Hydrodynamics of Metachronal Motion: Effects of Spatial Asymmetry on the Flow Interaction Between Adjacent Appendages

Abstract

Metachronal motion is a unique swimming strategy widely adopted by many small animals on the scale of microns up to several centimeters (e.g., ctenophores, copepods, krill, and shrimp). During propulsion, each evenly spaced appendage performs a propulsive stroke sequentially with a constant phaselag from its neighbor, forming a metachronal wave. To produce net thrust in the low-to-intermediate Reynolds number regime, where viscous forces are dominant, the beat cycle of a metachronal appendage must present significant spatial asymmetry between the power and recovery stroke. As the Reynolds number increases, the beat cycle is observed to change from high spatial asymmetry to lower spatial asymmetry. However, it is still unclear how the magnitude of spatial asymmetry can modify the shear layers near the tip of appendages and thus affect its associated hydrodynamic performance. In this study, ctenophores are used to investigate the hydrodynamics of multiple appendages performing a metachronal wave. Ctenophores swim using paddle-like ciliary structures (i.e., ctenes), which beat metachronally in rows circumscribing an ovoid body. Based on high-speed video recordings, we reconstruct the metachronal wave of ctenes for both a lower spatial asymmetry case and a higher spatial asymmetry case. An in-house immersed-boundary-method-based computational fluid dynamics solver is used to simulate the flow field and associated hydrodynamic performance. Our simulation results aim to provide fundamental fluid dynamic principles for guiding the design of bio-inspired miniaturized flexible robots swimming in the low-to-intermediate Reynolds number regime.

Going around the bend to understand the role of leg coalescence in metachronal swimming

“…The overall instantaneous force patterns during a beat are consistent with data obtained with our previous krill analog (Santos et al, 2023), but the contrast between the power and recovery strokes is stronger because we accounted for pleopod asymmetrical bending. By maximizing the thrust to drag ratio via spatial asymmetry between the power and recovery phases, shrimp can effectively overcome the resisting appendage and body drag to achieve propulsion (Byron et al, 2021;Herrera-Amaya and Byron, 2023;Lou et al, 2022;Vogel, 2020). Producing less overall drag during the recovery phase reduces the power needed to actuate the pleopod, thus promoting economical swimming and potentially lowering the cost of transport (COT) (Lionetti et al, 2023).…”

“…The induced wake travels in the opposite direction of the metachronal wave and can interact constructively with the downstream appendages to further enhance thrust (Ford and Santhanakrishnan, 2021;Garayev and Murphy, 2021). These mechanisms are particularly sensitive to appendage synchronicity (i.e., phase) and spacing (Alben et al, 2010;Ford and Santhanakrishnan, 2021;Ford et al, 2019;Garayev and Murphy, 2021) for which most metachronal swimmers fall within a narrow range (reviewed in (Byron et al, 2021) Metachronal appendages must also achieve significant spatial or temporal asymmetry between the power and recovery strokes to maximize thrust production (Herrera-Amaya and Lou et al, 2022).…”

“…At large scales, crustaceans have complex biramous swimming legs (pleopods) and fine setae that open and close during the power and recovery phases, respectively. Recent studies have highlighted the effect of dynamically modulating the effective surface area of the propulsors (the projected area perpendicular to the flow) in producing spatial asymmetry between the power and recovery strokes (Byron et al, 2021;Herrera-Amaya and Byron, 2023;Lou et al, 2022;Vogel, 2020). While this has been shown to effectively overcome both the resisting body drag and the drag on the appendages to achieve propulsion, the role of bending has yet to be evaluated.…”