Magnetically Propelled Fish‐Like Nanoswimmers

The swimming locomotion of fish involves a complex interplay between a deformable body and induced flow in the surrounding fluid. While innovative robotic devices, inspired by physicomechanical designs evolved in fish, have been created for underwater propulsion of large swimmers, scaling such powerful locomotion into micro‐/nanoscale propulsion remains challenging. Here, a magnetically propelled fish‐like artificial nanoswimmer is demonstrated that emulates the body and caudal fin propulsion swimming mechanism displayed by fish. To mimic the deformable fish body for periodic shape changes, template‐electrosynthesized multisegment nanowire swimmers are used to construct the artificial nanofishes (diameter 200 nm; length 4.8 μm). The resulting nanofish consists a gold segment as the head, two nickel segments as the body, and one gold segment as the caudal fin, with three flexible porous silver hinges linking each segment. Under an oscillating magnetic field, the propulsive nickel elements bend the body and caudal fin periodically to generate travelling‐wave motions with speeds exceeding 30 μm s^?1. The propulsion dynamics is studied theoretically using the immersed boundary method. Such body‐deformable nanofishes exhibit a high swimming efficiency and can serve as promising biomimetic nanorobotic devices for nanoscale biomedical applications.     

Classification of the pre-settlement behaviour of barnacle cyprids

Barnacle cyprids exhibit a complex swimming and exploratory behaviour on surfaces and settlement is a consequence of extensive surface probing and selection of suitable settlement sites. In this work, the behaviour of cyprids in their pre-settlement phase was studied by three-dimensional video stereoscopy. With this technique, three-dimensional trajectories were obtained that were quantitatively analysed. The velocity during vertical sinking of cyprids of Balanus amphitrite was used with a modified form of Stokes'' law to calculate their mean body density. Furthermore, a classification of the swimming patterns allowed the extension of existing models describing cyprid locomotion and swimming behaviour. The patterns were characterized with respect to their occurrence, transition between patterns and their velocity distribution, and motions were identified that led to surface contacts. This analysis provides a classification framework, which can assist future attempts to identify behavioural responses of cyprids to specific settlement cues.     

Analytical insights into optimality and resonance in fish swimming

This paper provides analytical insights into the hypothesis that fish exploit resonance to reduce the mechanical cost of swimming. A simple body–fluid fish model, representing carangiform locomotion, is developed. Steady swimming at various speeds is analysed using optimal gait theory by minimizing bending moment over tail movements and stiffness, and the results are shown to match with data from observed swimming. Our analysis indicates the following: thrust–drag balance leads to the Strouhal number being predetermined based on the drag coefficient and the ratio of wetted body area to cross-sectional area of accelerated fluid. Muscle tension is reduced when undulation frequency matches resonance frequency, which maximizes the ratio of tail-tip velocity to bending moment. Finally, hydrodynamic resonance determines tail-beat frequency, whereas muscle stiffness is actively adjusted, so that overall body–fluid resonance is exploited.     

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.     

Propulsive performance of a fish-like travelling wavy wall

Summary. A numerical simulation is performed to investigate the viscous flow over a smooth wavy wall undergoing transverse motion in the form of a streamwise travelling wave, which is similar to the backbone undulation of swimming fish. The objective of this study is to elucidate hydrodynamic features of the flow structure over the travelling wavy wall and to get physical insights to the understanding of fish-like swimming mechanisms in terms of drag reduction and optimal propulsive efficiency. The effect of phase speed, amplitude and Reynolds number on the flow structure over the wavy wall, the drag force acting on the wall, and the power consumption required for the propulsive motion of the wall is investigated. The phase speed and the amplitude, which are two important parameters in this problem, predicted based on the optimal propulsive efficiency agree well with the available data obtained for the wave-like swimming motion of live fish in nature.     

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.     

Direct numerical simulations for assessment of gas-solid drag models in two-dimensional random arrays of particles

The momentum exchange between the phases plays a vital role in modelling of gas–solid flows and it is mathematically described by drag models. However, no consensus exists on which drag model gives the most accurate prediction of the drag force, and, despite the increase in available computing power, the same drag models are used in two-dimensional and three-dimensional simulations. In this study, direct numerical simulations of gas flow through multiple random configurations of static monodisperse particles are performed. The variations of solid volume fraction and particle Reynolds number are in the ranges of 0.05–0.4 and 13.7–136.9, respectively. The drag force exerted on particles is calculated and properly averaged. Based on the simulation results, thirteen drag models are compared and correction factors are introduced using the stochastic gradient descent algorithm. The correction factors provide a simple adjustment for the models to be used in 2D modelling.     

Coordination of multiple appendages in drag-based swimming

Krill are aquatic crustaceans that engage in long distance migrations, either vertically in the water column or horizontally for 10 km (over 200 000 body lengths) per day. Hence efficient locomotory performance is crucial for their survival. We study the swimming kinematics of krill using a combination of experiment and analysis. We quantify the propulsor kinematics for tethered and freely swimming krill in experiments, and find kinematics that are very nearly metachronal. We then formulate a drag coefficient model which compares metachronal, synchronous and intermediate motions for a freely swimming body with two legs. With fixed leg velocity amplitude, metachronal kinematics give the highest average body speed for both linear and quadratic drag laws. The same result holds for five legs with the quadratic drag law. When metachronal kinematics is perturbed towards synchronous kinematics, an analysis shows that the velocity increase on the power stroke is outweighed by the velocity decrease on the recovery stroke. With fixed time-averaged work done by the legs, metachronal kinematics again gives the highest average body speed, although the advantage over synchronous kinematics is reduced.     

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.     

Dynamic capillary impact on longitudinal micro-flow in vacuum assisted impregnation and the unsaturated permeability of inner fiber tows

This paper addresses issues of the synergetic dynamic effect of capillary force on the longitudinal impregnation driven by external pressures, especially under vacuum assistance. An apparatus was designed to detect the axial infiltration along unidirectional fiber bundles which were all aligned closely to give a representation of micro-flow channel of inner fiber tows. The external driving pressures were controlled sufficiently low, 20–60 kPa, on the order of capillary pressures. Based on the analysis of infiltration velocities under different external pressures, dynamic capillary pressures can be determined experimentally. The results showed that capillary pressures, the most important force of microscopic flow through inner fiber yarns, acted as a drag force on the infiltration flow for vacuum assisted penetration into unidirectional fiber bundles. This unique drag effect is very different from traditional unsaturated infiltration, different from the compressed air driving permeation and the theoretical calculated data in this paper. Moreover, values and even signs of the dynamic capillary pressures varied with the fiber fraction of the assemblies as well as the fluid types. Further analysis demonstrated that the function of capillary pressure was closely related to the capillary number (Ca), acting as drag force when Ca larger than a critical value, and as a promotive force with smaller Ca. Consequently, unsaturated permeabilities of the unidirectional fiber bundles were estimated by taking consideration of both dynamic and quasi-static capillary pressures.     

A Method of Body Shape Optimization for Decreasing the Aerodynamic Drag Force in Gas Flow

Aerodynamic flow past bodies of various geometrical shapes was studied, and the aerodynamic drag force was reduced through optimization of the body shape using a specially proposed method. The resulting drag force was compared to that for bodies formed by revolution of the profiles of well-known standard series. The study was performed using the Ansys Fluent software for isothermal laminar steady-state flows of incompressible fluid with constant density in a velocity range of 0–10 m/s. It is shown that the aerodynamic drag force for a body with the optimized shape is lower than analogous values for the bodies of revolution with Su-26 and NASA-0006 reference profiles. In comparison to the aerodynamic-drag-force level of 100% for the body of revolution with NASA-0006 profile, the drag force for Su-26 profile at airflow velocity of 10 m/s is 89.4%, while that for the proposed optimized body shape is 89.2%.     

水下蛇形机器人机构设计及蜿蜒游动研究

仿效自然界蛇在水中的蜿蜒游动,设计了适于水中蜿蜒游动的蛇形机器人样机,并运用蛇形曲线对其蜿蜒游动进行实验研究。首先对蛇形机器人在水中的受力情形进行了分析;其次通过蛇形曲线控制蛇形机器人实现蜿蜒运动,并用依据样机搭建的动力学模型对蛇形机器人蜿蜒游动性能进行了仿真研究;最终对比分析了蛇形机器人在水中蜿蜒游动性能实验与动力学仿真中蜿蜒游动性能试验,验证了建模的必要性,为蛇形机器人的实用化提供了理论技术依据。     

Cost of flight and the evolution of stag beetle weaponry

Male stag beetles have evolved extremely large mandibles in a wide range of extraordinary shapes. These mandibles function as weaponry in pugnacious fights for females. The robust mandibles of Cyclommatus metallifer are as long as their own body and their enlarged head houses massive, hypertrophied musculature. Owing to this disproportional weaponry, trade-offs exist with terrestrial locomotion: running is unstable and approximately 40% more costly. Therefore, flying is most probably essential to cover larger distances towards females and nesting sites. We hypothesized that weight, size and shape of the weaponry will affect flight performance. Our computational fluid dynamics simulations of steady-state models (without membrane wings) reveal that male stag beetles must deliver 26% more mechanical work to fly with their heavy weaponry. This extra work is almost entirely required to carry the additional weight of the massive armature. The size and shape of the mandibles have only negligible influence on flight performance (less than 0.1%). This indicates that the evolution of stag beetle weaponry is constrained by its excessive weight, not by the size or shape of the mandibles and head as such. This most probably paved the way for the wide diversity of extraordinary mandible morphologies that characterize the stag beetle family.     

Unsteady motion: escape jumps in planktonic copepods,their kinematics and energetics

We describe the kinematics of escape jumps in three species of 0.3–3.0 mm-sized planktonic copepods. We find similar kinematics between species with periodically alternating power strokes and passive coasting and a resulting highly fluctuating escape velocity. By direct numerical simulations, we estimate the force and power output needed to accelerate and overcome drag. Both are very high compared with those of other organisms, as are the escape velocities in comparison to startle velocities of other aquatic animals. Thus, the maximum weight-specific force, which for muscle motors of other animals has been found to be near constant at 57 N (kg muscle)⁻¹, is more than an order of magnitude higher for the escaping copepods. We argue that this is feasible because most copepods have different systems for steady propulsion (feeding appendages) and intensive escapes (swimming legs), with the muscular arrangement of the latter probably adapted for high force production during short-lasting bursts. The resulting escape velocities scale with body length to power 0.65, different from the size-scaling of both similar sized and larger animals moving at constant velocity, but similar to that found for startle velocities in other aquatic organisms. The relative duration of the pauses between power strokes was observed to increase with organism size. We demonstrate that this is an inherent property of swimming by alternating power strokes and pauses. We finally show that the Strouhal number is in the range of peak propulsion efficiency, again suggesting that copepods are optimally designed for rapid escape jumps.     

Turbulence triggers vigorous swimming but hinders motion strategy in planktonic copepods

Calanoid copepods represent a major component of the plankton community. These small animals reside in constantly flowing environments. Given the fundamental role of behaviour in their ecology, it is especially relevant to know how copepods perform in turbulent flows. By means of three-dimensional particle tracking velocimetry, we reconstructed the trajectories of hundreds of adult Eurytemora affinis swimming freely under realistic intensities of homogeneous turbulence. We demonstrate that swimming contributes substantially to the dynamics of copepods even when turbulence is significant. We show that the contribution of behaviour to the overall dynamics gradually reduces with turbulence intensity but regains significance at moderate intensity, allowing copepods to maintain a certain velocity relative to the flow. These results suggest that E. affinis has evolved an adaptive behavioural mechanism to retain swimming efficiency in turbulent flows. They suggest the ability of some copepods to respond to the hydrodynamic features of the surrounding flow. Such ability may improve survival and mating performance in complex and dynamic environments. However, moderate levels of turbulence cancelled gender-specific differences in the degree of space occupation and innate movement strategies. Our results suggest that the broadly accepted mate-searching strategies based on trajectory complexity and movement patterns are inefficient in energetic environments.     

Homeostatic swimming of zooplankton upon crowding: the case of the copepod Centropages typicus

Crowding has a major impact on the dynamics of many material and biological systems, inducing effects as diverse as glassy dynamics and swarming. While this issue has been deeply investigated for a variety of living organisms, more research remains to be done on the effect of crowding on the behaviour of copepods, the most abundant metazoans on Earth. To this aim, we experimentally investigate the swimming behaviour, used as a dynamic proxy of animal adaptations, of males and females of the calanoid copepod Centropages typicus at different densities of individuals (10, 50 and 100 ind. l⁻¹) by performing three-dimensional single-organism tracking. We find that the C. typicus motion is surprisingly unaffected by crowding over the investigated density range. Indeed, the mean square displacements as a function of time always show a crossover from ballistic to Fickian regime, with poor variations of the diffusion constant on increasing the density. Close to the crossover, the displacement distributions display exponential tails with a nearly density-independent decay length. The trajectory fractal dimension, D_3D ≅ 1.5, and the recently proposed ‘ecological temperature’ also remain stable on increasing the individual density. This suggests that, at least over the range of animal densities used, crowding does not impact on the characteristics of C. typicus swimming motion, and that a homeostatic mechanism preserves the stability of its swimming performance.     

Snakes mimic earthworms: propulsion using rectilinear travelling waves

In rectilinear locomotion, snakes propel themselves using unidirectional travelling waves of muscular contraction, in a style similar to earthworms. In this combined experimental and theoretical study, we film rectilinear locomotion of three species of snakes, including red-tailed boa constrictors, Dumeril''s boas and Gaboon vipers. The kinematics of a snake''s extension–contraction travelling wave are characterized by wave frequency, amplitude and speed. We find wave frequency increases with increasing body size, an opposite trend than that for legged animals. We predict body speed with 73–97% accuracy using a mathematical model of a one-dimensional n-linked crawler that uses friction as the dominant propulsive force. We apply our model to show snakes have optimal wave frequencies: higher values increase Froude number causing the snake to slip; smaller values decrease thrust and so body speed. Other choices of kinematic variables, such as wave amplitude, are suboptimal and appear to be limited by anatomical constraints. Our model also shows that local body lifting increases a snake''s speed by 31 per cent, demonstrating that rectilinear locomotion benefits from vertical motion similar to walking.     

Numerical study on deposition of non-spherical shaped particles in cascade impactor

This study investigated the deposition of non-spherical particles in a cascade impactor using numerical simulations based on computational fluid dynamics and a discrete phase model (CFD-DPM). An optimum drag force model of non-spherical particles was used to calculate the dynamic behavior of the needle-shaped particles. The trajectory of these particles in an elbow pipe was computed and measured using a high-speed video camera. The computed trajectory agreed well with the experimental trajectory, and it was confirmed that the drag force model of non-spherical particles correctly expressed the drag force in the CFD-DPM numerical simulation. Next, the motion of the needle-shaped particles in a cascade impactor was numerically simulated and compared with that in the experimental results. The simulated classification efficiency agreed well with the experimental results. Additionally, the relationship between the aspect ratio of the needle-shaped particles and their behavior in the cascade impactor was numerically analyzed. The cut-off diameter decreased with the aspect ratio at a 50% classification efficiency in the cascade impactor. This was because the drag force of the particle was assumed to increase with the aspect ratio, and longer particles fell at a lower stage in the cascade impactor.     

MP-PIC modeling of CFB risers with homogeneous and heterogeneous drag models

In this paper, the MP-PIC (multiphase particle-in-cell) approach is used for three-dimensional (3D) modeling of the gas-solid flows in two types of circulating fluidized bed (CFB) risers with Geldart group A and B particles by incorporating the homogeneous and heterogeneous drag force models in the MP-PIC method, respectively. First, the effects of the three important simulation parameters, namely, the grid cell number, numerical particle-parcel size and time step, are investigated. Having determined the appropriate values for the three parameters, the hydrodynamic characteristics predicted by different drag force models are rigorously analyzed. The homogeneous drag models considered are the six models, the Wen-Yu, Wenyu-Ergun, Syamlal-O’Brien, Gidaspow, HKL, and BVK models, while the four heterogeneous models considered are Sarkar and EMMS-based models (EMMS-Yang, EMMS-Matrix and EMMS-QL). For the riser 1 with the Geldart A particles, all the six homogeneous models predict extremely high solid fluxes and inconsistent void fraction distributions compared with experimental results. The heterogeneous Sarkar and EMMS-based models can effectively improve the simulation accuracy and predict a typical core-annulus flow structure. The lately-developed EMMS-QL model produces the most accurate solid flux. For the riser 2 with the Geldart B particles, both the heterogeneous and homogeneous drag force models can predict a reasonable flow structure. Further, there are no significant differences in the void fraction and velocity profiles due to the choice of a drag force model over the other. These drag force models also successfully capture the meso-scale local particle clusters. Of these drag-force models, the Wenyu-Ergun drag-forec model predicts comparatively accurate solid flux. Generally, MP-PIC combined with heterogeneous Sarkar and EMMS-based drag force models reasonably improve the simulation accuracy for the Geldart A particles, while these heterogeneous models have no superiority over the homogeneous drag models for the Geldart B particles.     

On the path and efficiency of two micromachines with rigid tails

This paper reports on the results of investigation of the swimming of two different micro-machines. Mechanically each of these micro-machines consists of a head (containing an electromechanical power source) and a tail which moves relative to the head as a rigid body. The problem is approached theoretically by considering the types of movement which can occur for these micro-machines immersed in a viscous medium. The first micro-machine has a tail which oscillates in vertical plane, therefore the trajectory of this machine is in that plane too. The tail of the second micro-machine roates conically, so it produces a three dimensional helical path in space with its axis approximately along the direction of tail centreline.Using the boundary element method for solving the traction equations on the surface of the tail, and a time-dependent Euler kinematic scheme to plot the path, the net propulsive force and torque, the translational velocity, angular velocity and the trajectory of each machine are calculated. Evaluation of the path and the direction of motion for each micro-machine using different dimensional parameters can give an idea of the efficiency for such machines with rigid tails.