An efficient numerical method for simulating multiphase flows using a diffuse interface model

• A new diffuse interface model for multiphase flows is presented.
• Surface tension and buoyancy effects on multiphase flows are studied.
• We employ a new chemical potential that can eliminate spurious phase-field profiles.
• We consider a variable mobility to investigate the effect of the mobility on the fluid dynamics.
• We significantly improve the computational efficiency of the numerical algorithm.

This paper presents a new diffuse interface model for multiphase incompressible immiscible fluid flows with surface tension and buoyancy effects. In the new model, we employ a new chemical potential that can eliminate spurious phases at binary interfaces, and consider a phase-dependent variable mobility to investigate the effect of the mobility on the fluid dynamics. We also significantly improve the computational efficiency of the numerical algorithm by adapting the recently developed scheme for the multiphase-field equation. To illustrate the robustness and accuracy of the diffuse interface model for surface tension- and buoyancy-dominant multi-component fluid flows, we perform numerical experiments, such as equilibrium phase-field profiles, the deformation of drops in shear flow, a pressure field distribution, the efficiency of the proposed scheme, a buoyancy-driven bubble in ambient fluids, and the mixing of a six-component mixture in a gravitational field. The numerical result obtained by the present model and solution algorithm is in good agreement with the analytical solution and, furthermore, we not only remove the spurious phase-field profiles, but also improve the computational efficiency of the numerical solver.