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

Abstract

Introduction. 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 [1]. Anisotropy can be introduced by engraving a grid in one plate of the cell [2], 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 [3]. A magnetic field perpendicular to the plane of a radial Hele– Shaw cell has the same destabilizing effect as the pressure [4]. We have studied the effect of a magnetic field, normal to and in the plane of anisotropic radial Hele– Shaw cells [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.