Deformation of a Ferrofluid Droplet in Simple Shear Flows under Uniform Magnetic Fields

We numerically investigate the deformation and orientation of a ferrofluid droplet in a simple shear flow under a uniform magnetic field. The numerical simulation is based on the finite element method and couples the magnetic and flow fields. A level set method is used to model the dynamic motion of the droplet interface. Systematic numerical simulations are used to assess the effects of the direction and the strength of the magnetic field. Focusing on low Reynolds number flows (Re ≲ 0.02), the numerical results indicate that at a small capillary number (Ca ≈ 0.02), the magnetic field dominates over the shear flow above a certain magnetic bond number (Bom ≈ 3). The orientation of the droplet is aligned with the direction of the magnetic field, while the deformation of the droplet varies slightly when the direction of the magnetic field is varied. On the other hand, for large capillary numbers (Ca ≈ 0.23), the deformation and orientation of the droplet is influenced by both the shear flow and the magnetic field, except for a small magnetic bond number (Bom ≲ 0.2). In both the small and large capillary number cases, the droplet deformation is found to be maximum at α = 45° (the direction of magnetic field) and minimum at α = 135°. In addition, the effect of the magnetic field on the flow field inside and outside the droplet at different conditions is examined. We demonstrate active control of lateral migration of ferrofluid droplets in wall-bounded simple shear flows. The direction of the lateral migration depends on the orientation of the deformed droplets due to uniform magnetic fields at different directions