Swimming Dynamics Research Articles

Performance of a Helical Microswimmer Traversing a Discrete Viscoelastic Network with Dynamic Remodeling

Microorganisms often navigate a complex environment composed of a viscous fluid with suspended microstructures such as elastic polymers and filamentous networks. These microstructures can have similar length scales to the microorganisms, leading to complex swimming dynamics. Some microorganisms secrete enzymes that dynamically change the elastic properties of the viscoelastic networks through which they move. In addition to biological organisms, microrobots have been engineered with the goals of mucin gel penetration or dissolving blood clots. In order to gain insight into the coupling between swimming performance and network remodeling, we used a regularized Stokeslet boundary element method to compute the motion of a microswimmer consisting of a rotating spherical body and counter-rotating helical flagellum. The viscoelastic network is represented by a network of points connected by virtual elastic linkages immersed in a viscous fluid. Here, we model the enzymatic dissolution of the network by bacteria or microrobots by dynamically breaking elastic linkages when the cell body of the swimmer falls within a given distance from the link. We investigate the swimming performance of the microbes as they penetrate and move through networks of different material properties, and also examine the effect of network remodeling.

An inertial mechanism behind dynamic station holding by fish swinging in a vortex street

Many aquatic and aerial animal species are known to utilise their surrounding flow field and/or the induced flow field of a neighbour to reduce their physical exertion, however, the mechanism by which such benefits are obtained has remained elusive. In this work, we investigate the swimming dynamics of rainbow trout in the wake of a thrust-producing oscillating hydrofoil. Despite the higher flow velocities in the inner region of the vortex street, some fish maintain position in this region, while exhibiting an altered swimming gait. Estimates of energy expenditure indicate a reduction in the propulsive cost when compared to regular swimming. By examining the accelerations of the fish, an explanation of the mechanism by which energy is harvested from the vortices is proposed. Similar to dynamic soaring employed by albatross, the mechanism can be linked to the non-equilibrium hydrodynamic forces produced when fish encounter the cross-flow velocity generated by the vortex street.

Formation of a strong negative wake behind a helical swimmer in a viscoelastic fluid

We investigate the effects of helical swimmer shape (i.e. helical pitch angle and tail thickness) on swimming dynamics in a constant viscosity viscoelastic (Boger) fluid via a combination of particle tracking velocimetry, particle image velocimetry and three-dimensional simulations of the finitely extensible nonlinear elastic model with Peterlin approximation (FENE-P). The 3D-printed helical swimmer is actuated in a magnetic field using a custom-built rotating Helmholtz coil. Our results indicate that increasing the swimmer tail thickness and pitch angle enhances the normalized swimming speed (i.e. ratio of swimming speed in the Boger fluid to that of the Newtonian fluid). Strikingly, unlike the Newtonian fluid, the viscoelastic flow around the swimmer is characterized by formation of a front–back flow asymmetry that is characterized by a strong negative wake downstream of the swimmer's body. Evidently, the strength of the negative wake is inversely proportional to the normalized swimming speed. Three-dimensional simulations of the swimmer with the FENE-P model with conditions that match those of experiments, confirm formation of a similar front–back flow asymmetry around the swimmer. Finally, by developing an approximate force balance in the streamwise direction, we show that the contribution of polymer stresses in the interior region of the helix may provide a mechanism for swimming enhancement or diminution in the viscoelastic fluid.

Galvanotaxis of ciliates: spatiotemporal dynamics of Coleps hirtus under electric fields

Galvanotaxis describes the functional response of organisms to electric fields. In ciliates, the electric field influences the electrophysiology, and thus, the cilia beat dynamics. This leads to a change of the swimming direction toward the cathode. The dynamical response to electric fields of Coleps hirtus has not been studied since the observations of Verworn in 1890 Pflüger Arch. 46 267–303. While galvanotaxis has been studied in other ciliates, C. hirtus exhibit properties not found elsewhere, such as biomineralization processes of alveolar plates with impact on the intracellular calcium regulation and a bimodal resting membrane potential, which leads to unique electrophysiological driven bimodal swimming dynamics. Here, we statistically analyze the galvanotactic dynamics of C. hirtus by automated cell tracking routines. We found that the number of cells that show a galvanotactic response, increases with the increase of the applied electric field strength with a mean at about 2.1 V cm−1. The spatiotemporal swimming dynamics change and lead to a statistical increase of linear elongated cell trajectories that point toward the cathode. Further, the increase of the electric fields decreases the mean velocity variance for electric fields larger than about 1.3 V cm−1, while showing no significant change in the absolute velocity for any applied electric field. Fully functional galvanotactic responses were observed at a minimum extracellular calcium concentration of about 5 μM. The results add important insights to the current understanding of cellular dynamics of ciliates and suggest that the currently accepted model lacks the inclusion of the swimming dynamics and the complex calcium regulatory system of the cell. The results of this study not only extend the fundamental understanding of current physical models for galvanotaxis and C. hirtus dynamics, but also open possibilities for technical applications, such as biosensors or microrobots in the future.

Laterally biased diffusion of males of the water flea Daphnia magna.

The water flea, Daphnia magna, is a representative zooplankton that lives in freshwater environments. It primarily propagates via asexual reproduction in normal and healthy environmental conditions. Unsuitable environmental conditions induce D. magna to change its mode of reproduction from asexual to sexual reproduction. During sexual reproduction, D. magna produces special tough eggs (resting eggs) that can survive severe environmental conditions. Despite an increase in our understanding of their mating behavior, the sex-specific characteristics of swimming behavior among daphnid species are poorly understood. In this study, we analysed the swimming patterns and dynamics of female and male adult D. magna using computer modeling. Males displayed laterally biased diffusion in contrast to the homogeneous, nondirectional diffusion of females. Computer modeling analysis using a discrete-time Markov chain simulation, in which the frequencies of turning behavior were evaluated as probability distributions, explained the greater diffusion of males in the horizontal direction. We presumed that high diffusion in the horizontal direction would increase the probability of encountering a distant mate. Our findings suggest that male D. magna increases genotypic heterogeneity by effectively selecting certain motion parameters.

Force and torque-free helical tail robot to study low Reynolds number micro-organism swimming.

Helical propulsion is used by many micro-organisms to swim in viscous-dominated environments. Their swimming dynamics are relatively well understood, but a detailed study of the flow fields is still needed to understand wall effects and hydrodynamic interactions among swimmers. In this letter, we describe the development of an autonomous swimming robot with a helical tail that operates in the Stokes regime. The device uses a battery-based power system with a miniature motor that imposes a rotational speed on a helical tail. The speed, direction, and activation are controlled electronically using an infrared remote control. Since the robot is about 5 cm long, we use highly viscous fluids to match the Reynolds number, Re, to be less than 0.1. Measurements of swimming speeds are conducted for a range of helical wavelengths, λ, head geometries, and rotation rates, ω. We provide comparisons of the experimental measurements with analytical predictions derived from resistive force theory. This force and torque-free neutrally buoyant swimmer mimics the swimming strategy of bacteria more closely than previously used designs and offers a lot of potential for future applications.

Dynamic Modeling of Magnetic Helical Microrobots

Magnetic helical microrobots driven by low-strength rotating magnetic fields have found wide applications, particularly in biomedical research. The motion dynamics of magnetic helical microrobots is critical for their intelligent control and for performing tasks in complex environments. These microrobots can convert rotational motion into translational motion along their central axis. Many factors contribute to their swimming dynamics, such as the geometry of the helix, the properties of the coated magnetic layer, the viscosity of the fluid, and the wettability of the helix in the fluid. In this letter, we establish a comprehensive dynamic model to analyze the swimming properties of magnetic helical microrobots that consist of a rigid helical flagellum, at low Reynolds numbers. The influence of different designs of this kind of magnetic helical microrobots on their swimming velocity, step-out frequency, and maximum velocity is analyzed comprehensively, providing valuable guidance for the design of helical microrobots for different applications. Our results are supported by a number of experimental studies.

Physical models and vortex dynamics of swimming and flying: a review

Physical models and vortex dynamics of swimming and flying: a review

Reevaluating hydrodynamic performance of Late Triassic–Early Jurassic ammonoid shells with a 1D trajectory model

Biomechanical analyses provide unique insights on state shifts in the ecology of extinct communities. Ammonoids present a compelling case study for coupling biomechanical analysis with ecology given their robust fossil record of external conchs. We present a trajectory model to evaluate hydrodynamical advantages and challenges associated with ammonoid conch form. The model is a one-dimensional calculation estimating the dynamic feedbacks between different components of an ammonite’s motion including thrust, drag, acceleration, and distance traveled. Computational fluid dynamics simulations were performed on eleven different ammonoid conch morphotypes and integrated into a mathematical model to analyze the dynamics of swimming across a combination of conch diameters (5, 10, and 20 cm) and jet rhythms (a single jet or series of three pulses). We compared the efficacy of short-term bursts of motion to that of long-term cruising and found: inflated shapes (i.e., spherocones) offer the fastest short-term motion, but at the greatest costs; heavily streamlined shapes (i.e., platycones) offer long cruise distances, but with ineffective short-term motion; and visibly-coiled shapes (i.e., serpenticones) appear to offer intermediate performance in both locomotion styles. Size is critical in ranking the performance of different conch shapes in both locomotion styles because ranking is determined predominantly by the amount of thrust an animal is capable of generating. With increasing size, Reynolds number increases and the effects of second-order morphological characters become more pronounced and alter the performance ranking of conchs. Finally, we present a visual analysis of the flow regimes and shape details that may drive these hydrodynamic consequences. We speculate that serpenticone morphologies capitalized on these subtleties with a morphology that provided reasonably high-speed swimming at small sizes relevant to juveniles while maintaining relatively efficient coasting locomotion at the larger sizes relevant to adult animals. We highlight the ubiquitous serpenticones of the Early Jurassic as a case study for applying biomechanical data to a paleoecological context. The broad range of morphotypes expressed by ammonoids in the Late Triassic is dramatically pared down during the End Triassic extinction. In the few million years following the extinction, ammonoids diversify into a suite of shapes with a more restricted range of locomotor performance, and only much later is the full range of morphology recovered.

Chemical design of self-propelled Janus droplets

Chemical design of self-propelled Janus droplets

Swimming dynamics of a self-propelled droplet

Chemically active droplets often show intriguing self-propulsion behaviour in a surfactant solution. The drop motion is controlled by the nonlinear coupling among chemical transport in the bulk fluid, consumption of surfactant at the drop surface, and the fluid flow driven by the self-generated Marangoni stress. To quantify the underlying hydrodynamics, this work investigates the swimming motion of a two-dimensional drop that is determined by two dimensionless parameters, the Péclet number ($Pe$) and Damköhler number ($Da$). The weakly nonlinear analysis shows that near the instability threshold, the drop undergoes a supercritical bifurcation with velocity $U\sim \sqrt {Pe-Pe_c}$, where $Pe_c$ is the critical Péclet number for the onset of dipole mode. In the highly nonlinear regime, the drop transits from steady translation of pusher swimming to unsteady motion of mixed pusher–puller swimming along zigzaging trajectories of quadrangle and/or triangle waves. Mode decomposition shows that the zigzag motion is directly related to the interaction between the secondary wake of low surfactant concentration and the primary wake.

Effects of Currents on Human Freestyle and Breaststroke Swimming Analyzed by a Rigid-Body Dynamic Model

Swimming is a kind of complex locomotion that involves the interaction between the human body and the water. Here, to examine the effects of currents on the performance of freestyle and breaststroke swimming, a multi-body Newton-Euler dynamic model of human swimming is developed. The model consists of 18 rigid segments, whose shapes and geometries are determined based on the measured data from 3D scanning, and the fluid drags in consideration of the current are modeled. By establishing the interrelations between the fluid moments and the swimming kinematics, the underlying mechanism that triggers the turning of the human body is uncovered. Through systematic parametric analyses, the effects of currents on swimming performance (including the human body orientation, swimming direction, swimming speed, and propulsive efficiency) are elucidated. It reveals that the current would turn the human body counterclockwise in freestyle swimming, while clockwise in breaststroke swimming (which means that from the top view, the human trunk, i.e., the vector pointing from the bottom of feet to the top of the head, rotates counterclockwise or clockwise). Moreover, for both strokes, there exists a critical current condition, beyond which, the absolute swimming direction will be reversed. This work provides a wealth of fundamental insights into the swimming dynamics in the presence of currents, and the proposed modeling and analysis framework is promising to be used for analyzing the human swimming behavior in open water.

Planar Formation Control of a School of Robotic Fish: Theory and Experiments

This paper presents a nonlinear control design for the stabilization of parallel and circular motion in a school of robotic fish actuated with internal reaction wheels. The closed-loop swimming dynamics of the fish robots are represented by the canonical Chaplygin sleigh. They exchange relative state information according to a connected, undirected communication graph to form a system of coupled, nonlinear, second-order oscillators. Prior work on collective motion of constant-speed, self-propelled particles serves as the foundation of our approach. However, unlike a self-propelled particle, the fish robots follow limit-cycle dynamics to sustain periodic flapping for forward motion with time-varying speed. Parallel and circular motions are achieved in an average sense without feedback linearization of the agents’ dynamics. Implementation of the proposed parallel formation control law on an actual school of soft robotic fish is described, including system identification experiments to identify motor dynamics and the design of a motor torque-tracking controller to follow the formation torque control. Experimental results demonstrate a school of four robotic fish achieving parallel formations starting from random initial conditions.

A computational model of the swimming dynamics of a fish-like body in two dimensions

The undulatory swimming of a fish-like body is investigated by using an inviscid vortex shedding model in two dimensions. The body and separated vortices from the edge of the body are described by vortex sheets. We extend the model to include the forward and lateral motions as well as the net torque on the body and develop a new numerical method for a self-propelled deforming body. The numerical computation of the model successfully demonstrates the self-propulsion of the body and the formation of pairs of anti-rotating vortices shed from the body. At the starting stage, the body accelerates rapidly and turns the angle of incidence to some degree. The forward velocity reaches an asymptotic mean with oscillations, and the lateral velocity oscillates uniformly over time. The results of the model are in agreement with previous full numerical simulations. Furthermore, we examine the effects of the recoil motions of lateral translation and rotation of a body. The wake pattern and intensity significantly differ from the constraint of the recoil motions. It is found that free swimming requires less input power and affords more efficient energetic performance than the motions without recoil and with lateral translation. A body without recoil requires a large amount of power and is energetically inefficient. This shows that both recoil motions enhance the swimming efficiency.

Microswimming in viscoelastic fluids

The locomotion of microorganisms and spermatozoa in complex viscoelastic fluids is of critical importance in many biological processes such as fertilization, infection, and biofilm formation. Depending on their propulsion mechanisms, microswimmers display various responses to a complex fluid environment: increasing or decreasing their swimming speed and efficiency, modifying their propulsion kinematics and swimming gaits, and experiencing different hydrodynamic interactions with their surroundings. In this article, we review the fundamental physics of locomotion of biological and synthetic microswimmers in complex viscoelastic fluids. Starting from a continuum framework, we describe the main theoretical approaches developed to model microswimming in viscoelastic fluids, which typically rely on asymptotically-small dimensionless parameters. We then summarize recent progress on the mobility of single cells propelled by cilia, waving flagella and rotating helical flagella in unbounded viscoelastic fluids. We next briefly discuss the impact of other physical factors, including the micro-scale heterogeneity of complex biological fluids, the role of Brownian fluctuations of the microswimmers, the effect of polymer entanglement and the influence of shear-thinning viscosity. In particular, for solution of long polymer chains whose sizes are comparable to the radius of flagella, continuum models cannot be used and instead Brownian Dynamics for the polymers can predict the swimming dynamics. Finally, we discuss the effect of viscoelasticity on the dynamics of microswimmers in the presence of surfaces or external flows and its impact on collective cellular behavior.

A Numerical Model for the Analysis of the Locomotion of a Cownose Ray

Abstract Among all aquatic species, mantas and rays swim by flapping their pectoral fins; this motion is similar to other fishes in terms of efficiency, but it gives better maneuverability and agility in turning. The fin's motion is featured by a traveling wave going opposite to the forward motion, producing a force thanks to momentum conservation. This article aims at understanding the swimming dynamics of rays, focusing on energy efficiency. A computational fluid dynamics (CFD) model of the swimming motion of a cownose ray has been implemented in openfoam, simulating the acceleration of the fish from still to the steady-state velocity using an overset mesh. In this analysis, the one degree-of-freedom dynamics of forward swimming is solved together with the fluid velocity and pressure. The effect of frequency and wavelength of fin motion on thrust, power, and velocity has been investigated and an analysis of the vortices in the wake showed has been performed. The energy efficiency of a self-propelled body has been defined in a novel way and it has been calculated for different motion conditions. The results showed that batoid fishes swim with high energy efficiency and that they are a promising source of inspiration for biomimetic autonomous underwater vehicles.

Mathematical modeling of chemotaxis guided amoeboid cell swimming

Cells and microorganisms adopt various strategies to migrate in response to different environmental stimuli. To date, many modeling research has focused on the crawling-based Dictyostelium discoideum (Dd) cells migration induced by chemotaxis, yet recent experimental results reveal that even without adhesion or contact to a substrate, Dd cells can still swim to follow chemoattractant signals. In this paper, we develop a modeling framework to investigate the chemotaxis induced amoeboid cell swimming dynamics. A minimal swimming system consists of one deformable Dd amoeboid cell and a dilute suspension of bacteria, and the bacteria produce chemoattractant signals that attract the Dd cell. We use the mathematical amoeba model to generate Dd cell deformation and solve the resulting low Reynolds number flows, and use a moving mesh based finite volume method to solve the reaction–diffusion–convection equation. Using the computational model, we show that chemotaxis guides a swimming Dd cell to follow and catch bacteria, while on the other hand, bacterial rheotaxis may help the bacteria to escape from the predator Dd cell.

Numerical simulation of a one-dimensional flexible filament mimicking anguilliform mode of swimming using discrete vortex method

Using the discrete vortex method we perform numerical simulations of the Anguilliform mode of swimming dynamics of a one-dimensional flexible filament. Various parameters are varied to quantify the coefficient of thrust and swimming efficiency. We show that wake vortices are in a Benard--von Karman (BvK) configuration in the drag producing regime and rearrange to reverse-BVK (rBvK) when thrust producing. The resultant wake vortex distribution contour map and associated velocity field clarify differences between BvK in drag regime, the transition region, and rBvK in thrust regime. Optimal parameters for high thrust and swimming efficiency of two-dimensional flexible filaments are identified.

Stochastic force dynamics of the model microswimmer Chlamydomonasreinhardtii: Active forces and energetics.

We study the stochastic force dynamics of a model microswimmer (Chlamydomonas reinhardtii), using a combined experimental, theoretical, and numerical approach. While swimming dynamics have been extensively studied using hydrodynamic approaches, which infer forces from the viscous flow field, we directly measure the stochastic forces generated by the microswimmer using an optical trap via the photon momentum method. We analyze the force dynamics by modeling the microswimmer as a self-propelled particle, à la active matter, and analyze its energetics using methods from stochastic thermodynamics. We find complex oscillatory force dynamics and power dissipation on the order of 10^{6}k_{B}T/s(∼fW).

The ZE-Tunnel: An Affordable, Easy-to-Assemble, and User-Friendly Benchtop Zebrafish Swim Tunnel.

The popularity of zebrafish in both basic biological and biomedical research has led to an increased need for understanding their behavior. Locomotor behavior is an important outcome of different factors, such as specific genotypes or external stimuli that influence the nervous and musculoskeletal system. Locomotion can be studied by forced swimming in a swim tunnel, a device capable of generating a laminar water flow at different speeds in a chamber where zebrafish can be placed. However, commercially available swim tunnels are relatively expensive and in-house built systems are mostly presented without clear building instructions or proper validation procedures. In this study, we developed an alternative, cheap (<250 euro), and user-friendly, but customizable benchtop swim tunnel, called the "Zebrafish exercise-tunnel" (ZE-Tunnel). Detailed step-by-step instructions on how to construct the tunnel components, including the frame, mechanical, and electric components are given. The ZE-Tunnel was reliably used to exercise fish for prolonged periods and its performance was successfully validated by replicating previously published experiments on critical speed testing in zebrafish. Finally, implementation of behavioral video analysis using freely available motion-tracking software showed differences in swimming dynamics in the Chihuahua skeletal zebrafish mutant.