Fluid-structure interactions suppress flow in self-overlapping soft tubes

Fluid flow in flexible pipes is ubiquitous in nature. It is well-established that the deformation of individual soft channels impacts flow quantity and quality in, e.g., the human cardiovascular system. In some critical cases, however, flow occurs in a self-overlapping channel that loops back onto itself. This is the case, for instance, in an animal placenta, kidney, finger, lung, or in the coupled xylem-phloem vascular tissue in plants. However, the effects of self-interactions on fluid transport capacity remains poorly understood. Inspired by the Quake valve, we study the pressure drop versus flow rate relationship in a multilayer microfluidic device that contains two linked channels separated by an elastic sheet. The application of pressure modifies both channel geometries and the total flow capacity. We show that fluid-structure interactions suppress flow and examine the dependence on geometric and material parameters. Surprisingly, short self-overlapping channels are particularly vulnerable to this effect. Finally, potential implications for small organs, limbs, and tissue protrusions are discussed.