Low-Reynolds-number fluid–structure interactions in a check valve

Check valves are hydraulic elements that allow fluid to flow in only one direction. Flow control is enabled by fluid–structure interactions that link fluid motion to the deformation of a flexible element. This selectively blocks the valve, depending on the direction of the applied pressure drop. The link between pressure, geometry, elasticity, and flow during the closing process, however, is unclear. Using a 3D-printed valve model, we identify the main physical effects and parameters that control the transition from the open to the closed state: flow through the system causes the valve to close at a pressure determined by the flexural rigidity and dimensions of the soft element and the width of the valve aperture. Interestingly, the deformation of the flexible membrane produces an effective rheology reminiscent of non-Newtonian flow. This emergent pressure-dependent resistance captures key features of shear-thickening and yield-stress fluids. To rationalize the experimental data, we develop a mathematical model that reduces the three-dimensional fluid–structure interactions to a coupling between two-dimensional low-Reynolds-number lubrication flow and one-dimensional thin-plate deflections. The theory compared favorably with the experimental data and allows us to identify the main geometric and material control parameters.