Abstract

The interface between two fluids of differing viscosities can become unstable. This leads to complex pattern formation as the less viscous fluid extrudes into the more viscous fluid forming viscous fingers. We review the mechanism which generates the instability in a rectangular Hele-Shaw cell (where a singular Saffman-Taylor finger is produced). Surface tension is considered in the linear stability analysis as a way to stabilise the instability. We then introduce the use of an elastic membrane as the top boundary of a circular Hele-Shaw cell. This technique delays considerably the onset of the instability. The geometry is modelled through the use of a depth averaged lubrication equation coupled to a set of Foppl-von Karman equations describing the deformation of the elastic membrane.