Parallel flow in Hele-Shaw cells with ferrofluids

TL;DR

This paper investigates how magnetic fields influence the stability and dynamics of parallel flow interfaces in Hele-Shaw cells containing ferrofluids, revealing magnetic destabilization and soliton interactions.

Contribution

It introduces the effect of magnetic fields on Kelvin-Helmholtz instability in ferrofluid flows within Hele-Shaw cells, highlighting magnetic destabilization mechanisms.

Findings

Magnetic fields can destabilize the interface without inertial effects.

Magnetic fields do not change wave propagation speed at fixed wavenumber.

Magnetic interactions influence soliton behavior.

Abstract

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