A new capillary force model implemented in lattice Boltzmann method for gas-liquid-solid three-phase flows

A lattice Boltzmann method is developed for the direct numerical simulation of gas, liquid, and solid three-phase flows. The liquid-gas two-phase flow with a high density ratio is solved using a phase-field model where the interface evolution is described by the conservative Allen-Cahn equation, and the dynamics of the solid particle is captured by the momentum exchange method. By distributing the surface tension over the entire diffuse interface, a new model is proposed to account for the capillary force exerted on the particle, which not only is suited for curved boundaries but can also be implemented in a simple and accurate manner. Several typical benchmark cases, including the wetting behavior of a particle on the liquid-gas interface, a bubble adhering to a particle that can move freely, and the sinking of a horizontal cylinder through an air-water interface, are used to validate the present method. Results show the necessity to incorporate the capillary force on the contact lines, especially when the surface tension is a dominant factor, and that the new capillary force model is able to calculate the capillary force accurately and suppress the oscillations of the capillary force. In addition, the capability of the present method for particle interactions is further demonstrated by studying the self-assembling behavior of three hydrophilic particles on a liquid-gas interface.