Study of deformation of a ferrofluid droplet in simple shear flows under a uniform magnetic field

When a droplet is subjected to simple shear flows, it is deformed by the flow field. Magnetic field provides an additional means of controlling the deformation of ferrofluid droplets. Here, we have performed a thorough numerical investigation on the deformation and orientation of a ferrofluid droplet in a simple shear flow under a uniform magnetic field. Based on the finite element method, our two-dimensional simulation couples the magnetic field with the flow field. A level set method is used to track the dynamic motion of the droplet interface. Focusing on low Reynolds number flows (Re $\le 0.02$), we found that at a small capillary number (Ca $\approx 0.02$), with increasing magnetic field strength, the magnetic field dominates over shear flow and determines the deformation of the droplet. The orientation of the droplet is also found to be aligned with the direction of the magnetic field more as the magnetic field strength is increased. For small capillary number cases, the droplet deformation is found to be maximum at a = 45° (direction of magnetic field relative to the flow) and minimum at a = 135°. Additionally, the flow field inside and outside of the droplet are different due to different magnetic field conditions.