New insights on boundary layer control using magnetic fluids: a numerical study

Abstract This work investigates the effects of an applied magnetic field on the laminar flow of a ferrofluid over a backward-facing step. Both constitutive equation and global magnetization equation for a ferrofluid are considered. The resulting formulation consists in a coupled magnetic-hydrodynamic problem. Computational simulations are carried out in order to explore the physics of the flow and the consistency of theoretical aspects of our formulation. The unidirectional sudden expansion in a ferrofluid flow is investigated numerically under the perspective of Ferrohydrodynamics in a two-dimensional domain using a Finite Volumes Method. The boundary layer detachment induced by the sudden expansion results in a recirculating zone, which has been extensively studied in purely hydrodynamic problems for a wide range of Reynolds numbers. Similar investigations can be found in literature regarding the sudden expansion under the Magnetohydrodynamics framework, but none considering a colloidal suspension of magnetic particles out of the superparamagnetic regime in the framework of Ferrohydrodynamics. The vorticity-stream function formulation is implemented. Our simulations show a clear coupling between the flow vorticity and the magnetization field. We observe a systematic decay on the length of the recirculating zone as we increase the magnetic parameters of the flow, such as the intensity of the applied field and the volume fraction of particles. The results are discussed from a physical perspective in terms of the dynamical non-dimensional parameters. We argue that the reduction of the recirculating region is a direct consequence of the magnetic torque balancing the action of the torque produced by viscous and inertial forces of the flow. For the limiting case of small Reynolds and magnetic Reynolds numbers, the diffusion of vorticity balances the diffusion of the magnetic torque on the flow. This mechanism controls the growth of the recirculating region.