Field-induced control of the breakup of ferrofluid droplets in planar extensional and simple shear flows

This study investigates the breakup of ferrofluid droplets in both planar extensional and simple shear flows under the influence of external magnetic fields. Using a three-dimensional model, we analyze the impact of the external field configuration on the minimum strain rate required to induce droplet breakup, covering a wide range of droplet-to-ambient liquid viscosity ratios. The methodology involves solving the incompressible Navier–Stokes equations augmented by capillary and magnetic terms, Maxwell's equations at the magnetostatic limit, and an evolution equation for the level set function used to capture the droplet interface. In planar extensional flows, we find that magnetic fields applied in the extension direction facilitate droplet breakup, while fields in the compression and neutral directions have the opposite effect. In simple shear flows, we find that magnetic fields applied in either the velocity or vorticity directions prevent droplet breakup. In contrast, we find that magnetic fields applied in the velocity gradient direction induce droplet breakup. Importantly, we show that magnetic fields in the velocity gradient direction can be used to break very viscous droplets, highlighting a strong contrast with the standard case of purely viscous droplets well established in the literature. As importantly, we report a unique tumbling-like dynamics for high viscosity droplets with S- and N-like shapes that periodically return to the initial spherical shape, further underscoring the complex coupling between viscous, capillary, and magnetic effects in magnetic multiphase systems.