Stability of layered channel flow of magnetic fluids

Abstract

The stability of a sheared interface separating a viscous magnetic fluid (ferrofluid) and an ordinary viscous fluid is examined for arbitrary wavelength disturbances using three dimensional linear perturbation theory. The unperturbed state corresponds to a two-layer Poiseuille profile in which a uniform magnetic field of arbitrary orientation is imposed. Coupling between the field and fluid occurs via the magnetic Maxwell stress tensor, formulated here for nonlinear magnetic material, expanding the scope of previous studies of linear media. Neutral curves and stability characteristics at low Reynolds number are presented and analyzed, and are found to depend sensitively on the linear and nonlinear magnetic properties of the material. The stability properties of the flow are shaped by a small set of the least stable modes of the spectrum, a result that evades single mode or potential flow analyses. The gravest modes can be of different character, resembling either interfacial or shear modes, modified by magnetic effects. The commonly cited ferrofluid interface properties of “stabilization by a tangential field” and “destabilization by a normal field” are shown to be invalid here, although the origins of these features can be identified within this problem.