the incompressible Navier-Stokes (N-S) equations. Based on the idea of geometric formulation, two wetting boundary schemes corresponding to the modified phase-field LB model are proposed. In the first scheme, a layer of virtual nodes is utilized to realize the geometric formulation. The values of the order parameter at the virtual nodes are determined by the central difference method. In the second scheme, the geometric formulation is realized through a local scheme for the gradient terms of the order parameter where the nonequilibrium parts of the distribution function are utilized. Compared with the first wetting boundary scheme and some previous models, the second wetting boundary scheme does not require the virtual nodes and simplifies the numerical implementation. The developed two schemes are validated through a series of benchmark simulations, including droplet spreading on idea substrate, capillary intrusion and droplet shearing on nonideal substrate. It is found that satisfactory accuracy can be achieved by both two schemes, and the second scheme can obtain better stability while the first scheme shows better performance in simulating contact angle hysteresis.