A unified lattice Boltzmann model for immiscible and miscible ternary fluids

Abstract

Based on the phase-field theory, we develop a unified lattice Boltzmann model for ternary flow, in which the miscibility between the three fluid components can be adjusted independently. Based on a modified free energy function, we derive the conservative phase-field equations using the gradient flow method. A generalized continuous surface tension force formulation is deduced by using the virtual work method. The wetting boundary condition is derived based on mass conservation law. The proposed model for ternary fluids is consistent with the binary-fluid models in the absence of one fluid. A lattice Boltzmann (LB) model is developed to solve the phase-field equations and hydrodynamic equations, and this model can deal with problems involving high density and viscosity contrasts. The proposed method is examined through several test cases. A layered Poiseuille flow and droplet coalescence problems are carried out to validate the present LB model. Several dynamic problems in ternary fluid problems involving a solid are simulated, including the wetting of two droplets on a circular cylinder and impacting of a multiphase droplet on a fixed particle. Finally, we apply the model to a three-dimensional multi-bubbles rising problem to access its numerical accuracy and stability.