Propulsion of the Water Flea, Daphnia magna: Experiments, Scaling, and Modelling

The freshwater crustacean Daphnia magna is a widely studied zooplankton in relation to food webs, predator-prey interactions, and other biological/ecological considerations; however, their locomotion is poorly quantified and understood. These water fleas utilize a hop-and-sink mechanism that consists of making quick, impulsive jumps by beating their antennae to propel themselves forward (~1 body length). The animals then sink for a period, during which they stretch out their antennae to increase drag and thereby reduce their sinking velocity. Time-resolved three-dimensional flow fields surrounding the animals were quantified with a unique infrared tomographic particle image velocity (tomo-PIV) system. Three-dimensional kinematics data were also extracted from the image sequences. In the current work, we compared body kinematics and flow disturbance among organisms of size in the range of 1.3 to 2.8 mm. The stroke cycle averaged 150 ms in duration, ranging from 100 to 180 ms; this period is generally evenly split between the power and recovery strokes. The range of peak hop velocity was 27.2 to 32.5 mm/s, and peak acceleration was in the range of 0.68 to 1.8 m/s². The results showed a distinct relationship between peak hop speed (V_max ~ 14 BL/s) and body size; these data collapsed onto a single time-record curve during the power stroke when properly non-dimensionalized. The fluid flow induced by each antennae consisted of a viscous vortex ring that demonstrated a slow decay in the wake. The strength, size, and decay of the induced viscous vortex rings were compared as a function of organism size. Finally, the viscous vortex rings were analyzed in the context of a double Stokeslet model that consisted of two impulsively applied point forces separated by the animal width.