Taper-induced control of viscous fingering in variable-gap Hele-Shaw flows

Variable-gap Hele-Shaw flows consider viscous fluid displacements resulting from the lifting or squeezing of the upper cell plate, while the lower plate remains at rest. Conventionally, researchers focus on the situation in which the cell plates are perfectly parallel. We study a slightly different version of the problem, where the upper plate is gently inclined so that the plates are no longer parallel. Within this tapered Hele-Shaw cell context we examine how the presence of such a small gap gradient affects the stability properties of the fluid-fluid interface. Linear stability analysis indicates that the existence of the taper offers a simple geometric way to control the development of interfacial fingering instabilities under both lifting and squeeze flow circumstances.