Abstract
A number of geophysical problems involve a viscous fluid spreading between two elastic materials, a prime example being volcanic intrusions in the Earth’s crust. At the same time, many new engineering applications involve microfluidic devices that deform elastically. The interaction of fluid flow and elastic deformation is therefore of general interest. In this talk I will discuss the seemingly simple problem of injecting a viscous fluid beneath an elastic sheet resting on a rigid substrate. Calculating the spreading rate and the uplift rate are of interest. Using lubrication theory to describe the fluid flow results in a sixth order non-linear diffusion equation for the fluid depth. In common with other such non-linear diffusion problems, behaviour near the fluid edges must be regularized in some way. I will discuss the use of a pre-wetting film, or a fluid lag, and investigate the impact of such regularizations on the solutions to the problem. For the case of two-dimensional injection on a slope, a travelling wave develops, with an intriguing bulbous structure.