Effect of normal and parallel magnetic fields on the stability of interfacial flows of magnetic fluids in channels

Abstract

The effect of an imposed magnetic field on the linear stability of immiscible two-fluid Poiseuille flow in a channel is examined for low Reynolds numbers. Surface tension acts on the interface, the fluids have different densities and viscosities, and one fluid is magnetic (ferrofluid). A Langevin function is used to model the fluid magnetization, resulting in a nonlinear permeability; the stability properties depend on this permeability relation both directly and indirectly, through the base state solution. Uniform magnetic fields applied normal or parallel to the interface both lead to an interfacial instability. Normal fields excite longer wavelength modes, generally having higher growth rates, but parallel fields can excite faster growing modes in high permeability fluids at large applied field strength. Whether or not the field stabilizes or destabilizes the flow depends on the viscosity and layer thickness ratios in a simple way, while the placement of the magnetic fluid layer does not play a major role. Growth rates predicted for realistic microchannel conditions are shown to be large enough to make ferrofluid manipulation a practical method of control.