Viscoplastic Blisters

The spreading of a viscous fluid injected between a thin sheet and an underlying rigid plane has been well explored for the case of an elastic sheet. In this talk we modify this problem to consider viscous flow underneath a thin sheet of viscoplastic fluid described by a Herschel-Bulkley constitutive law. We assume a large effective viscosity contrast between the sheet and the underlying viscous fluid such that the sheet is described by the viscoplastic counterpart of the Föppl-von Kármán plate model of solid mechanics. The dynamics of the flow is controlled by a boundary layer at the fluid front whereby the sheet is lifted off the underlying plane by the advancing fluid. By imposing a pre-wetted film between the sheet and the underlying rigid plane, we explore solutions when the sheet has a Bingham rheology influenced by bending forces. These results provide insight into a number of industrial and geophysical problems.