Viscous fingering patterns in ferrofluids

TL;DR

This paper investigates how magnetic fields influence viscous fingering patterns in ferrofluids within a Hele-Shaw cell, revealing magnetic effects on pattern complexity and interface asymmetry through a mode-coupling analysis.

Contribution

It introduces a perturbative mode-coupling analysis to study magnetic effects on viscous fingering in ferrofluids, highlighting magnetic repulsion's role in finger tip-splitting.

Findings

Viscosity contrast causes interface asymmetry independent of magnetic forces.

Magnetic repulsion induces finger tip-splitting in ferrofluids.

Magnetic effects lead to complex labyrinthine patterns in viscous fingering.

Abstract

Viscous fingering occurs in the flow of two immiscible, viscous fluids between the plates of a Hele-Shaw cell. Due to pressure gradients or gravity, the initially planar interface separating the two fluids undergoes a Saffman-Taylor instability and develops finger-like structures. When one of the fluids is a ferrofluid and a perpendicular magnetic field is applied, the labyrinthine instability supplements the usual viscous fingering instability, resulting in visually striking, complex patterns. We consider this problem in a rectangular flow geometry using a perturbative mode-coupling analysis. We deduce two general results: viscosity contrast between the fluids drives interface asymmetry, with no contribution from magnetic forces; magnetic repulsion within the ferrofluid generates finger tip-splitting, which is absent in the rectangular geometry for ordinary fluids.