How body torque and Strouhal number change with swimming speed and developmental stage in larval zebrafish

Small undulatory swimmers such as larval zebrafish experience both inertial and viscous forces, the relative importance of which is indicated by the Reynolds number (Re). Re is proportional to swimming speed (v_swim) and body length; faster swimming reduces the relative effect of viscous forces. Compared with adults, larval fish experience relatively high (mainly viscous) drag during cyclic swimming. To enhance thrust to an equally high level, they must employ a high product of tail-beat frequency and (peak-to-peak) amplitude fA_tail, resulting in a relatively high fA_tail/v_swim ratio (Strouhal number, St), and implying relatively high lateral momentum shedding and low propulsive efficiency. Using kinematic and inverse-dynamics analyses, we studied cyclic swimming of larval zebrafish aged 2–5 days post-fertilization (dpf). Larvae at 4–5 dpf reach higher f (95 Hz) and A_tail (2.4 mm) than at 2 dpf (80 Hz, 1.8 mm), increasing swimming speed and Re, indicating increasing muscle powers. As Re increases (60 → 1400), St (2.5 → 0.72) decreases nonlinearly towards values of large swimmers (0.2–0.6), indicating increased propulsive efficiency with v_swim and age. Swimming at high St is associated with high-amplitude body torques and rotations. Low propulsive efficiencies and large yawing amplitudes are unavoidable physical constraints for small undulatory swimmers.     

Experiments and theory of undulatory locomotion in a simple structured medium

Undulatory locomotion of micro-organisms through geometrically complex, fluidic environments is ubiquitous in nature and requires the organism to negotiate both hydrodynamic effects and geometrical constraints. To understand locomotion through such media, we experimentally investigate swimming of the nematode Caenorhabditis elegans through fluid-filled arrays of micro-pillars and conduct numerical simulations based on a mechanical model of the worm that incorporates hydrodynamic and contact interactions with the lattice. We show that the nematode''s path, speed and gait are significantly altered by the presence of the obstacles and depend strongly on lattice spacing. These changes and their dependence on lattice spacing are captured, both qualitatively and quantitatively, by our purely mechanical model. Using the model, we demonstrate that purely mechanical interactions between the swimmer and obstacles can produce complex trajectories, gait changes and velocity fluctuations, yielding some of the life-like dynamics exhibited by the real nematode. Our results show that mechanics, rather than biological sensing and behaviour, can explain some of the observed changes in the worm''s locomotory dynamics.     

Passive elastic mechanism to mimic fish-muscle action in anguilliform swimming

Swimmers in nature use body undulations to generate propulsive and manoeuvring forces. The anguilliform kinematics is driven by muscular actions all along the body, involving a complex temporal and spatial coordination of all the local actuations. Such swimming kinematics can be reproduced artificially, in a simpler way, by using the elasticity of the body passively. Here, we present experiments on self-propelled elastic swimmers at a free surface in the inertial regime. By addressing the fluid–structure interaction problem of anguilliform swimming, we show that our artificial swimmers are well described by coupling a beam theory with the potential flow model of Lighthill. In particular, we show that the propagative nature of the elastic wave producing the propulsive force is strongly dependent on the dissipation of energy along the body of the swimmer.     

Effect of counterface roughness on adhesion of mushroom-shaped microstructure

In this study, the effect of the substrate roughness on adhesion of mushroom-shaped microstructure was experimentally investigated. To do so, 12 substrates having different isotropic roughness were prepared from the same material by replicating topography of different surfaces. The pull-off forces generated by mushroom-shaped microstructure in contact with the tested substrates were measured and compared with the pull-off forces generated by a smooth reference. It was found that classical roughness parameters, such as average roughness (R_a) and others, cannot be used to explain topography-related variation in pull-off force. This has led us to the development of an integrated roughness parameter capable of explaining results of pull-off measurements. Using this parameter, we have also found that there is a critical roughness, above which neither smooth nor microstructured surface could generate any attachment force, which may have important implications on design of both adhesive and anti-adhesive surfaces.     

Measurements on hydrophobic and hydrophilic surfaces using a porous gamma alumina nanoparticle aggregate mounted on Atomic Force Microscopy cantilevers

Atomic Force Microscopy (AFM) measurements are extensively used for a detailed understanding of molecular and surface forces. In this study, we present a technique for measuring such forces, using an AFM cantilever attached with a porous gamma alumina nanoparticle aggregate. The modified cantilever was used to measure the forces of interaction of the aggregate with hydrophilic and hydrophobic surfaces. A strong force of attraction was observed between the aggregate and hydrophilic surfaces when the aggregate was kept dry. However, the force of interaction on the aggregate in wet form (water filled in pores) was larger when the adjoining surface had hydrophobic characteristics. The results presented in this study show the versatility of the current technique and indicate its usefulness in directly characterizing hydrophilic/hydrophobic properties of nano-scale surfaces and patterns.     

Optimum blade configurations for the cutting of soft solids

For the same amount of work in separating surfaces of soft solids, the forces normal and tangential to an element of a cutting blade are determined by the local velocities of the material past the cutting edge, in particular by the ratio ξ of ‘slice’ to ‘push’ velocities. The greater the ξ, the lower the forces and hence reduced damage to the cut surfaces (i.e., better surface finish). Different examples are considered of flat blades of variable curvature (such spiral-profiled blades in food cutting machinery, scythes, sickles, sabres, etc.) where the local forces vary along the edge of the blade as the curvature changes. How to maximise ξ is discussed along with questions of whether the material to be cut is restrained or not. The mechanics of cutting by a cylinder lawn mower is also investigated. Here the blades are arranged on helices around the cylinder and ξ is determined by the helix angle and by N = (rω/f) which is the ‘gearing’ of the cylinder with respect to the forward speed of the machine. There is a compromise between low cutting forces and flatness of cut surface that has to be adopted in design of practical machines.     

A consistent muscle activation strategy underlies crawling and swimming in Caenorhabditis elegans

Although undulatory swimming is observed in many organisms, the neuromuscular basis for undulatory movement patterns is not well understood. To better understand the basis for the generation of these movement patterns, we studied muscle activity in the nematode Caenorhabditis elegans. Caenorhabditis elegans exhibits a range of locomotion patterns: in low viscosity fluids the undulation has a wavelength longer than the body and propagates rapidly, while in high viscosity fluids or on agar media the undulatory waves are shorter and slower. Theoretical treatment of observed behaviour has suggested a large change in force–posture relationships at different viscosities, but analysis of bend propagation suggests that short-range proprioceptive feedback is used to control and generate body bends. How muscles could be activated in a way consistent with both these results is unclear. We therefore combined automated worm tracking with calcium imaging to determine muscle activation strategy in a variety of external substrates. Remarkably, we observed that across locomotion patterns spanning a threefold change in wavelength, peak muscle activation occurs approximately 45° (1/8th of a cycle) ahead of peak midline curvature. Although the location of peak force is predicted to vary widely, the activation pattern is consistent with required force in a model incorporating putative length- and velocity-dependence of muscle strength. Furthermore, a linear combination of local curvature and velocity can match the pattern of activation. This suggests that proprioception can enable the worm to swim effectively while working within the limitations of muscle biomechanics and neural control.     

Plant surfaces with cuticular folds are slippery for beetles

Plant surfaces covered with three-dimensional (3D) waxes are known to strongly reduce insect adhesion, leading to slippery surfaces. Besides 3D epicuticular waxes, cuticular folds are a common microstructure found on plant surfaces, which have not been quantitatively investigated with regard to their influence on insect adhesion. We performed traction experiments with Colorado potato beetles on five plant surfaces with cuticular folds of different magnitude. For comparison, we also tested (i) smooth plant surfaces and (ii) plant surfaces possessing 3D epicuticular waxes. Traction forces on surfaces with medium cuticular folds, of about 0.5 µm in both height and thickness and a spacing of 0.5–1.5 µm, were reduced by an average of 88 per cent in comparison to smooth plant surfaces. Traction forces were reduced by the same order of magnitude as on plant surfaces covered with 3D epicuticular waxes. For surface characterization, we performed static contact angle measurements, which proved a strong effect of cuticular folds also on surface wettability. Surfaces possessing cuticular folds of greater magnitude showed higher contact angles up to superhydrophobicity. We hypothesize that cuticular folds reduce insect adhesion mainly due to a critical roughness, reducing the real contact area between the surface and the insect''s adhesive devices.     

Speed limits on swimming of fishes and cetaceans.

Physical limits on swimming speed of lunate tail propelled aquatic animals are proposed. A hydrodynamic analysis, applying experimental data wherever possible, is used to show that small swimmers (roughly less than a metre long) are limited by the available power, while larger swimmers at a few metres below the water surface are limited by cavitation. Depending on the caudal fin cross-section, 10-15 m s(-1) is shown to be the maximum cavitation-free velocity for all swimmers at a shallow depth.     

Generalized squirming motion of a sphere

A number of swimming microorganisms, such as ciliates (Opalina) and multicellular colonies of flagellates (Volvox), are approximately spherical in shape and swim using beating arrays of cilia or short flagella covering their surfaces. Their physical actuation on the fluid may be mathematically modeled as the generation of surface velocities on a continuous spherical surface—a model known in the literature as squirming, which has been used to address various aspects of the biological physics of locomotion. Previous analyses of squirming assumed axisymmetric fluid motion and hence required all swimming kinematics to take place along a line. In this paper we generalize squirming to three spatial dimensions. We derive analytically the flow field surrounding a spherical squirmer with arbitrary surface motion and use it to derive its three-dimensional translational and rotational swimming kinematics. We then use our results to physically interpret the flow field induced by the swimmer in terms of fundamental flow singularities up to terms decaying spatially as \({\sim } 1/r^3\) . Our results will make it possible to develop new models in biological physics, in particular in the area of hydrodynamic interactions and collective locomotion.     

Solid-solid contacts due to surface roughness and their effects on suspension behaviour

Solid-solid contacts due to microscopic surface roughness in viscous fluids were examined by observing the translational and rotational behaviours of a suspended sphere falling past a lighter sphere or down an inclined surface. In both cases, a roll-slip behaviour was observed, with the gravitational forces balanced by not only hydrodynamic forces but also normal and tangential solid-solid contact forces. Moreover, the nominal separation between the surfaces due to microscopic surface roughness elements is not constant but instead varies due to multiple roughness scales. By inverting the system, so that the heavy sphere fell away from the lighter sphere or the plane, it was found that the average nominal separation increases with increasing angle of inclination of the plane or the surface of the lighter sphere from horizontal; the larger asperities lift the sphere up from the opposing surface and then gravity at large angles of inclination is too weak to pull the sphere back down to the opposing surface before another large asperity is encountered. The existence of microscopic surface roughness and solid-solid contacts is shown to modify the rheological properties of suspensions. For example, the presence of compressive, but not tensile, contact forces removes the reversibility of sphere-sphere interactions and breaks the symmetry of the particle trajectories. As a result, suspensions of rough spheres exhibit normal stress differences that are absent for smooth spheres. For the conditions studied, surface roughness reduces the effective viscosity of a suspension by limiting the lubrication resistance during near-contact motion, and it also modifies the suspension microstructure and hydrodynamic diffusivity.     

仿鱼鳍推进水下机器人流体动力测试系统

以基于仿生柔性长鳍波动推进的水下机器人试验模型为背景,主要研究如何构建满足多种水下机器人试验模型在各种姿态下流体动力/力矩的静态与动态测量要求的测试系统.文章首先提出流体动力测试系统的功能需求与设计准则,并按照模块化设计思想设计其体系结构,重点研究了6分力测量原理、传感器阵列配置结构以及测试流程,最后对整个系统进行了误差源分析.论文研究的测试系统具有6分力测量、2自由度运动导向以及载体运动参数测量等功能,是支撑柔性长鳍波动推进水下机器人研究的重要试验平台.     

Free‐surface effects on an oblique towing flat plate

Abstract

This paper applies a finite difference method in calculating the free surface profiles, the lateral hydrodynamic forces as well as the moments acting on a plate during the oblique towing of a flat plate on the free surface. The 3‐D fluid motion in the infinite region is approximated by the unsteady 2‐D flow in the finite region with an artificial open boundary on which a more relaxed Sommerfeld's radiation condition is imposed. The free surface profiles, nondimensional side forces and yawing moments are calculated by the present method and are compared satisfactorily with the experimental results [15], Chapman's results [4], and Yamasaki's computational results [16].     

Insect adhesion on rough surfaces: analysis of adhesive contact of smooth and hairy pads on transparent microstructured substrates

Insect climbing footpads are able to adhere to rough surfaces, but the details of this capability are still unclear. To overcome experimental limitations of randomly rough, opaque surfaces, we fabricated transparent test substrates containing square arrays of 1.4 µm diameter pillars, with variable height (0.5 and 1.4 µm) and spacing (from 3 to 22 µm). Smooth pads of cockroaches (Nauphoeta cinerea) made partial contact (limited to the tops of the structures) for the two densest arrays of tall pillars, but full contact (touching the substrate in between pillars) for larger spacings. The transition from partial to full contact was accompanied by a sharp increase in shear forces. Tests on hairy pads of dock beetles (Gastrophysa viridula) showed that setae adhered between pillars for larger spacings, but pads were equally unable to make full contact on the densest arrays. The beetles'' shear forces similarly decreased for denser arrays, but also for short pillars and with a more gradual transition. These observations can be explained by simple contact models derived for soft uniform materials (smooth pads) or thin flat plates (hairy-pad spatulae). Our results show that microstructured substrates are powerful tools to reveal adaptations of natural adhesives for rough surfaces.     

Corrections to the theory and the optimal line in the swimming diagram of Taylor (1952)

The analysis of undulatory swimming gaits requires knowledge of the fluid forces acting on the animal body during swimming. In his classical 1952 paper, Taylor analysed this problem using a ‘resistive-force’ theory. The theory was used to characterize the undulatory gaits that result in the smallest energy dissipation to the fluid for a given swim velocity. The optimal gaits thus found were compared with data recorded from movies of a snake and a leech swimming. This report identifies and corrects a mathematical error in Taylor’s paper, showing that his theory applies even better to animals of circular cross section.     

Numerical investigations of strong hydrodynamic interaction between neighboring particles inertially driven in microfluidic flows

Dispersed particles traveling at a high throughput in microchannels laterally migrate and focus into a streamline at each channel face. The focusing attractors within the cross-section are determined by the balance between the lift forces. However, particles in close proximity (e.g. due to high concentration and abrupt particle contact) suffer a breakdown of distinct focusing due to excessive hydrodynamic interaction. Here, I present numerical investigations into the effects of the strong hydrodynamic interaction on the inertial focusing. The direct numerical simulation is used to calculate the focusing/defocusing of particles, specifically since the particle-induced disturbance flows vary at the particle scale and hence affect the individual particle motion. The simulated defocusing of many-body systems prefer finite inter-particle separation, in contrast with sedimentation of two mobile particles, whereby the trailing particle catches up with the leading particle due to reduced drag in its wake. I numerically demonstrate that the finite separation between nearest neighbors is a consequence of hydrodynamic repulsive motion unique to wall-bound shear flows. The author further presents direct demonstrations of the effects of the strong hydrodynamic interaction on the inertial focusing in an experimentally unachievable manner. The excessive hydrodynamic interaction drastically dissipates the near-wall focusing attractors and thus causes irreversible defocusing by breaking the balance between the lift forces. Unexpectedly, I also find that moderate hydrodynamic interaction can alter focusing speed on specific conditions, suggesting that an optimum concentration may significantly boost the inertial focusing in microfluidic-based applications.     

Nanostructuration of self-assembled poly(styrene-b-isoprene-b-styrene) block copolymer thin films in a highly oriented pyrolytic graphite substrate

Highly oriented pyrolitic graphite (HOPG) is a useful substrate to visualize epitaxial formation due to its crystallographic structure. The morphology of a poly(styrene-b-isoprene-b-styrene) block copolymer thin film on a HOPG substrate was investigated by atomic force microscopy. Block copolymer domains generated a morphology with triangular regularity. This arrangement was induced by the HOPG substrate structure due to van der Waals attraction between the HOPG π-conjugated system and aromatic ring of polystyrene domains. However, increasing the film thickness, the substrate effect on the surface morphology decreased. As a consequence, film surfaces showed the coexistence of different structures such as highly aligned cylinders and perforated lamellae. When film thickness exceeded a threshold value, the substrate did not have effect in the surface arrangements and the surface showed a similar morphology to that existing in bulk.     

Aquatic manoeuvering with counter-propagating waves: a novel locomotive strategy

Many aquatic organisms swim by means of an undulating fin. These undulations often form a single wave travelling from one end of the fin to the other. However, when these aquatic animals are holding station or hovering, there is often a travelling wave from the head to the tail, and another moving from the tail to the head, meeting in the middle of the fin. Our study uses a biomimetic fish robot and computational fluid dynamics on a model of a real fish to uncover the mechanics of these inward counter-propagating waves. In addition, we compare the flow structure and upward force generated by inward counter-propagating waves to standing waves, unidirectional waves, and outward counter-propagating waves (i.e. one wave travelling from the middle of the fin to the head, and another wave travelling from the middle of the fin to the tail). Using digital particle image velocimetry to capture the flow structure around the fish robot, and computational fluid dynamics, we show that inward counter-propagating waves generate a clear mushroom-cloud-like flow structure with an inverted jet. The two streams of fluid set up by the two travelling waves ‘collide’ together (forming the mushroom cap) and collect into a narrow jet away from the cap (the mushroom stem). The reaction force from this jet acts to push the body in the opposite direction to the jet, perpendicular to the direction of movement provided by a single travelling wave. This downward jet provides a substantial increase in the perpendicular force when compared with the other types of fin actuation. Animals can thereby move upward if the fin is along the bottom midline of the body (or downward if on top); or left–right if the fins are along the lateral margins. In addition to illuminating how a large number of undulatory swimmers can use elongated fins to move in unexpected directions, the phenomenon of counter-propagating waves provides novel motion capabilities for systems using robotic undulators, an emerging technology for propelling underwater vehicles.     

The fluid dynamics of swimming by jumping in copepods

Copepods swim either continuously by vibrating their feeding appendages or erratically by repeatedly beating their swimming legs, resulting in a series of small jumps. The two swimming modes generate different hydrodynamic disturbances and therefore expose the swimmers differently to rheotactic predators. We developed an impulsive stresslet model to quantify the jump-imposed flow disturbance. The predicted flow consists of two counter-rotating viscous vortex rings of similar intensity, one in the wake and one around the body of the copepod. We showed that the entire jumping flow is spatially limited and temporally ephemeral owing to jump-impulsiveness and viscous decay. In contrast, continuous steady swimming generates two well-extended long-lasting momentum jets both in front of and behind the swimmer, as suggested by the well-known steady stresslet model. Based on the observed jump-swimming kinematics of a small copepod Oithona davisae, we further showed that jump-swimming produces a hydrodynamic disturbance with much smaller spatial extension and shorter temporal duration than that produced by a same-size copepod cruising steadily at the same average translating velocity. Hence, small copepods in jump-swimming are in general much less detectable by rheotactic predators. The present impulsive stresslet model improves a previously published impulsive Stokeslet model that applies only to the wake vortex.     

The influence of different preparation methods on the aggregation status of pyrogenic nanosilicas used in concrete

Investigation of the effects of nanosilica materials in cementitious mixtures has attracted considerable research attention due to the very high specific surfaces of these materials. However, high surface area leads to aggregation of these materials due to high surface attraction forces, which could seriously reduce their nano filler effect. In this research the dispersion of pyrogenic nanosilicas in water and parameters influencing it were investigated. The results show that serious aggregation of pyrogenic nanosilicas in water occurs. Increasing the amount of applied forces, particularly the use of ultrasonic waves, has considerable effect in breaking aggregates into smaller aggregates with maximum size up to 0.9 μm. Increasing the pH was found to be very effective in improving dispersion of nanosilicas and through combined use of high pH and applying high levels of energy such as ultrasonic method it is possible to break all the aggregates into primary aggregates with maximum size of about 0.06 μm.