Speed Of Swimmer Research Articles

The motion of a self-propelling two-sphere swimmer in a weakly viscoelastic fluid

We study analytically the propulsion of a force- and torque-free swimmer composed of two counterrotating spheres of differing radii through a viscoelastic fluid described by the Giesekus constitutive model. Our analysis includes both swimmers composed of directly touching spheres and those composed of spheres separated by some finite distance. The propulsion speed of the swimmer is calculated by first expanding the equations of motion and the Giesekus constitutive model as a power series in the Weissenberg number, and then using the Lorentz reciprocal theorem to determine the first-order propulsion speed using the known flow fields for rotating and translating two-sphere geometries at zeroth order. We calculate the relative rotation speeds of the two spheres necessary to maintain the torque-free condition, including an approximate correction for fluid elasticity. The impact of the separation distance between the two spheres, the ratio of their radii, and the value of the Giesekus mobility parameter α on the propulsion speed are all examined; we find that the propulsion speed of the swimmer is maximized for two touching spheres with a radius ratio of approximately 0.7, with a Giesekus mobility parameter of α=0, corresponding to an Oldroyd-B fluid. We also quantify how increased shear-thinning in the fluid, represented by increasing values of α, results in a significant decrease in the swimmer speed. Finally, through calculations of the fluid stresses around the two-sphere swimmer, we demonstrate the development of enhanced hoop stresses around the smaller sphere, which drive the expulsion of stretched fluid behind the smaller sphere and induce motion of the swimmer in the direction of the larger sphere.

Motion of microswimmers in cylindrical microchannels.

Biological and artificial microswimmers often have to propel through a variety of environments, ranging from heterogeneous suspending media to strong geometrical confinement. Under confinement, local flow fields generated by microswimmers, and steric and hydrodynamic interactions with their environment determine the locomotion. We propose a squirmer-like model to describe the motion of microswimmers in cylindrical microchannels, where propulsion is generated by a fixed surface slip velocity. The model is studied using an approximate analytical solution for cylindrical swimmer shapes, and by numerical hydrodynamics simulations for spherical and spheroidal shapes. For the numerical simulations, we employ the dissipative particle dynamics method for modelling fluid flow. Both the analytical model and simulations show that the propulsion force increases with increasing confinement. However, the swimming velocity under confinement remains lower than the swimmer speed without confinement for all investigated conditions. In simulations, different swimming modes (i.e. pusher, neutral, puller) are investigated, and found to play a significant role in the generation of propulsion force when a swimmer approaches a dead end of a capillary tube. Propulsion generation in confined systems is local, such that the generated flow field generally vanishes beyond the characteristic size of the swimmer. These results contribute to a better understanding of microswimmer force generation and propulsion under strong confinement, including the motion in porous media and in narrow channels.

Confinement, chaotic transport, and trapping of active swimmers in time-periodic flows.

Microorganisms encounter complex unsteady flows, including algal blooms in marine settings, microbial infections in airways, and bioreactors for vaccine and biofuel production. Here, we study the transport of active swimmers in two-dimensional time-periodic flows using Langevin simulations and experiments with swimming bacteria. We find that long-term swimmer transport is controlled by two parameters, the pathlength of the unsteady flow and the normalized swimmer speed. The pathlength nonmonotonically controls swimmer dispersion dynamics, giving rise to three distinct dispersion regimes. Weak flows hinder swimmer transport by confining cells toward flow manifolds. As pathlength increases, chaotic transport along flow manifolds initiates, maximizing the number of unique flow cells traveled. Last, strong flows trap swimmers at the vortex core, suppressing dispersal. Experiments with Vibrio cholerae showed qualitative agreement with model dispersion patterns. Our results reveal that nontrivial chaotic transport can arise in simple unsteady flows and suggest a potentially optimal dispersal strategy for microswimmers in nature.

Topological defect-propelled swimming of nematic colloids.

Topological defects on colloids rotating in nematic liquid crystals form far-from-equilibrium structures that perform complex swim strokes in which the defects periodically extend, depin, and contract. These defect dynamics propel the colloid, generating translation from rotation. The swimmer's speed and direction are determined by the topological defect's polarity and extent of elongation. Defect elongation is controlled by a rotating external magnetic field, allowing control over particle trajectories. The swimmers' translational motion relies on broken symmetries associated with lubrication forces between the colloid and the bounding surfaces, line tensions associated with the elongated defect, and anisotropic viscosities associated with the defect elongation adjacent to the colloid. The scattering or effective pair interaction of these swimmers is highly anisotropic, with polarization-dependent dimer stability and motion that depend strongly on entanglement and sharing of their extended defect structures. This research introduces transient, far-from-equilibrium topological defects as a class of virtual functional structures that generate modalities of motion and interaction.

Experimental and theoretical studies of the fluid elasticity on the motion of macroscopic models of active helical swimmers

This work presents experimental and theoretical studies on the locomotion of helical artificial swimmers at low Reynolds number in both Newtonian and viscoelastic ambient liquids. We examine the effect of fluid elasticity on the propulsive force and torque on the body and speed velocity of the swimmer in terms of two physical parameters: Deborah number (De) and Strouhal number (Sh). For this end, some experiments with prototype microorganisms in creeping flow motion are conducted. In the experiments, a macroscopic swimmer that propels itself by mimicking helical flagella are developed and tested. Three swimming models propelled by a helical tail with different wavelengths are investigated, and their motions examined for both cases: when the ambient solvent is a pure Newtonian viscous fluid and when the base fluid is an elastic polymeric solution. In addition, we also apply the slender body theory and the method of regularized Stokeslet in order to calculate theoretically the force and torque, as function of the Strouhal number (Sh), produced by the helical swimmer moving in a Newtonian fluid. The theoretical results are compared with experimental data, and a very good agreement is observed especially for higher values of Sh within the error bars of the experimental data. In the case of a non-Newtonian base fluid, the flow problem of an Oldroyd-B elastic fluid is solved numerically using a computational code based on a finite element method. The helical swimmer propulsive velocity is calculated in terms of the elastic parameter Deborah number and also compared with the experimental observation when the base fluid is non-Newtonian. It is shown experimentally that the swimming speed increases as the elastic effect in the base fluid increases until a critical Deborah number O(1), when the velocity saturates for a constant value within the experimental error bars. The velocity anisotropy measured experimentally by the ratio of the swimmer speed in two different directions is insensitive to the elastic effect in the base fluids. We complete our discussion on the helical swimmers motion in creeping flow by presenting a comparison between predictions of the speed velocity given by finite elements simulations using an Oldroyd-B model for the base elastic fluid and experimental data. The agreement between the two sets of results is very good within the experimental error bars for the elastic parameter varying from 0 to 2. It may be remarked, however, that while the experimental data tend to saturate at larger De, the simulations results seem to have a continuous increase according to the constitutive model used to describe the base elastic liquid.

Noise-Induced Aggregation of Swimmers in the Kolmogorov Flow

We investigate a model for the dynamics of ellipsoidal microswimmers in an externally imposed, laminar Kolmogorov flow. Through a phase-space analysis of the dynamics without noise, we find that swimmers favor either cross-stream or rotational drift, depending on their swimming speed and aspect ratio. When including noise, i.e., rotational diffusion, we find that swimmers are driven into certain parts of phase space, leading to a nonuniform steady-state distribution. This distribution exhibits a transition from swimmer aggregation in low-shear regions of the flow to aggregation in high-shear regions as the swimmer’s speed, aspect ratio, and rotational diffusivity are varied. To explain the nonuniform phase-space distribution of swimmers, we apply a weak-noise averaging principle that produces a reduced description of the stochastic swimmer dynamics. Using this technique, we find that certain swimmer trajectories are more favorable than others in the presence of weak rotational diffusion. By combining this information with the phase-space speed of swimmers along each trajectory, we predict the regions of phase space where swimmers tend to accumulate. The results of the averaging technique are in good agreement with direct calculations of the steady-state distributions of swimmers. In particular, our analysis explains the transition from low-shear to high-shear aggregation.

Dynamics of a helical swimmer crossing viscosity gradients

We study how helical swimmers move across a viscosity gradient, motivated by the need to understand how such heterogenous environments affect the motion of microorganisms. We find that the swimmer's speed can be either decreased or increased while crossing the viscosity gradient, depending on the orientation of the tail and the gradient of viscosity. Our experimental findings are sustained by good agreement with a resistive-force based model.

Active and Passive Motion in Complex pH‐Fields

AbstractWe create pH landscapes of increasing spatial complexity by placing ion exchange resin beads of different types and sizes in a closed cell featuring a negatively charged bottom substrate. We thus extend previous measurements in a chemically homogeneous background to investigations in chemically structured backgrounds, which evolve in time. We determine local pH gradients by photometry and study the resulting solvent flows along the substrate by tracking passive tracer particles. Analytical modelling of the dispersion of chemicals is possible for situations with dominantly diffusive transport. We then release phoretic swimmers in differently shaped pH fields and study their motion for selected examples. Catalytic Janus swimmers assembled in the wake of a mobile pH source form a modular swimmer showing a noise‐dominated trajectory. For standard modular swimmers with passive cargo, we identify well‐defined and reproducible swimming trajectory types at and around single pH sources. These include swimmer deflection and swing‐by maneuvers, swimmer trapping and escape, as well as circular orbits. More complicated paths result from combining the pH fields of multiple pH sources. Finally, we address swimmer‐swimmer interactions resulting from the superposition of their own pH fields. Our findings clearly demonstrate the high potential of chemically structured environments for swimmer steering. They can further be rationalized in a simple heuristic model considering the interplay of phoretic flows on different length and time scales and its influence on swimmer speed, orientation and emerging propulsion direction. In view of the vast range of possible combinations, our study has to remain preliminary. We anticipate, however, that it will aid the general understanding of transport experiments in pH‐driven systems and other types of phoresis and thus also help design novel and useful strategies for directed transport on the micro‐scale.

Lorentz Force-Driven Autonomous Janus Swimmers.

Autonomous swimmers have been intensively studied in recent years due to their numerous potential applications in many areas ranging from biomedicine to environmental remediation. Their motion is based either on different self-propulsion mechanisms or on the use of various external stimuli. Herein, the synergy between the ion flux around self-electrophoretic Mg/Pt Janus swimmers and an external magnetic field is proposed as an efficient alternative mechanism to power swimmers on the basis of the resulting Lorentz force. A strong magnetohydrodynamic effect is observed due to the orthogonal combination of magnetic field and spontaneous ionic currents, leading to an increase of the swimmer speed by up to 2 orders of magnitude. Furthermore, the trajectory of the self-propelled swimmers can be controlled by the orientation of the magnetic field, due to the presence of an additional torque force caused by a horizontal cation flux along the swimmer edges, resulting in predictable clockwise or anticlockwise motion. In addition, this effect is independent of the swimmer size, since a similar type of rotational motion is observed for macro- and microscale objects.

An underwater propulsion system with (Bi,Na,Ba) (Ti, Mn)O3 transducer

Underwater propulsion system using PZT transducer, as a new type of underwater propulsion system, has been studied. At that time, (Bi, Na, Ba)(Ti, Mn)O3, namely BNBTM lead-free piezoelectric ceramics were noticed. Through comparative experiments, lead-free BNBTM piezoelectric ceramics are not only friendly to the environment and the human body, but it is also that the material properties of BNBTM piezoelectric ceramics are more stable than that of PZT piezoelectric ceramics. Therefore, this research mainly discusses the feasibility of using a BNBTM transducer in the underwater propulsion system by the measurement of the system’s propulsion, BNBTM transducer’s admittance characteristic, and the speed of swimmer with the underwater propulsion system.

Shaping the gradients driving phoretic micro-swimmers: influence of swimming speed, budget of carbonic acid and environment

pH gradient-driven modular micro-swimmers are investigated as a model for a large variety of quasi-two-dimensional chemi-phoretic self-propelled entities. Using three-channel micro-photometry, we obtain a precise large field mapping of pH at a spatial resolution of a few microns and a pH resolution of sim 0.02~hbox {pH} units for swimmers of different velocities propelling on two differently charged substrates. We model our results in terms of solutions of the three-dimensional advection–diffusion equation for a 1:1 electrolyte, i.e. carbonic acid, which is produced by ion exchange and consumed by equilibration with dissolved hbox {CO}_{2}. We demonstrate the dependence of gradient shape and steepness on swimmer speed, diffusivity of chemicals, as well as the fuel budget. Moreover, we experimentally observe a subtle, but significant feedback of the swimmer’s immediate environment in terms of a substrate charge-mediated solvent convection. We discuss our findings in view of different recent results from other micro-fluidic or active matter investigations. We anticipate that they are relevant for quantitative modelling and targeted applications of diffusio-phoretic flows in general and artificial micro-swimmers in particular.Graphic

Trapping of swimmers in a vortex lattice.

We examine the motion of rigid, ellipsoidal swimmers subjected to a steady vortex flow in two dimensions. Numerical simulations of swimmers in a spatially periodic array of vortices reveal a range of possible behaviors, including trapping inside a single vortex and motility-induced diffusion across many vortices. While the trapping probability vanishes at a sufficiently high swimming speed, we find that it exhibits surprisingly large oscillations as this critical swimming speed is approached. Strikingly, at even higher swimming speeds, we find swimmers that swim perpendicular to their elongation direction can again become trapped. To explain this complex behavior, we investigate the underlying swimmer phase-space geometry. We identify the fixed points and periodic orbits of the swimmer equations of motion that regulate swimmer trapping inside a single vortex cell. For low to intermediate swimming speeds, we find that a stable periodic orbit surrounded by invariant tori forms a transport barrier to swimmers and can trap them inside individual vortices. For swimming speeds approaching the maximum fluid speed, we find instead that perpendicular swimmers can be trapped by asymptotically stable fixed points. A bifurcation analysis of the stable periodic orbit and the fixed points explains the complex and non-monotonic breakdown and re-emergence of swimmer trapping as the swimmer speed and shape are varied.

Rip Current Hazard Analysis

Zhang, K.; Zhang, M.C.; Leatherman, S.B., and Leatherman, S.P., 2020. Rip current hazard analysis. In: Malvarez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 969–973. Coconut Creek (Florida), ISSN 0749-0208.The effect of rip currents on swimmers was analyzed based on the drag force acting on swimmers and the power they need to generate to overcome the drag force. The drag force and power increase quadratically and cubically, respectively, with increase of rip current and swimming speeds. An additional 50% increase in rip current speed above swimmer's speed results in a 125% increase in drag force, requiring a 238% increase in power by the swimmer to overcome the additional drag. Hence, even rip currents of low velocity can be dangerous and swimming against the current should be avoided.

Optimal motion of triangular magnetocapillary swimmers.

A system of ferromagnetic particles trapped at a liquid-liquid interface and subjected to a set of magnetic fields (magnetocapillary swimmers) is studied numerically using a hybrid method combining the pseudopotential lattice Boltzmann method and the discrete element method. After investigating the equilibrium properties of a single, two, and three particles at the interface, we demonstrate a controlled motion of the swimmer formed by three particles. It shows a sharp dependence of the average center-of-mass speed on the frequency of the time-dependent external magnetic field. Inspired by experiments on magnetocapillary microswimmers, we interpret the obtained maxima of the swimmer speed by the optimal frequency centered around the characteristic relaxation time of a spherical particle. It is also shown that the frequency corresponding to the maximum speed grows and the maximum average speed decreases with increasing interparticle distances at moderate swimmer sizes. The findings of our lattice Boltzmann simulations are supported by bead-spring model calculations.

Кінематичні характеристики техніки плавання кролем на спині кваліфікованих плавців з наслідками дитячого церебрального паралічу

Vasiliy BoskoPurpose: to determine kinematic characteristics of backstroke swimming technique of athletes with spastic cerebral palsy (CP). Material & Methods: 12 swimmers with consequences of cerebral palsy were involved in the experiment (level of sports qualification – master of sports and candidate of master of sports); Video shooting and computer video analysis of their technique of backstroke swimming; The obtained data were analyzed and generalized using the methods of mathematical statistics. Results: kinematic characteristics of the technique of backstroke swimming of disabled athletes with spastic diplegia and a hemiparetic form of CP, such as the body position of swimmer in water (angle of attack, angle of rotation of the trunk around the longitudinal axis), position and work the hands and feet of the swimmer (the angles of flexion the main joints and their movement), integral characteristics (cycle time, step, rate and ratio of these characteristics at a constant swimmer speed). Conclusions: determined biomechanical characteristics motions skilled swimmers with spastic CP forms, which indicate the specificity of their technique of backstroke swimming, so we recommend that you take into account the findings in the search for effective means and methods of sports training.

Emergent propagation modes of ferromagnetic swimmers in constrained geometries

Magnetic microswimmers, composed of hard and soft ferromagnets connected by an elastic spring, are modelled under low Reynolds number conditions in the presence of geometrical boundaries. Approaching a surface, the magneto-elastic swimmer's velocity increases and its trajectory bends parallel to the surface contour. Further confinement to form a planar channel generates new propagation modes as the channel width narrows, altering the magneto-elastic swimmer's speed, orientation, and direction of travel. Our results demonstrate that constricted geometric environments, such as occuring in microfluidic channels or blood vessels, may influence the functionality of magneto-elastic microswimmers for applications such as drug delivery.

水中ドルフィンキック時における人体周り流れの数値シミュレーション

Dolphin kick swimming is an underwater undulatory motion which is similar to the way dolphin and other cetaceans swim, and it's utilized after dives and turns in competitive swimming. Since in the international rules underwater limit is 15m which is 30% of 50m pool, this swimming technique has large effect on swimming records. Thus, it is essential to know and control fluid dynamics of dolphin kick swimming. In this paper, flow around human in dolphin kick swimming is simulated and the results are evaluated. To implement the simulation, dolphin kick movement is reproduced on computer by 3D model of male swimmer and changes of 5 joint angles are captured from the video footage, and the flow around swimmer model is computed by means of a moving grid finite volume method. This computational approach completely fulfills geometric conservation laws, so that moving boundary problems become resolvable. Also, a moving computational domain method actualizes unrestricted move of swimmer model. Furthermore, coupling of these methods and kinematics allows swimmer model to dynamically accelerate and decelerate by the forces applied to itself. The result shows that most of the thrust is produced in down-kick, and the ring vortex is generated in the wake, which appears in practical dolphin kick swimming. And the speed of swimmer model agrees with the speed of swimmer in the video footage.

Graphene Jet Nanomotors in Remote Controllable Self-Propulsion Swimmers in Pure Water.

A remote controllable working graphite nanostructured swimmer based on a graphene jet nanomotor has been demonstrated for the first time. Graphite particles with pyramidal-like morphologies were fabricated by the creation of suitable defects in wide high-purity graphite flakes followed by a severe sonication. The particles were able to be self-exfoliated in water after Na intercalation between the graphene constituents. The self-exfoliation resulted in jet ejection of graphene flakes from the end of the swimmers (with speeds as high as ∼7000 m/s), producing a driving force (at least ∼0.7 L (pN) where L (μm) is swimmer size) and consequently the motion of the swimmer (with average speed of ∼17-40 μm/s). The jet ejection of the graphene flakes was assigned to the explosion of H2 nanobubbles produced between the Na intercalated flakes. The direction of motion of the swimmers equipped with TiO2 nanoparticles (NPs) can be controlled by applying a magnetic field in the presence of UV irradiation (higher UV intensity, lower radius of rotation). In fact, the negative surface charge of the graphene flakes of the swimmers increased by UV irradiation due to transferring the photoexcited electrons of TiO2 NPs into the flakes. Because of higher production of H2 nanobubbles under UV irradiation, the speed of swimmers exposed to UV light significantly increased. In contrast, UV irradiation with various intensities could not affect total distance traversed by the self-exfoliated swimmers having the same initial sizes. These confirmed the mass ejection mechanism for motion of the swimmers. The self-exfoliation of swimmers (and so their motion) occurred only in water (and not, e.g., in organic solutions). Such swimmers promise the design of remote controllable nanovehicles with the capability of initiating and/or improving their operations in response to environmental changes in order to realize broad ranges of versatile and fantastic nanotechnology-based applications.

A study of self-propelled elastic cylindrical micro-swimmers using modeling and computation

We study propulsion of micro-swimmers in 3D creeping flow. The swimmers are assumed to be made of elastic cylindrical hollow tubes. The swimming is generated by the contractions of the tube's elastic membrane walls producing a traveling wave in the form of a “step-function” traversing the swimmer from right to left, propelling the swimmer from left to right. The problem is motivated by medical applications such as drug delivery. The influence of several non-dimensional design parameters on the velocity of the swimmer is investigated, including the swimmer aspect ratio, and the amplitude of the traveling wave relative to the swimmer radius. An immersed boundary method based on a finite element method approach is successfully combined with an elastic spring network model to simulate the two-way fluid–structure interaction coupling between the elastic cylindrical tube and the flow of a 3D viscous, incompressible fluid. To gain a deeper insight into the influence of various parameters on the swimmer speed, a reduced 1D fluid–structure interaction model was derived and validated. It was found that fast swimmers are those with large tube aspect ratios, and with the amplitude of the traveling wave which is roughly 50% of the reference swimmer radius. It was shown that the speed of our “optimal swimmer” is around 1.5 swimmer lengths per second, which is at the top of the class of all currently manufactured micro-swimmers swimming in low Reynolds number flows ( Re = 10 − 6 ), reported in [11] .

Gait and speed selection in slender inertial swimmers.

Inertial swimmers use flexural movements to push water and generate thrust. We quantify this dynamical process for a slender body in a fluid by accounting for passive elasticity and hydrodynamics and active muscular force generation and proprioception. Our coupled elastohydrodynamic model takes the form of a nonlinear eigenvalue problem for the swimming speed and locomotion gait. The solution of this problem shows that swimmers use quantized resonant interactions with the fluid environment to enhance speed and efficiency. Thus, a fish is like an optimized diode that converts a prescribed alternating transverse motion to forward motion. Our results also allow for a broad comparative view of swimming locomotion and provide a mechanistic basis for the empirical relation linking the swimmer's speed U, length L, and tail beat frequency f, given by U/L ~ f [Bainbridge R (1958) J Exp Biol 35:109-133]. Furthermore, we show that a simple form of proprioceptive sensory feedback, wherein local muscle activation is function of body curvature, suffices to drive elastic instabilities associated with thrust production and leads to a spontaneous swimming gait without the need for a central pattern generator. Taken together, our results provide a simple mechanistic view of swimming consistent with natural observations and suggest ways to engineer artificial swimmers for optimal performance.