Lattice Boltzmann modeling of wall-bounded ternary fluid flows

Starting from the phase-field perspective, we first formulate a novel wetting boundary condition to describe the interactions among ternary fluids and a solid and then we propose a boundary scheme for its implementation in the framework of the lattice Boltzmann (LB) method. This scheme for three-phase fluids can preserve the reduction consistency property of the diphasic case such that it can give physically relevant results. Combining this wetting boundary scheme and the LB ternary fluid model based on multicomponent phase-field theory, we simulated several ternary fluid flow problems involving a solid substrate, including the spreading of binary drops on a substrate, the spreading of a compound drop on a substrate, the capillary intrusion of ternary fluids, and the shear of a compound liquid drop on a substrate. The numerical results are found to be good agreement with the analytical solutions and some available results. Finally, as an application, we use the LB model coupled with the present wetting boundary scheme to numerically investigate the impact of a compound drop on a solid circular cylinder. It is found that the dynamics of a compound drop can be remarkably influenced by the wettability of the solid surface and the dimensionless Weber number.