Phase-field-based lattice Boltzmann model for multiphase ferrofluid flows

In this work, the phase-field-based lattice Boltzmann model is extended to simulate the multiphase ferrofluid flows. The hydrodynamical behavior of the ferrofluids is modeled by the incompressible Navier-Stokes equations with the nonlinear Langevin magnetization law. The phase interface is tracked by the conservative Allen-Cahn equation. A modified magnetic potential equation is used to describe the magnetic field. All governing equations are solved by the lattice Boltzmann method. Several typical problems, including a circular cylinder in a uniform applied magnetic field, deformation of a ferrofluid droplet under a uniform applied magnetic field, bubble merging in ferrofluid under a uniform applied magnetic field, and ferrofluid droplets moving and merging on a flat surface in the presence of a permanent magnet, are simulated to test the accuracy and numerical stability of the present model. The computations are performed in the range of density ratios from 1.975 to 850.7 and viscosity ratios from 20 to 279.3. Some basic phenomenological features of multiphase ferrofluid flows are captured.