Effects of substrate geometry on the hydrodynamics of ciliary propulsion

Previous studies of micron-scale cilia hydrodynamics have only examined cilia embedded in a flat substrate. However, in nature, the substrate of ciliated invertebrates is nontrivially curved. The hydrodynamic effects of substrate curvature on ciliary hydrodynamics are unknown. In this study, ctenophores (comb jellies, the largest animals in the world to locomote via cilia) were selected to investigate the effects of substrate geometry on hydrodynamics. Unlike other ciliated invertebrates, ctenophore cilia are grouped into paddle-like structures (called ctenes), which beat metachronally in rows circumscribing an ovoid body. We reconstructed the beating kinematics of ctenes based on high-speed images and then conducted numerical simulations using an in-house CFD solver. Our results showed that in order to overcome the fluid drag, the sixteen ctenes along the row work collaboratively to maintain a relatively constant thrust force along the direction of motion. Compared to a flat substrate, arranging ctenes on a curved substrate can boost the overall thrust up to 20%. The findings from this study will provide important implication guidance for the design of bio-inspired miniaturized flexible robots swimming in the low-to-intermediate Reynolds number regime.