Magnetic control of a two-layer pipe flow

The gap between two solid, coaxial cylinders is filled with two ferrofluids of differing viscosity and magnetic susceptibility. Axial motion is driven by a pressure gradient and/or translation of the inner cylinder. An axial magnetic field is imposed externally, while current flowing in the inner cylinder generates an azimuthal field. It is known that the axisymmetric capillary instability of the cylindrical fluid interface may be controlled either by hydrodynamic shear or magnetic effects, but each of these can give rise to other instabilities, often nonaxisymmetric. This paper investigates the 10-dimensional parameter space to determine when combined action of shear and magnetic effects can provide overall stability, essentially using shear to stabilize the troublesome helical "tearing" mode, while magnetic stresses control the hydrodynamic instability. Stability is easier to obtain when the inner fluid is more magnetic.