Hydraulic Asymmetries for Biological and Bioinspired Valves in Tubular Channels: A Numerical Analysis

Biological, biomimetic, and engineering systems make extensive use of hydraulic asymmetries to control flow inside tubular structures. Examples span physiological valves, the guided transport observed in shark intestines, and passive devices such as Tesla valves. Here we investigate the mechanisms that generate these asymmetries using the notion of diodicity, defined as the ratio between pressure drops required to drive the same flow in opposite directions. We first focus on 2D geometries, which allow us to identify and study the main contributions to hydraulic asymmetry: channel geometry and internal obstacles embedded within a channel with rigid walls. By considering both rigid and deformable obstacles, we model channels that always remain open in both directions and channels that can be completely blocked by valve-like structures. We then extend the analysis to 3D geometries, again considering rigid and elastic cases. As a general trend, we find that geometry alone establishes a baseline diodicity, while higher dimensionality and structural reconfiguration consistently amplify the effect.