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Free surface flows driven by boundary undulations are observed in many biological phenomena, including the feeding and locomotion of water snails. To simulate the feeding strategy of apple snails, we develop a centimetric robotic undulator that drives a thin viscous film of liquid with the wave speed$$V_w$$. Our experimental results demonstrate that the behaviour of the net fluid flux$$Q$$strongly depends on the Reynolds number$$Re$$. Specifically, in the limit of vanishing$$Re$$, we observe that$$Q$$varies non-monotonically with$$V_w$$, which has been successfully rationalised by Pandeyet al.(Nat. Commun., vol. 14, no. 1, 2023, p. 7735) with the lubrication model. By contrast, in the regime of finite inertia ($${Re} \sim O(1)$$), the fluid flux continues to increase with$$V_w$$and completely deviates from the prediction of lubrication theory. To explain the inertia-enhanced pumping rate, we build a thin-film, two-dimensional model via the asymptotic expansion in which we linearise the effects of inertia. Our model results match the experimental data with no fitting parameters and also show the connection to the corresponding free surface shapes$$h_2$$. Going beyond the experimental data, we derive analytical expressions of$$Q$$and$$h_2$$, which allow us to decouple the effects of inertia, gravity, viscosity and surface tension on free surface pumping over a wide range of parameter space. 

Abstract Examples of fluid flows driven by undulating boundaries are found in nature across many different length scales. Even though different driving mechanisms have evolved in distinct environments, they perform essentially the same function: directional transport of liquid. Nature-inspired strategies have been adopted in engineered devices to manipulate and direct flow. Here, we demonstrate how an undulating boundary generates large-scale pumping of a thin liquid near the liquid-air interface. Two dimensional traveling waves on the undulator, a canonical strategy to transport fluid at low Reynolds numbers, surprisingly lead to flow rates that depend non-monotonically on the wave speed. Through an asymptotic analysis of the thin-film equations that account for gravity and surface tension, we predict the observed optimal speed that maximizes pumping. Our findings reveal how proximity to free surfaces, which ensure lower energy dissipation, can be leveraged to achieve directional transport of liquids. 

Synopsis Metachronal motion is used across a wide range of organisms for a diverse set of functions. However, despite its ubiquity, analysis of this behavior has been difficult to generalize across systems. Here we provide an overview of known commonalities and differences between systems that use metachrony to generate fluid flow. We also discuss strategies for standardizing terminology and defining future investigative directions that are analogous to other established subfields of biomechanics. Finally, we outline key challenges that are common to many metachronal systems, opportunities that have arisen due to the advent of new technology (both experimental and computational), and next steps for community development and collaboration across the nascent network of metachronal researchers. 

The means by which aquatic animals such as freshwater snails collect food particles distributed on the water surface are of great interest for understanding life at the air–water interface. The apple snail Pomacea canaliculata stabilizes itself just below the air–water interface and manipulates its foot such that it forms a cone-shaped funnel into which an inhalant current is generated, thereby drawing food particles into the funnel to be ingested. We measured the velocity of this feeding current and tracked the trajectories of food particles around and on the snail. Our experiments indicated that the particles were collected via the free surface flow generated by the snail’s undulating foot. The findings were interpreted using a simple model based on lubrication theory, which considered several plausible mechanisms depending on the relative importance of hydrostatic pressure, capillary action and rhythmic surface undulation. 

We consider efficient controls for swimming with multiple rigid legs at low Reynolds number. We derive equations governing the translation and rotation of a general class of multi-legged swimmers, and we formulate energy-efficient controls of symmetric swimmers as a problem in geometric control theory. We then focus on the case of symmetric swimmers with multi pairs of legs. In the framework of sub-Riemannian geometry, abnormal geodescics are analyzed and shown to depend on the number of pairs of legs. Inspired by larval copepods possessing three pairs of legs, we compute various swimming strokes and explore optimal controls in that specific situation. We also compare our results to experimental measurements of larval copepod.