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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. 

Abstract Animals swim in water, fly in air, or dive into water to find mates, chase prey, or escape from predators. Even though these locomotion modes are phenomenologically distinct, we can rationalize the underlying hydrodynamic forces using a unified fluid potential model. First, we review the previously known complex potential of a moving thin plate to describe circulation and pressure around the body. Then, the impact force in diving or thrust force in swimming and flying are evaluated from the potential flow model. For the impact force, we show that the slamming or impact force of various ellipsoid-shaped bodies of animals increases with animal weight, however, the impact pressure does not vary much. For fliers, birds and bats follow a linear correlation between thrust lift force and animal weight. For swimming animals, we present a scaling of swimming speed as a balance of thrust force with drag, which is verified with biological data. Under this framework, three distinct animal behaviors (i.e., swimming, flying, and diving) are similar in that a thin appendage displaces and pressurizes a fluid, but different in regards to the surroundings, being either fully immersed in a fluid or at a fluid interface. 

Seed dispersal through wind was historically considered a random process; however, plants can influence their dispersal through non-random seed detachment or abscission. Dandelion seeds facing the wind tend to abscise before those facing downwind, yet the mechanism that supports this has remained unclear. We measured the force needed for abscission in different directions and performed imaging of the detachment process. This revealed an asymmetry in the seed attachment morphology, which results in massive differences in the abscission force needed relative to the direction. We developed a mechanistic model to explain this directional bias and identified morphological factors that determine the properties of seed abscission. This discovery highlights plant adaptations that shape the seed dispersal profile to enhance reproductive success and can be used to improve population dynamic models of wind-dispersed plants. 

Biological flyers periodically flap their appendages to generate aerodynamic forces. Extensive studies have made significant progress in explaining the physics behind their propulsion in cruising by developing scaling laws of their flight kinematics. Notably Strouhal number (St; ratio of flapping frequency times stroke amplitude to cruising speed) has been found to fall in a narrow range for animal cruising flights. However, St exhibits strong correlation to flight conditions; as such, its universality has been confined to preferred flight conditions. Since the leading-edge vortices (LEV) on flapping appendages generate the majority of propulsive forces, here we take the perspective of LEV circulation maximization, which generalizes the dimensionless vortex formation time to flapping flight. The generalized vortex formation time scales the duration of vorticity injection with the rate of total vorticity growth inside the LEV and the maximum vorticity allowed inside it. By comparing the new scaling with St of previously reported animal cruising flights of 28 species, we show that the generalized vortex formation time is consistent across different animals and cruising locomotion, independent of flight conditions. This finding advances the fundamental principles underlying the complex wing kinematics of biological flyers and highlights a unifying framework for understanding biolocomotion. 

Certain fox species plunge-dive into snow to catch prey (e.g., rodents), a hunting mechanism called mousing. Red and arctic foxes can dive into snow at speeds ranging between 2 and 4 m/s. Such mousing behavior is facilitated by a slim, narrow facial structure. Here, we investigate how foxes dive into snow efficiently by studying the role of skull morphology on impact forces it experiences. In this study, we reproduce the mousing behavior in the lab using three-dimensional (3D) printed fox skulls dropped into fresh snow to quantify the dynamic force of impact. Impact force into snow is modeled using hydrodynamic added mass during the initial impact phase. This approach is based on two key facts: the added mass effect in granular media at high Reynolds numbers and the characteristics of snow as a granular medium. Our results show that the curvature of the snout plays a critical role in determining the impact force, with an inverse relationship. A sharper skull leads to a lower average impact force, which allows foxes to dive head-first into the snow with minimal tissue damage. 

The cuttlebone, a chambered gas-filled structure found in cuttlefish, serves a crucial role in buoyancy control for the animal. This study investigates the motion of liquid-gas interfaces within cuttlebone-inspired artificial channels. The cuttlebone’s unique microstructure, characterized by chambers divided by vertical pillars, exhibits interesting fluid dynamics at small scales while pumping water in and out. Various channels were fabricated with distinct geometries, mimicking cuttlebone features, and subjected to different pressure drops. The behavior of the liquid-gas interface was explored, revealing that channels with pronounced waviness facilitated more non-uniform air-water interfaces. Here, Lyapunov exponents were employed to characterize interface separation, and they indicated more differential motions with increased pressure drops. Channels with greater waviness and amplitude exhibited higher Lyapunov exponents, while straighter channels exhibited slower separation. This is potentially aligned with cuttlefish’s natural adaptation to efficient water transport near the membrane, where more straight channels are observed in real cuttlebone. 

Water stuck in the ear is a common problem during showering, swimming or other water activities. Having water trapped in the ear canal for a long time can lead to ear infections and possibly result in hearing loss. A common strategy for emptying water from the ear canal is to shake the head, where high acceleration helps remove the water. In this present study, we rationalize the underlying mechanism of water ejection/removal from the ear canal by performing experiments and developing a stability theory. From the experiments, we measure the critical acceleration to remove the trapped water inside different sizes of canals. Our theoretical model, modified from the Rayleigh–Taylor instability, can explain the critical acceleration observed in experiments, which strongly depends on the radius of the ear canal. The resulting critical acceleration tends to increase, especially in smaller ear canals, which indicates that shaking heads for water removal can be more laborious and potentially threatening to children due to their small size of the ear canal compared with adults.