Effect of substrate rigidity and temporal asymmetry on the force production of a bioinspired flexible paddle at intermediate Reynolds number*

Flexibility is one of the key factors that enhances the performance and efficiency of animal swimming relative to rigid analogues. Often, flexible biological appendages (e.g. fins, legs, pleopods, cilia, flagella) protrude from a larger body wall or substrate; the proximity and relative geometry of this substrate can affect the flow generated by protruding appendages as they row or flap. However, previous work in both numerical and laboratory experiments has often assumed that biological propulsors are embedded in a rigid, flat surface, neglecting any hydrodynamic contribution due to the substrate's flexibility and curvature. To address this missing link, we attach a flexible paddle to a servomotor whose shaft is adjacent and parallel to a substrate that extends far beyond the edges of the paddle. Inspired by the paddle-like appendages (ctenes) of ctenophores, as well as the pleopods of crustaceans, we oscillate the paddle next to the substrate with glycerol as a working fluid, achieving Reynolds number on the order of 100. This oscillation ranges from highly temporally asymmetric (with a fast power stroke and a slow recovery stroke), to temporally symmetric (power stroke and recovery stroke are nearly identical in duration). Using Particle Image Velocimetry, we evaluate the velocity and pressure field of the generated flow to calculate the thrust and lift produced by the paddle under three different substrate conditions (rigid, flexible, and no substrate). In general, the presence of any substrate leads to a higher lift coefficient; thrust generation is dependent on both substrate condition and temporal asymmetry. These findings emphasize the importance of the potential contribution of substrate or body in biologically generated flows, as well as in bioinspired applications.