Numerical Simulation of a Falling Ferrofluid Droplet in a Uniform Magnetic Field by the VOSET Method

Abstract

This article presents a two-dimensional numerical simulation of the dynamics of a ferrofluid droplet falling in a non-magnetic fluid under a uniform magnetic field. A new interface tracking method called VOSET (a coupled volume-of-fluid and level set method) is used for capturing the evolution of interface. The Continuum Surface Force (CSF) model is used to model the surface tension force. A linearly magnetizable ferrofluid is assumed, and the magnetic force caused by the jump of magnetic permeability across the interface is incorporated into the Navier-Stokes equation as a body force. The effects of the magnetic Bond number, susceptibility, Weber number, Reynolds number, and magnetic field direction on the motion and deformation of the droplet are investigated. The results show that the increase in magnetic Bond number or susceptibility leads to the larger deformation of the droplet. For a high Weber number, even the formation of a teardrop-like droplet and an oblate elliptical-cap droplet occurs in the vertical and horizontal magnetic fields, respectively.