Lattice Boltzmann model for ternary fluids with solid particles

On the basis of phase-field theory, we develop a lattice Boltzmann model for ternary fluids containing solid. We develop a modified bounce-back method to describe the interactions between the solid and N-phase (N >= 2) fluids. We derive a wetting boundary condition for three-phase flows from the point of mass conservation and propose a scheme for implementing the wetting condition on curved boundaries. We develop a diffuse interface method to compute the capillary force acting on the moving solid objects at the ternary fluids-sold contact lines. In addition, this model can deal with problems involving high density and viscosity contrasts. The proposed method is examined through several test cases. We test the modified bounce-back scheme, wetting boundary condition, and capillary force model in three different cases, and the numerical results agree well with the analytical solutions. Finally, we apply the model to two three-dimensional problems to assess its numerical accuracy and stability.