Motion, deformation, and coalescence of ferrofluid droplets subjected to a uniform magnetic field

Abstract

In this article, we present the motion, deformation, and coalescence of ferrofluid droplets suspended in a nonmagnetic fluid, subjected to a uniform magnetic field in both vertical and horizontal directions. A coupling between the simplified multiphase lattice Boltzmann method and the self-correcting scheme is constructed to numerically solve the two-dimensional flow field and the magnetostatics equations, respectively. The Cahn-Hilliard equation is employed to seize the diffuse interface between magnetic and nonmagnetic fluids. In order to validate the model, deformation of a ferrofluid droplet suspended in nonmagnetic fluid is simulated as a test case and the results are compared with numerical and experimental results. Furthermore, a detailed analysis on the behavior of falling ferrofluid droplets and the coalescence between a pair of ferrofluid droplets under the effect of different magnetic fields and different droplets configurations are also presented in this article. The results provide significant insight and a better understanding of these phenomena. It is found that for higher values of magnetic bond number and susceptibility, the droplet deformation is significant and the falling process is faster while a reverse behavior is observed for higher values of Eötvös number. Moreover, the magnetic energy density exhibits an interesting behavior in the vicinity of the droplets. It is concentrated between the droplets with a nonuniform distribution when the droplets are close to each other.