The interaction of thin elastomeric substrates with viscous flows: From elastohydrodynamic sedimentation to Hele-Shaw flow

Elastic substrates bounding fluid flows are common in many experimental and industrial settings; their principal purpose is usually to drive or suppress the flow of fluid. The deformation of such elastic layers is becoming increasingly recognised, but the model appropriate for describing its deformation depends on how close to incompressible the coating is. While Poisson's ratios of the most frequently used materials are quoted as being in the range 0.49–0.5, the precise value may change the behaviour of the coating and have knock-on consequences. We will present a model for thin, near-incompressible, elastic foundations, and discuss how its behaviour when coupled to flows at low Reynolds numbers can depend sensitively on how incompressible the coating is. We will demonstrate this by considering two concrete problems: the sedimentation of a cylinder in a viscous fluid above a thin elastic foundation and Hele-Shaw flow bounded by an elastic layer, which has recently been shown to exhibit a flow choking instability.