  A numerical method for simulating three-phase flows with moving contact lines
on arbitrarily complex surfaces is developed in the framework of lattice
Boltzmann method. In this method, the immiscible three-phase flow is modeled
through a multiple-relaxation-time color-gradient model, which not only allows
for a full range of interfacial tensions but also produces stable outcomes for
a wide range of viscosity ratios. A characteristic line model is introduced to
implement the wetting boundary condition, which is not only easy to implement
but also able to handle arbitrarily complex boundaries with prescribed contact
angles. The developed method is first validated by the simulation of a Janus
droplet resting on a flat surface, a perfect Janus droplet deposited on a
cylinder, and the capillary intrusion of ternary fluids for various viscosity
ratios. It is then used to study a compound droplet subject to a uniform
incoming flow passing through a multi-pillar structure, where three different
values of surface wettability are considered. The simulated results show that
the surface wettability has significant impact on the droplet dynamic behavior
and final fluid distribution.
