Hydrodynamics of metachronal paddling in crustaceans

Long-tailed crustaceans such as crayfish and krill swim by rhythmically paddling a set of four to five limbs (swimmerets) originating from their abdomen. Despite variations in limb size and stroke frequency, movements of ipsilateral limbs always maintain a tail-to-head metachronal rhythm with an approximate quarter-period inter-limb phase difference. Relatively few studies have examined the fluid dynamics of metachronal limb stroke for the range of Reynolds numbers at which crustaceans operate. The objective of this study is to investigate metachronal paddling as a function of Reynolds number (Re) for quantifying hydrodynamic scalability of this swimming mechanism, including the effect of hinges on paddles as seen in crustacean swimmerets. Our approach included experiments on a scaled physical model and computational fluid dynamics (CFD) simulations using the immersed boundary (IB) method. The scaled robotic model of metachronal paddling consisted of a rectangular aquarium tank fitted above with four stepper motors coupled to a four-bar linkage that actuated four acrylic paddles immersed in water-glycerin fluid medium. 2D particle image velocimetry (PIV) was used for quantitative flow visualization in the experiments. The swimmerets were modeled in CFD simulations as rigid 1D rods in a 2D fluid. The inter-limb phase difference was varied from 0% (synchronous paddling) through 50% across Re range of O(10-1000). Two types of experimental limb models were tested, including a simple flat plate and a ‘split-paddle’ structure with two flat plates connected halfway with hinges. Our results show that the natural tail-to-head metachronal rhythm with an approximate quarter-period phase difference is the most effective and efficient rhythm across a wide range of Reynolds numbers. Limb models with hinges generated increased horizontal flow compared to the simple flat plate paddles, suggesting that asymmetry between power and return stroke is important to augment thrust.