Phase-field-based lattice Boltzmann model for ternary fluid flows considering the wettability effect

Abstract

A phase-field-based lattice Boltzmann model for ternary fluid flows is proposed, where the conservative Allen-Cahn equation for ternary fluids is used to track the interface of fluids. A time derivative term is introduced into the lattice Boltzmann equation for the conservative Allen-Cahn equation and a forcing distribution function is used in the lattice Boltzmann equation for the Navier-Stokes equations. The computational accuracy and capability of the proposed model are verified by benchmark cases related to stationary droplets, spreading of a liquid lens, and phase separation of a ternary fluid mixture. Moreover, a wetting boundary scheme based on the framework of the lattice Boltzmann method applicable to ternary fluid flows is developed. This model performs well in eliminating the undesired numerical artifact after consideration of the wettability effect. Typical wettability problems are simulated to verify the applicability of the wetting boundary scheme, including the spreading of binary droplets and compound droplets on a surface. The numerical results for static contact angles and spreading length show a good fit of the data to the theoretical results within the scope of permissible error. Furthermore, the reliability of this wetting boundary condition for the dynamic case is verified by our modeling the motion of compound droplets subjected to shear flow on a substrate. This boundary scheme performs well for the motion of ternary fluids with a small density ratio and a large density ratio. In conclusion, the phase-field-based lattice Boltzmann model for ternary fluid flows considering the wetting effect has good applicability for modeling ternary fluid flows with a density ratio of 1000.