Parallel flow in Hele-Shaw cells with ferrofluids

Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow w ith relative velocity parallel to the interface between them. The interface is unstable due to a Kelvin-Helmholtz type of instability in which fluid f low couples with inertial effects to cause an initial small perturbation to grow. Large amplitude disturbances form stable solitons. We consider the e ffects of applied magnetic fields when one of the two fluids is a ferroflui d. The dispersion relation governing mode growth is modified so that the ma gnetic held can destabilize the interface even in the absence of inertial e ffects. However, the magnetic field does not affect the speed of wave propo gation for a given wave number. We note that the magnetic field creates an effective interaction between the solitons.