Viscous flows with thin, compliant boundaries

Viscous fluids flowing in channels with solid, but compliant, boundaries are common in a range of biological and industrial settings. The presence of flexibility can qualitatively alter the behaviour of such systems, forcing us to revisit basic principles with which such viscous flows are usually understood: the reversibility of Stokes flow no longer holds and the relationship between flux and driving pressure may be nonlinear. In other situations, the mere presence of boundary compliance, combined with capillarity is enough to spontaneously generate fluid motion. I will give examples of some of these unusual behaviours, focussing on situations in which the compliant boundary is in some sense thin, as well as discussing the validity of the different models of boundary deformation.