Ferro-hydrodynamic interactions between ferrofluid droplet pairs in simple shear flows

Abstract

A numerical investigation on the interactions between a pair of equal-sized ferrofluid droplets in a simple shear flow subjected to uniform magnetic fields is carried out in this paper. Our numerical model utilizes a finite element method based level set algorithm to trace the topological changes along the droplet interface in two phase flows by coupling the flow and magnetic fields. Systematic numerical simulations with a well-resolved droplet interface are carried out in the Stokes flow limit (i.e., Re=0.03) to explore the effects of magnetic field direction, strength, and initial vertical offset on the pairwise interactions between the droplets. The findings indicate that in a solitary shear flow, a critical capillary number Cacr exists, beyond which the droplets exhibit separation through a sliding-over motion, instead of coalescence. Applying a uniform magnetic field along α=0° (i.e., parallel to the flow direction) results in a faster coalescence between the droplets. At α=90°, a critical magnetic bond number Bocr appears where the droplets show a reversing motion behavior, instead of a passing-over motion leading to coalescence. In contrast, at α=45°, the droplets separate away from each other, following a reversal motion at a capillary number where the droplets usually coalesce with each other in a solitary shear flow. Moreover, the effect of initial vertical offset on the interaction behavior of the droplets is examined, and it is found that the collision event is dependent on the initial vertical separation distance between the droplets. Increasing the vertical separation distance along α=0° initiates faster coalescence, while at α=90°, coalescence is delayed. Furthermore, at α=45°, the droplets undergo a reversing motion and experience larger migration at increased vertical separation distances.