Numerical investigation of magnetic multiphase flows by the fractional-step-based multiphase lattice Boltzmann method

In the present study, a fractional-step-based multiphase lattice Boltzmann (LB) method coupled with a solution of a magnetic field evolution is developed to predict the interface behavior in magnetic multiphase flows. The incompressible Navier-Stokes equations are utilized for the flow field, while the Cahn-Hilliard equation is adopted to track the interface, and these governing equations are solved by reconstructing solutions within the LB framework with the prediction-correction step based on a fractional-step method. The proposed numerical model inherits the excellent performance of kinetic theory from the LB method and integrates the good numerical stability from the fractional-step method. Meanwhile, the macroscopic variables can be simply and directly calculated by the equilibrium distribution functions, which saves the virtual memories and simplifies the computational process. The proposed numerical model is validated by simulating two problems, i.e., a bubble rising with a density ratio of 1000 and a viscosity ratio of 100 and a stationary circular cylinder under an external uniform magnetic field. The interfacial deformations of a ferrofluid droplet in organic oil and an aqueous droplet in ferrofluid under the external magnetic field are, then, simulated, and the underlying mechanisms are discussed. Moreover, the rising process of a gas bubble in the ferrofluid is investigated, which shows that the rising velocity is accelerated under the effect of the external magnetic field. All the numerical examples demonstrate the capability of the present numerical method to handle the problem with the interfacial deformation in magnetic multiphase flows.