Phase field-lattice Boltzmann model for axisymmetric two-phase ferrofluid flows

In this paper, a phase field-based lattice Boltzmann model is developed to simulate axisymmetric two-phase ferrofluid flows. The three-population multi-relaxation time lattice Boltzmann models are constructed to solve the conservative Allen-Cahn phase field equation, the velocity-based Navier-Stokes equations, and the magnetic scalar potential equation. To deal with axisymmetric effects, some appropriate equilibrium distribution functions and discrete source/forcing terms are given. The Chapman-Enskog analysis is used to show the consistencies between the present newly proposed multi-relaxation time flow field lattice Boltzmann model and macroscopic governing equations. In the numerical validation section, the Laplace law and a sphere in a uniform magnetic field were simulated, which the simulation results show good agreement with the analytical solutions. Then several typical problems such as ferrofluid droplet deformation, Rayleigh–Plateau instability, two bubbles merging and bubble rising in ferrofluids are numerically studied to explore the mechanism of phase field interface dynamics in two-phase ferrofluid flows. As the density ratio between the two phases ranges from 1.975 to 1000, and the dynamic viscosity ratio ranges from 1 to 200, the numerical simulation results are satisfactory. This indicates that the proposed model can effectively deal with complex two-phase ferrofluid flows with large density and viscosity ratios.