Laminar Shear in a Ferrofluid: Stability Studies

We consider steady solutions for a planar-Couette magnetic fluid flow under the influence of magnetic fields applied transverse to the flow direction. Keeping a small non-zero value for the spin viscosity, we solve the coupled system for the linear and angular momentum equations. The imposed magnetic fields are time-independent and have a dissipative effect on the flow. However, by considering spatially varying fields, the mid-plane symmetry of the planar Couette flow can be broken. Assuming periodic boundary conditions at the inflow and outflow boundaries of the planar Couette flow in two dimensions, we use COMSOL to solve the coupled equations for velocity and spin. A linear stability analysis shows that slow channel flows can be destabilized by a spatially varying magnetic field and this is corroborated by our numerical calculations. The instability criterion is correlated to the spatial gradient of the applied external field