Capillary-gravity waves generated by a slow moving object

Overcoming Drag at the Water-Air Interface Constrains Body Size in Whirligig Beetles

Whirligig beetles (Coleoptera: Gyrinidae) are among the best swimmers of all aquatic insects. They live mostly at the water’s surface and their capacity to swim fast is key to their survival. We present a minimal model for the viscous and wave drags they face at the water’s surface and compare them to their thrust capacity. The swimming speed accessible is thus derived according to size. An optimal size range for swimming at the water’s surface is observed. These results are in line with the evolutionary trajectories of gyrinids which evolved into lineages whose members are a few milimeter’s long to those with larger-sized genera being tens of millimeters in length. The size of these beetles appears strongly constrained by the fluid mechanical laws ruling locomotion and adaptation to the water-air interface.

Spiral Thermal Waves Generated by Self-Propelled Camphor Boats

Spiral thermal surface waves arising from self-propulsion of the camphor-driven objects are reported. Spiral thermal waves were registered for dissolution and evaporation-guided self-propulsion. Soluto-capillarity is accompanied by thermo-capillarity under self-propulsion of camphor boats. The jump in the surface tension due to the soluto-capillarity is much larger than that due to the thermo-capillarity. The spiral patterns inherent for the surface thermal waves are imposed by the self-rotational motion of camphor grains. The observed thermal effect is related to the adsorption of camphor molecules at the water/vapor interface. The observed spirals are shaped as Archimedean ones.

Space-Time Folding of the Wake Produced by a Supervelocity Rotating Point Source

Wave sources moving faster than the waves they emit create a wake whose topological features are directly related to the geometry of the source trajectory. These features can be understood by considering space-time surfaces representing past emitted wave fronts. Specifically, for a supervelocity source moving along a circular path the space-time envelope folds and a cusp appears on the inner part of the wake. As a result, the wake is ultimately contained within two parallel corotating spiraling branches. In this Letter we take advantage of the low phase speed of water waves to study experimentally supervelocity sources moving at velocities up to several time the wave speed. We image in real time their emission patterns and characterize the topological features of their wakes.

Capillary interactions between dynamically forced particles adsorbed at a planar interface and on a bubble

We investigate the dynamic interfacial deformation induced by micrometric particles exerting a periodic force on a planar interface or on a bubble, and the resulting lateral capillary interactions. Assuming that the deformation of the interface is small, neglecting the effect of viscosity, and assuming point particles, we derive analytical formulas for the dynamic deformation of the interface. For the case of a planar interface the dynamic point force simply generates capillary waves, while for the case of a bubble it excites shape oscillations, with a dominat deformation mode that depends on the bubble radius for a given forcing frequency. We evaluate the lateral capillary force acting between two particles, by superimposing the deformations induced by two point forces. We find that the lateral capillary forces experienced by dynamically forced particles are non monotonic and can be repulsive. The results are applicable to micrometric particles driven by different dynamic forcing mechanisms such as magnetic, electric or acoustic fields.

Design of hair-like appendages and comparative analysis on their coordination toward steady and efficient swimming

The locomotion of water beetles has been widely studied in biology owing to their remarkable swimming skills. Inspired by the oar-like legs of water beetles, designing a robot that swims under the principle of drag-powered propulsion can lead to highly agile mobility. But its motion can easily be discontinuous and jerky due to backward motions (i.e. retraction) of the legs. Here we proposed novel hair-like appendages and consider their coordination to achieve steady and efficient swimming on the water surface. First of all, we propose several design schemes and fabrication methods of the hair-like appendages, which can passively adjust their projected area while obtaining enough thrust. The coordination between the two pairs of legs, as with water beetles in nature, were also investigated to achieve steady swimming without backward movement by varying the beating frequency and phase of the legs. To verify the functionality of the hair-like appendages and their coordinations, six different types of appendages were fabricated, and two robots (one with a single pair of legs and the other with two pairs of legs) were built. Locomotion of the robots was extensively compared through experiments, and it was found that steady swimming was achieved by properly coordinating the two pairs of legs without sacrificing their speed. Also, owing to the lower velocity fluctuation during swimming, it was shown that using two pairs of legs was more energy efficient than the robot with single pair of legs.

Capillary-gravity waves on a liquid film of arbitrary depth: analysis of the wave resistance

We discuss the wave resistance in the case of an externally perturbed viscous liquid film of arbitrary thickness. Emphasis is placed on the dependence of the wave resistance on the film thickness H, the length scale b characterizing the external perturbation, and its velocity V. In particular, the effectiveness of the mechanisms of capillary-gravity waves and the viscous dissipation localized in the vicinity of the perturbation are compared and discussed as functions of H and V. We show that, in general, the wave resistance is a nonmonotonous function of H with a maximum whose amplitude and position depend on b and V. In the case of small H the wave resistance depends on a parameter S proportional V/H(3). We find three different regimes of this parameter in which the wave resistance behaves like S(r) with the exponent r equal to 1, 1/3, and -1. These results are also obtained independently within the thin liquid film approximation. This allows us to assess the range of validity of the thin liquid film approximation in various cases, in particular its dependence on the perturbation length scale b.

Experimental studies and dynamics modeling analysis of the swimming and diving of whirligig beetles (Coleoptera: Gyrinidae)

Whirligig beetles (Coleoptera, Gyrinidae) can fly through the air, swiftly swim on the surface of water, and quickly dive across the air-water interface. The propulsive efficiency of the species is believed to be one of the highest measured for a thrust generating apparatus within the animal kingdom. The goals of this research were to understand the distinctive biological mechanisms that allow the beetles to swim and dive, while searching for potential bio-inspired robotics applications. Through static and dynamic measurements obtained using a combination of microscopy and high-speed imaging, parameters associated with the morphology and beating kinematics of the whirligig beetle's legs in swimming and diving were obtained. Using data obtained from these experiments, dynamics models of both swimming and diving were developed. Through analysis of simulations conducted using these models it was possible to determine several key principles associated with the swimming and diving processes. First, we determined that curved swimming trajectories were more energy efficient than linear trajectories, which explains why they are more often observed in nature. Second, we concluded that the hind legs were able to propel the beetle farther than the middle legs, and also that the hind legs were able to generate a larger angular velocity than the middle legs. However, analysis of circular swimming trajectories showed that the middle legs were important in maintaining stable trajectories, and thus were necessary for steering. Finally, we discovered that in order for the beetle to transition from swimming to diving, the legs must change the plane in which they beat, which provides the force required to alter the tilt angle of the body necessary to break the surface tension of water. We have further examined how the principles learned from this study may be applied to the design of bio-inspired swimming/diving robots.

The whirligig beetles belong to the family Gyrinidae, consisting of over 700 species of water beetles. They are characterized by a divided eye, ellipsoidal body, and rapidly swim in circles when alarmed. Perhaps the most interesting characteristic of whirligig beetles is their ability to rapidly swim on the surface of water, and also to quickly transition to diving beneath the surface. In this study, we have measured the key physical parameters that allow whirligig beetles to swim and dive, and have used these values to develop dynamics models of the swimming and diving processes. Based on these models, we were able to analyze how the beetle is capable of making sharp turns, the efficiency of varying leg beating patterns, and the key parameters involved in swimming, as well as diving. We were then able to identify fundamental principles used by the beetle to transition from swimming to diving, and examine how the morphology and “design” of the beetle leads to its ability to rapidly swim and maneuver. Based on the results obtained, we further identified principles and components of the beetle design that could be translated into the development of bio-inspired robotics.

Self-consistent theory of capillary-gravity-wave generation by small moving objects

We investigate theoretically the onset of capillary-gravity waves created by a small object moving at the water-air interface. It is well established that, for straight uniform motion, no steady waves appear at velocities below the minimum phase velocity c(min)=23 cm/s. At higher velocities, the emission of capillary-gravity waves creates an additional drag force. The behavior of this force near the critical velocity is still poorly understood. A linear-response theory where the object is replaced by an effective pressure source predicts a singular behavior for the wave drag. However, experimental data tend to indicate a more continuous transition. In this paper, we show that a proper treatment of the flow equations around the obstacle can regularize wave emission, even in the linear wave approximation, thereby ensuring a continuous behavior of the drag force.

The management of fluid and wave resistances by whirligig beetles

Whirligig beetles (Coleoptera: Gyrinidae) are semi-aquatic insects with a morphology and propulsion system highly adapted to their life at the air-water interface. When swimming on the water surface, beetles are subject to both fluid resistance and wave resistance. The purpose of this study was to analyse swimming speed, leg kinematics and the capillarity waves produced by whirligig beetles on the water surface in a simple environment. Whirligig beetles of the species Gyrinus substriatus were filmed in a large container, with a high-speed camera. Resistance forces were also estimated. These beetles used three types of leg kinematics, differing in the sequence of leg strokes: two for swimming at low speed and one for swimming at high speed. Four main speed patterns were produced by different combinations of these types of leg kinematics, and the minimum speed for the production of surface waves (23 cm s(-1)) corresponded to an upper limit when beetles used low-speed leg kinematics. Each type of leg kinematics produced characteristic capillarity waves, even if the beetles moved at a speed below 23 cm s(-1). Our results indicate that whirligig beetles use low- and high-speed leg kinematics to avoid maximum drag and swim at speed corresponding to low resistances.