A hybrid immersed interface and phase-field-based lattice Boltzmann method for multiphase ferrofluid flow

In this study, we developed a hybrid immersed interface and phase-field lattice Boltzmann (LB) method to simulate multiphase ferrofluid flows. The Laplace equation for the magnetic potential with an interface jump condition was numerically solved using a phase-field-based immersed interface method. The phase interface was tracked by the conservative Allen-Cahn equation. One LB equation was used to capture the interfaces between the two immiscible fluids and another to solve for the hydrodynamic properties. The magnetic stress was treated as an interfacial force at the interface, and thus both the magnetic and capillary forces could be formulated in a unified phase-field method framework. Several typical problems, including a circular cylinder in a uniform magnetic field, deformation of a ferrofluid droplet under a uniform magnetic field, two bubbles merging in the ferrofluid, and a ferrofluid droplet suspension under a shear flow to study the rheological characteristics, were simulated to test the accuracy, applicability, and numerical stability of the present model. The numerical examples demonstrated that the present model is able to capture basic phenomenological features in magnetic multiphase flow problems with high density and high viscosity ratios.