Displacement of a viscous fluid from an annular Hele–Shaw cell with a sink within the framework of the Brinkman model

Abstract

The stability of the radial front of viscous fluid displacement from an annular Hele–Shaw cell with a sink of finite radius is analyzed. It is shown that in the absence of the surface tension and at a minimal manifestation of molecular diffusion the role of the stabilizing factor determining the displacement front structure can be played by small viscous forces in the cell plane. The viscous fingers formed in this case turn out to be wider than those in a rectangular cell.