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.     

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.     

Fin sweep angle does not determine flapping propulsive performance

The importance of the leading-edge sweep angle of propulsive surfaces used by unsteady swimming and flying animals has been an issue of debate for many years, spurring studies in biology, engineering, and robotics with mixed conclusions. In this work, we provide results from three-dimensional simulations on single-planform finite foils undergoing tail-like (pitch-heave) and flipper-like (twist-roll) kinematics for a range of sweep angles covering a substantial portion of animals while carefully controlling all other parameters. Our primary finding is the negligible 0.043 maximum correlation between the sweep angle and the propulsive force and power for both tail-like and flipper-like motions. This indicates that fish tails and mammal flukes with similar range and size can have a large range of potential sweep angles without significant negative propulsive impact. Although there is a slight benefit to avoiding large sweep angles, this is easily compensated by adjusting the fin’s motion parameters such as flapping frequency, amplitude and maximum angle of attack to gain higher thrust and efficiency.     

Swimming of the semi-infinite strip revisited

Idealized mathematical models have been devised over the years for study of the fundamentals of the swimming of fishes. The two-dimensional flexible strip propelled by execution of transverse traveling-wave undulation is one of the most well-studied of the simple models. This model is redeveloped here, with the finding that higher propulsive efficiencies are theoretically available within the undulatory swimming mode than have been previously exposed. This is by configuring the displacement wave-form for continuously zero circulation over the body length with time, and thereby avoiding the shedding of a vortex wake and its attendant induced drag. The thrust is reactive, via acceleration processes, rather than inductive via relative velocity and lift. As in most of the classical work on fish propulsion, the analysis assumes high Reynolds number and a thin boundary layer, which provides the use of ideal-flow theory. The advance speed is assumed constant and the analysis is initially linearized, but both nonlinear and linear transient analysis are provided in supporting the basic “wakeless swimming” possibility.     

行波壁抑制圆柱涡激振动的数值模拟研究

采用CFD数值模拟方法完成了圆柱绕流-涡激振动-行波壁流动控制全过程的数值模拟,重点研究行波壁流动控制方法对低雷诺数下两自由度弹性支撑单圆柱涡激振动的抑制作用。详细分析各阶段圆柱横向和流向位移、质心运动轨迹、升力和阻力系数等随频率比的变化。结果表明:行波壁圆柱的波谷处可以产生一系列稳定的随行波壁运动的小尺度旋涡,有效抑制圆柱表面分离涡的产生,达到消除圆柱绕流尾迹和抑制涡激振动的目的;在计算初始和中途启动的行波壁流动控制方法显著抑制了圆柱横向和流向振动、降低了圆柱升力系数脉动值和阻力系数均值,但阻力系数脉动值则明显增大。     

Effect of inertia on electrified film flow over a wavy wall

The effect of inertia on the steady flow of a liquid layer down a wavy wall in the presence of an electric field is investigated. Both the liquid film and the region above it are assumed to act as perfect dielectrics. A linearised perturbation analysis is performed for flow down a wall with small-amplitude sinusoidal corrugations, and the free-surface amplitude and phase shift are computed numerically for a broad range of flow conditions. It is shown that the electric field can be used to manipulate the phase shift between the free surface and the wall. In particular, when the Reynolds number lies below a threshold value, an electric field of sufficient strength will bring the free surface precisely into phase with the wall. An electric field can also be used to mitigate the resonance effect identified by previous workers, in which the free surface suffers significant amplification in comparison to the height of the wall corrugations at a particular Reynolds number. Working on the basis of the lubrication approximation, a nonlinear equation for the film thickness is derived featuring a non-local term due to the electric field. Numerical solutions for flow over a wavy wall of finite amplitude reveal that the effect of inertia on the free-surface characteristics depends on the electrical properties of the fluid layer and the strength of the imposed electric field.     

Hydrodynamic drag constrains head enlargement for mouthbrooding in cichlids

Presumably as an adaptation for mouthbrooding, many cichlid fish species have evolved a prominent sexual dimorphism in the adult head. Since the head of fishes serves as a bow during locomotion, an evolutionary increase in head volume to brood more eggs can trade-off with the hydrodynamic efficiency of swimming. Here, the differences between males and females in three-dimensional shape and size of the external head surfaces and the effect thereof on drag force during locomotion was analysed for the Nile tilapia (Oreochromis niloticus), a maternal mouthbrooder. To do so, three-dimensional body surface reconstructions from laser scans and computational fluid dynamics simulations were performed. After scaling the scanned specimens to post-cranial body volume, in order to theoretically equalize propulsive power, the external volume of the head of females was 27% larger than that of males (head length + 14%; head width + 9%). These differences resulted in an approximate 15% increase in drag force. Yet, hydrodynamics imposed important constraints on the adaptation for mouthbrooding as a much more drastic drop in swimming efficiency seems avoided by mainly enlarging the head along the swimming direction.     

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.     

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.     

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.     

On laminar small reynolds-number flow over wavy walls

Summary In the present paper a perturbation method is developed in order to study viscous, laminar flow over a small amplitude wavy solid boundary. The wall is transformed into a straight solid boundary in order to simplify the use of boundary conditions of the problem on the wall. The flow field is calculated numerically up to first perturbation order. separation of the flow is included.With 7 Figures     

Numerical Investigation of Phase Distribution and Liquid Turbulence Modulation in Dilute Particle-Laden Flow

Studies on the motion of particles in turbulence and interactions between particles and turbulence are extremely significant, which can help us to improve the efficiency of industrial processes. In this article, we investigated the particle distribution and particle-turbulence interaction in a solid-liquid channel flow with the Euler-Lagrange two-way model. The liquid phase was solved using direct numerical simulation (DNS), and the particle motion was tracked by Newtonian equations of motion considering effects of drag force, pressure gradient force, and gravity. Two-way coupling was used to explain the effect of particles on the turbulence structure. The results show that the local void fraction of particles indicates the wall-peaked profile, particles scatter uniformly in the spanwise direction, and the injection of particles suppresses the turbulence activities in the near wall region. Suppression of the liquid turbulence is mainly caused by vortexes decay of different sizes.     

Non-equilibrium linearized magnetogasdynamic flow over a wavy wall (aligned)

Summary A steady, linearized flow of a conducting fluid withn non-equilibrium processes in parallel has been considered and neglecting the effects due to viscosity, heat conduction and diffusion and assuming the electrical conductivity to be infinite, a single equation for the flow variables has been derived when the undisturbed uniform magnetic field is aligned to the undisturbed uniform fluid stream. The solution of the equation has been obtained for a flow over a two-dimensional wavy wall. The pressure, net pressure i.e. the difference between the local static, pressure and force per unit area arising from the surface current, drag coefficient and total drag coefficient have been calculated and the results have been discussed. It is found that for certain values of the equilibrium Mach number and the magnetic pressure number negative drag coefficient as well as negative total drag coefficient occur in the flow.With 6 Figures     

Two-layer flow in a corrugated channel

The flow of two superposed viscous fluid layers in a two-dimensional channel confined between a plane and a wavy or indented wall is studied by analytical and numerical methods at arbitrary Reynolds numbers. The interface between the two fluids may exhibit constant or variable surface tension due to an insoluble surfactant. The flow is computed from a specified initial condition using the immersed-interface method on a curvilinear grid constructed by conformal mapping. The numerical simulations illustrate the effect of geometrical nonlinearity and reveal that inertia may increase or decrease the amplitude of the interface profile at steady state depending on the flow parameters. Increasing either the Reynolds number or the wall amplitude above a certain threshold value provokes flow instability and overturning of the interface. In the Appendix, a linear perturbation analysis is performed for arbitrary Reynolds numbers on the assumption of small-amplitude sinusoidal undulations, and results for the amplitude and phase shift of the interfacial and surfactant concentration wave are documented for a broad range of flow conditions. It is found that inertia may have a mixed effect on the deformation and phase shift, while the surfactant promotes the deformation of the interface under most conditions.     

行波推进仿生机器鱼

介绍5种常见的鱼类游动模式,分析讨论仿生机器鱼的生物学原型。基于对裸臀鱼属（gymnarchus niloticus）与裸背鳗属（gymnotus carapo）活体鱼的实验研究,建立了长背鳍扭转行波动态曲面的数学模型。依靠长鳍行波实现推进与控制的新型仿生机器鱼,其基本结构是“刚性身体”与“柔性背鳍”的组合,这有利于改善现有摆动式机器鱼的技术性能。裸臀鱼属与裸背鳗属鱼类可作为发展特种机器鱼潜艇的生物学原型,以提高现行水下航行器的效率和机动性能。     

Dynamical characteristics of wave-excited channel flow

This paper is part of a study on the receptivity characteristics of the shear flow in a channel whose walls are subjected to a wave-like excitation. The small amplitude forced wavy wall motion is characterised by a wave number vectorλ ₁,λ ₂ and a frequencyω _g . The basic flow in the problem is a superposition of the Poiseuille flow and a periodic component that corresponds to the wave excitation of the wall. The aim of the study is to examine the susceptibility of this flow to transition. The problem is approached through studying the stability characteristics of the basic flow with respect to small disturbances. The theoretical framework for this purpose is Floquet theory. The solution procedure for solving the eigenvalue problem is the spectral collocation method. Preliminary results showing the influence of the amplitude and the wave number of the wall excitation on the stability boundary of the flow are presented.     

A microcontinuum analysis of the self propulsion of the spermatozoa in the cervical canal

The hydrodynamics of the self propulsion of a spermatozoa, swimming through the mucus filling the cervical channel, is investigated. The mucus is modeled as a micropolar fluid and the spermatozoa as a 2-dimensional sheet swimming at low Reynolds number between two rigid walls. The wavelengths of the propulsive waves passing down the sheet are assumed to be very large compared to the channel spacing, but the amplitude of the propulsive waves is arbitrary. Expressions for the propulsive velocity and the energy expended by the swimming sheet are obtained in terms of various parameters involved. The results are elaborated through graphs. It is found that both the propulsive velocity and the rate of working by the sheet increase as the value of the micropolar parameters $\text{N}$ increases and that of $\text{L}$ decreases.     

Timoshenko梁功率流主动控制研究

为了研究扰动影响下梁式结构的动力学响应与主动控制,首先基于Timoshenko梁理论,采用行波方法建立了悬臂梁结构的动力学模型并获得了其在扰动下的精确动力学响应,进一步得到结构中传播的功率流,并以此为目标函数,优化得到了最优控制力的大小与相位,然后对结构施加最优控制力,实现了Timoshenko梁结构的功率流主动控制。对Timoshenko梁结构动力学响应与功率流主动控制方法进行了数值计算,并与Euler-Bernoulli梁理论计算结果进行了对比分析。结果表明：采用行波方法计算梁结构的动力学响应准确可靠;Timoshenko梁模型较Euler-Bernoulli梁模型在中、高频段更为精确,且更接近工程实际;通过数值计算与分析验证了基于行波方法功率流主动控制的正确性与有效性,并且功率流主动控制可以明显降低梁式结构全频域内的抖动。     

蒙皮波动对飞艇阻力的影响

通过求解雷诺平均Navier-Stokes方程,采用SST两方程湍流模型,研究了蒙皮以不同波长、频率以及波幅作波动时对飞艇流场特性产生的影响。研究结果表明:沿流向蒙皮的波动会引起绕飞艇流场的显著改变。当蒙皮上下表面的波动同相位时,在固定波动幅度和频率条件下,波动的波长减小,流动分离会加剧,时间平均的阻力系数增加;在固定波动波长和频率条件下,波动的波幅增加,流动分离加剧,时间平均的阻力系数增加,而当波幅减小到一定程度时,蒙皮波动对阻力系数基本没有影响;在固定波动波长和幅度条件下,波动频率增加,非定常效应增强,阻力系数减小,甚至出现负值,即可以为飞艇提供推力;此外,适当的波幅和波长组合也可以减小阻力系数。当蒙皮上下表面的波动相位相反时,波长与波幅变化带来的影响与同相位的情况相似;固定波动波长、幅度,波动频率增加,非定常效应增加,由于上下表面的非定常效应是相互抵消的,虽然阻力系数会出现瞬时负值,但是时间平均的阻力系数不会出现负值。     

流固耦合S-型自主游动柔性鱼运动特性分析

以S-型游动鱼作为对象,采用不可压缩Neo-Hookean材料描述鱼游动过程中的柔性变形及其与流体相互作用产生推力的自主游动特性。基于浸入边界法(IBM)的有限单元(FEM)离散模型,模拟了考虑鱼体肌肉作用力效应的柔性鱼在不可压缩粘性流体中自主游动的动力学过程,分析了流固耦合柔性鱼的游动机制及柔性变形的水弹性动力学特性。研究发现:随着鱼尾部不断呈S-型往复摆动,鱼体运动速度也呈波动形状,且受流固耦合的水动力学特性控制,并与鱼体的刚度密切相关。游动过程中,在鱼头的部位首先有涡旋形成,随着鱼向前游动,这些涡旋附着在鱼体表面向后滑移,并在鱼尾末端脱落形成S-型状的尾流。S-型状尾流直接影响鱼游动的速度及稳 定性。