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A numerical method for simulating three-phase flows with moving contact lineson arbitrarily complex surfaces is developed in the framework of latticeBoltzmann method. In this method, the immiscible three-phase flow is modeledthrough a multiple-relaxation-time color-gradient model, which not only allowsfor a full range of interfacial tensions but also produces stable outcomes fora wide range of viscosity ratios. A characteristic line model is introduced toimplement the wetting boundary condition, which is not only easy to implementbut also able to handle arbitrarily complex boundaries with prescribed contactangles. The developed method is first validated by the simulation of a Janusdroplet resting on a flat surface, a perfect Janus droplet deposited on acylinder, and the capillary intrusion of ternary fluids for various viscosityratios. It is then used to study a compound droplet subject to a uniformincoming flow passing through a multi-pillar structure, where three differentvalues of surface wettability are considered. The simulated results show thatthe surface wettability has significant impact on the droplet dynamic behaviorand final fluid distribution.

Lattice Boltzmann simulation of three-phase flows with moving contact lines on curved surfaces