Magnetic field effects on viscous fingering of a ferrofluid in an anisotropic Hele--Shaw cell

R. Ballou - P. Molho

Laboratoire Louis Néel, CNRS, BP 166, 38042 Grenoble Cedex 9, France

Abstract
When a viscous fluid is pushed into a more viscous one in a Hele--Shaw cell, the interface between the two fluids may become unstable, leading to fingering and ramified patterns. Anisotropy can be introduced by engraving a grid in one plate of the cell, allowing one to obtain dendritic patterns. The use of a ferrofluid as one of the viscous fluid is a way to introduce magnetism in the problem, especially the magnetic field as a control parameter. Magnetic field effects on viscous fingering of ferrofluids have already been studied: in a rectangular Hele--Shaw cell, a magnetic field applied in the cell plane is stabilizing when parallel to the interface between the two fluids and destabilizing when normal to the interface. A magnetic field perpendicular to the plane of a radial Hele--Shaw cell has the same destabilizing effect as the pressure. We have studied the effect of a magnetic field, normal to and in the plane of anisotropic radial Hele--Shaw cells \cite{5}, to characterize the competing effects of hydrodynamics, magnetic field and dipolar energy, and anisotropy. Here we study more precisely the effect of a magnetic field normal to a radial anisotropic Hele--Shaw cell. Figs 8, Refs 9.