Magnetic fluid in a time-dependent gap Hele–Shaw cell

Abstract

The traditional Saffman–Taylor problem addresses the flow of non-magnetic fluids in a fixed gap Hele–Shaw cell. Under such circumstances interfacial singularities arise if the surface tension between the fluids is zero. In this work, we study a variant of this interesting hydrodynamic situation and consider the flow of a magnetic fluid in a Hele–Shaw cell with a time-dependent gap spacing. We focus on the zero surface tension limit and investigate the possibility of controlling interfacial singularities with an appropriate magnetic field. Our analytical mode-coupling approach shows evidence that the action of an azimuthal magnetic field and plus the inclusion of stresses originated from normal velocity gradients conspire to singularity inhibition.