We investigate the flow of two immiscible, viscous fluids in the confined geometry of a Hele-Shaw cell. We consider that one of the fluids is a ferrofluid and that an external magnetic field is applied. The interfacial instabilities which arise between the fluids are studied for various situations: (a) different cell geometries (radial, rectangular); (b) frontal and parallel flows; (c) distinct applied field configurations (tangential, perpendicular, normal) and (d) motionless and rotating cells. The interplay between applied magnetic field and several other destabilizing/stabilizing factors in determining the interface behavior is analyzed. Stability analysis and numerical simulations are used to describe linear and nonlinear stages of the interface evolution.
