Deformation of a Sheared Magnetic Droplet in a Viscous Fluid (Communications in Computational Physics, 2018)
A fully three-dimensional numerical study of the dynamics and field-induceddeformation of a sheared, superparamagnetic ferrofluid droplet immersed in a Newtonian viscous fluid is presented. The system is a three-dimensional, periodic channelwith top and bottom walls displaced to produce a constant shear rate and with an external, uniform magnetic field perpendicular to the walls. The model consists of theincompressible Navier-Stokes equations with the extra magnetic stress coupled to thestatic Maxwell's equations. The coupled system is solved with unprecedented resolution and accuracy using a fully adaptive, Immersed Boundary Method. For smalldroplet distortions, the numerical results are compared and validated with an asymptotic theory. For moderate and strong applied fields, relative to surface tension, andweak flows a large field-induced droplet deformation is observed. Moreover, it isfound that the droplet distortion in the vorticity direction can be of the same orderas that occurring in the shear plane. This study highlights the importance of the three-dimensional character of a problem of significant relevance to applications, where adispersed magnetic phase is employed to control the rheology of the system.