Viscous flow between soft planar surfaces

Various applications, from drug delivery to bioreactor homeostasis, require precise control of liquid flow rates. Fluid-structure interactions in miniaturized fluidic systems were recently proposed as a novel tool to achieve this goal (Duprat and Stone, Royal Society of Chemistry, 2015). We report a combined experimental, theoretical, and numerical study of pressure-driven radial flow in the narrow gap between a solid wall and a soft polymer membrane. Our experiments indicate that when the applied pressure is relatively small, the flow velocity (and hence flow rate) in the gap scales linearly with pressure. However, above a certain threshold value, the flow rate decreases with increasing applied pressure. This reversal of flow characteristics is due to elastic deformations of the soft membrane. A theory based on low-Reynolds-number lubrication theory and linear elasticity is developed which capture the main physical effects. The theoretical predictions agree qualitatively with the experimental results and quantitatively in certain configurations.