Stable Swimming Research Articles

Study on the effect of geometric shape on microswimmer upstream motion

The upstream motility of three microswimmer shapes (circular squirmer, squirmer rod, and elliptical squirmer) at the center of a Poiseuille flow is numerically investigated using the lattice Boltzmann method. Based on the stability and upstream ability, the swimming velocities and four motion states (stable motion, progressively unstable motion, unstable motion, and upstream failure) are summarized. The results show that the circular squirmer and squirmer rod are more stable than the elliptical squirmer; however, the elliptical squirmer has the greatest advantage in velocity and can swim up to twice as fast as the circular squirmer under the same conditions. The swimming type is also the key to influencing the motion state, which is reflected differently in the distinct microswimmer shapes. The increase in the Reynolds number (Re) and self-propelled strength (α) aggravates the motion instability; however, for elongated microswimmers, the aspect ratio (ε) plays a role in velocity rather than the motion state. Moreover, the upstream velocity of the pusher is always better than that of the puller, especially when Re increases. Notably, all microswimmers can maintain stable swimming when the preset velocity is twice the maximum velocity of the flow field. These findings can provide guidelines for the selection of design parameters and the appearance of microswimmers that resist complex incoming flows.

Uncovering loggerhead (Caretta caretta) navigation strategy in the open ocean through the consideration of their diving behaviour.

While scientists have been monitoring the movements and diving behaviour of sea turtles using Argos platform terminal transmitters for decades, the precise navigational mechanisms used by these animals remain an open question. Until now, active swimming motion has been derived from total motion by subtracting surface or subsurface modelled ocean currents, following the approximation of a quasi-two-dimensional surface layer migration. This study, based on tracking and diving data collected from 25 late-juvenile loggerhead turtles released from Reunion Island during their pre-reproductive migration, demonstrates the importance of considering the subsurface presence of the animals. Using a piecewise constant heading model, we investigate navigation strategy using daily time-at-depth distributions and three-dimensional currents to calculate swimming velocity. Our results are consistent with a map and compass strategy in which swimming movements follow straight courses at a stable swimming speed (approx. 0.5 m s-1), intermittently segmented by course corrections. This strategy, previously hypothesized for post-nesting green and hawksbill turtles, had never been observed in juvenile loggerheads. These results confirm a common open-ocean navigation mechanism across ages and species and highlight the importance of considering diving behaviour in most studies of sea turtle spatial ecology.

Environmental Adaptability of Legged Robots with Cutaneous Inflation and Sensation

In this article, a novel approach to enhance the maneuverability and adaptability of legged robots in challenging environments is proposed. This approach involves the integration of soft inflatable sensing skin, which provides additional mobile modes and environmental adaptability. The inflated skin's structural properties, such as buoyancy, volumed shape, and physical compliance, enable quadruped robots to extend their mobility to stable swimming and crawling modes. The inflated skin also offers physical protection through cushioning and backing effects, allowing robots to roll down stair‐like structures. Furthermore, the integration of tactile sensors provides the host robot with accurate and intuitive contact information, enabling increased environmental adaptability and responsive behavior. The robot can protect itself from impacts, detect and detour obstacles, and dynamically interact with its surrounding environment. Overall, the proposed approach offers a synergistic integration of soft inflatable sensing skin and tactile sensors to enhance legged robots’ maneuverability and adaptability in harsh environments. The integrated system enables robots to achieve challenging missions, extending their capabilities beyond conventional locomotive modes. The proposed approach has significant potential applications in fields such as search and rescue, surveillance, and exploration.

Slippery rheotaxis: new regimes for guiding wall-bound microswimmers

The near-surface locomotion of microswimmers under the action of background flows has been studied extensively, whereas the intervening effects of complex surface properties remain hitherto unknown. Intending to delineate the shear-driven dynamics near a planar slippery wall, we adopt the squirmer model of microswimmers and employ a three-dimensional analytical-numerical framework in bispherical coordinates. It is interpreted that both the self-propulsion and the external shear flow are redistributed due to hydrodynamic slippage, followed by modulations in the thrust torque on the microswimmer. Phase portraits of the quasi-steady dynamics indicate that the stable upstream swimming states, known as ‘rheotaxis’, are significantly modulated by the slip length compared with the no-slip case. For puller swimmers, an intricate interplay among the modulated interfacial friction near a slippery surface, velocity gradients of the shear flow and the strength of the squirmer parameter promotes a critical shear rate beyond which a wide range of new rheotactic states exist. Consequently, an escaping microswimmer may exhibit rheotaxis or an existing rheotactic state annihilates due to crashing. Although stable states are absent for pushers without steric interactions, transitions from escaping and undamped oscillations to ‘rheotaxis’ occur in the presence of wall repulsion, but only until the other characteristics are overwhelmed by escape due to enhanced shear. Disclosing the ability of hydrodynamic slippage in broadening the scope of migration against a background flow for a wide range of parameters, the present work paves the way for investigations on the entrapment of microswimmers near complex pathways or sorting using selective rheotaxis.

Research and Experiment on a Bionic Fish Based on High-Frequency Vibration Characteristics.

This paper takes the high-frequency vibration characteristics of a bionic robot fish as the research object. Through research on the vibration characteristics of a bionic fish, we quantified the role of voltage and beat frequency in high-speed and stable swimming. We proposed a new type of electromagnetic drive. The tail is made of 0° silica gel to simulate the elastic characteristics of fish muscles. We completed a series of experimental studies on the vibration characteristics of biomimetic robotic fish. Through the single-joint fishtail underwater experiment, the influence of vibration characteristics on parameters during swimming was discussed. In terms of control, the central mode generator control method (CPG) control model is adopted, and a replacement layer is designed in combination with particle swarm optimization (PSO). By changing the elastic modulus of the fishtail, the fishtail resonates with the vibrator, and the swimming efficiency of the bionic fish is improved. Finally, through the prototype experiment, it is found that the bionic robot fish can achieve high-speed swimming through high-frequency vibration.

Clostridioides difficile minimal nutrient requirements for flagellar motility.

As many gastro-intestinal pathogens, the majority of Clostridioides difficile strains express flagella together with a complete chemotaxis system. The resulting swimming motility is likely contributing to the colonization success of this important pathogen. In contrast to the well investigated general energy metabolism of C. difficile, little is known about the metabolic requirements for maintaining the ion motive force across the membrane, which in turn powers the flagellar motor. We studied here systematically the effect of various amino acids and carbohydrates on the swimming velocity of C. difficile using video microscopy in conjunction with a software based quantification of the swimming speed. Removal of individual amino acids from the medium identified proline and cysteine as the most important amino acids that power swimming motility. Glycine, which is as proline one of the few amino acids that are reduced in Stickland reactions, was not critical for swimming motility. This suggests that the ion motive force that powers the flagellar motor, is critically depending on proline reduction. A maximal and stable swimming motility was achieved with only four compounds, including the amino acids proline, cysteine and isoleucine together with a single, but interchangeable carbohydrate source such as glucose, succinate, mannose, ribose, pyruvate, trehalose, or ethanolamine. We expect that the identified "minimal motility medium" will be useful in future investigations on the flagellar motility and chemotactic behavior in C. difficile, particularly for the unambiguous identification of chemoattractants.

Effects of Bionic Bone Flexibility on the Hydrodynamics of Pectoral Fins

Compared with traditional underwater equipment powered by propeller, the manta-ray-inspired vehicle with MPF mode (Median fin/paired fin) has the advantages of stable swimming attitude, high maneuverability, and low noise, etc. As one of the sources of advancing power when the manta-ray-inspired vehicle swims, the flexible deformation of the pectoral fin is an important factor affecting the hydrodynamic performance. In this paper, a mechanical analysis of the two-dimensional flexible pectoral fin using thin wing theory shows that the main factor affecting the hydrodynamic force of the two-dimensional flexible pectoral fin is the level of curvature of the pectoral fin chordal section. By designing a two-stage bionic skeleton at the leading and rear edges of the manta-ray-inspired vehicle, the root–tip section width of the bionic skeleton is used to characterize the level of the bionic pectoral fin’s flexibility, and a tensiometer is used to quantitatively measure the level of flexibility. The root-to-tip ratio of the cross-section was varied to obtain different levels of pectoral fin flexibility, and the hydrodynamic properties of the pectoral fins during flapping were measured using a force sensor and normalized for analysis. The experimental results show that the reduction of the flexibility of the leading edge and the increase of the flexibility of the rear edge are beneficial to the improvement of the thrust performance, and the experimental results are the same as the distribution of the skeletal flexibility in real organisms. Fitting curves of the pectoral fins’ relative flexibility and the normalized thrust/lift show that the flexibility of the pectoral fins has a significant effect on its hydrodynamic force, and a stiffer leading edge and a softer rear edge can improve the hydrodynamic characteristics of the manta-ray-inspired vehicle. Phase differences interacting with flexibility can also enhance bionic pectoral fins’ dynamic properties within 10~30 degree.

Hydrodynamic Behavior of Self-Propelled Particles in a Simple Shear Flow.

The hydrodynamic properties of a squirmer type of self-propelled particle in a simple shear flow are investigated using the immersed boundary-lattice Boltzmann method in the range of swimming Reynolds number 0.05 ≤ Res ≤ 2.0, flow Reynolds number 40 ≤ Rep ≤ 160, blocking rate 0.2 ≤ κ ≤ 0.5. Some results are validated by comparing with available other results. The effects of Res, Rep and κ on the hydrodynamic properties of squirmer are discussed. The results show that there exist four distinct motion modes for the squirmer, i.e., horizontal mode, attractive oscillation mode, oscillation mode, and chaotic mode. Increasing Res causes the motion mode of the squirmer to change from a constant tumbling near the centerline to a stable horizontal mode, even an oscillatory or appealing oscillatory mode near the wall. Increasing the swimming intensity of squirmer under the definite Res will induce the squirmer to make periodic and stable motion at a specific distance from the wall. Increasing Rep will cause the squirmer to change from a stable swimming state to a spiral motion or continuous rotation. Increasing κ will strengthen the wall’s attraction to the squirmer. Increasing swimming intensity of squirmer will modify the strength and direction of the wall’s attraction to the squirmer if κ remains constant.

Morphological differences in tardigrade spermatozoa induce variation in gamete motility

BackgroundFertilization is an event at the beginning of ontogeny. Successful fertilization depends on strategies for uniting female and male gametes that developed throughout evolutionary history. In some species of tardigrades, investigations of reproduction have revealed that released spermatozoa swim in the water to reach a female, after which the gametes are stored in her body. The morphology of the spermatozoa includes a coiled nucleus and a species-specific-length acrosome. Although the mating behaviour and morphology of tardigrades have been reported, the motility of male gametes remains unknown. Here, using a high-speed camera, we recorded the spermatozoon motilities of two tardigrades, Paramacrobiotus sp. and Macrobiotus shonaicus, which have longer and shorter spermatozoa, respectively.ResultsThe movement of spermatozoa was faster in Paramacrobiotus sp. than in M. shonaicus, but the beat frequencies of the tails were equal, suggesting that the long tail improved acceleration. In both species, the head part consisting of a coiled nucleus and an acrosome did not swing, in contrast to the tail. The head part of Paramacrobiotus sp. spermatozoa swung harder during turning; in contrast, the tail of M. shonaicus moved more widely than the head. Finally, after mating, the spermatozoa that reached the female aggregated around the cloaca while waiting to enter her body in both tested species.ConclusionsThis study provides results for the first observations and analyses of individual spermatozoon motility in tardigrades. A comparison of the spermatozoon movements of the two tardigrades suggested that the motilities of the male gametes were affected by morphological differences, where the longer spermatozoa swam faster and the shorter ones showed more stable swimming. Swimming was mainly induced by tail movement, but the long head of Paramacrobiotus sp. spermatozoa might be especially important for turning. In addition, observations of mated female cloacae suggested that the head parts of the spermatozoa were required for aggregation around the cloaca of a mated female.

How inertial lift affects the dynamics of a microswimmer in Poiseuille flow

The transport of motile microorganisms is strongly influenced by fluid flows that are ubiquitous in biological environments. Here we demonstrate the impact of fluid inertia. We analyze the dynamics of a microswimmer in pressure-driven Poiseuille flow, where fluid inertia is small but non-negligible. Using perturbation theory and the reciprocal theorem, we show that in addition to the classical inertial lift of passive particles, the active nature generates a ‘swimming lift’, which we evaluate for neutral and pusher/puller-type swimmers. Accounting for fluid inertia engenders a rich spectrum of complex dynamics including bistable states, where tumbling coexists with stable centerline swimming or swinging. The dynamics is sensitive to the swimmer’s hydrodynamic signature and goes well beyond the findings at vanishing fluid inertia. Our work will have non-trivial implications on the transport and dispersion of active suspensions in microchannels.

A Manta Ray-Inspired Biosyncretic Robot with Stable Controllability by Dynamic Electric Stimulation

Biosyncretic robots, which are new nature-based robots in addition to bionic robots, that utilize biological materials to realize their core function, have been supposed to further promote the progress in robotics. Actuation as the main operation mechanism relates to the robotic overall performance. Therefore, biosyncretic robots actuated by living biological actuators have attracted increasing attention. However, innovative propelling modes and control methods are still necessary for the further development of controllable motion performance of biosyncretic robots. In this work, a muscle tissue-based biosyncretic swimmer with a manta ray-inspired propelling mode has been developed. What is more, to improve the stable controllability of the biosyncretic swimmer, a dynamic control method based on circularly distributed multiple electrodes (CDME) has been proposed. In this method, the direction of the electric field generated by the CDME could be real-time controlled to be parallel with the actuation tissue of the dynamic swimmer. Therefore, the instability of the tissue actuation induced by the dynamic included angle between the tissue axis and electric field direction could be eliminated. Finally, the biosyncretic robot has demonstrated stable, controllable, and effective swimming, by adjusting the electric stimulation pulse direction, amplitude, and frequency. This work may be beneficial for not only the development of biosyncretic robots but also other related studies including bionic design of soft robots and muscle tissue engineering.

Instability caused swimming of ferromagnetic filaments in pulsed field

Magnetic filaments driven by external magnetic field are an interesting topic of research in-terms of the possible bio-medical applications. In this paper, we investigated the applicability of using ferromagnetic filaments as micro swimmers both experimentally and numerically. It was found that applying a pulse wave field profile with a duty cycle of 30% induced experimentally observable swimming, which is similar to the breast stroke of micro algae. Good agreement with numerical simulations was found. Moreover, for stable continuous swimming, an initial filament shape is required to avoid transition to the structurally preferred non-swimming S-like mode.

Design and analysis of a novel tendon-driven continuum robotic dolphin

In this paper, a novel continuum robotic dolphin termed ‘ConRoDolI’ is proposed and developed. The biomimetic robot features dual tendon driving continuum mechanisms that are utilized to replicate the twisting and bending motions of the dolphin’s caudal vertebrae and thoracic vertebrae. More importantly, a central pattern generator based kinematics is analyzed to yield stable dolphin-like swimming. In the meantime, the relationship between the backbone shape and both the tendon length as well as position and orientation are explored. Furthermore, multimodal swimming gaits are designed to pave the way for a three-dimensional (3D) swimming decoupling solution, involving forwarding swimming, multiple yaw patterns, and multiple pitch patterns. All of these endow the robotic dolphin with 3D maneuverability. Finally, extensive experiments demonstrate the feasibility of the proposed biomimetic mechatronic design and control approach. The forward swimming speed is 0.44 body lengths per second (BL/s). The steering radius of the robot is about 0.11 BL with an angular velocity of 10°/s and the diving speed is about 0.13 BL/s. The average propulsion efficiency is about 0.6 with the maximum is over 0.8. The obtained results shed light on the improvement of aquatic maneuverability associated with new-concept underwater vehicles.

DiffAqua

The computational design of soft underwater swimmers is challenging because of the high degrees of freedom in soft-body modeling. In this paper, we present a differentiable pipeline for co-designing a soft swimmer's geometry and controller. Our pipeline unlocks gradient-based algorithms for discovering novel swimmer designs more efficiently than traditional gradient-free solutions. We propose Wasserstein barycenters as a basis for the geometric design of soft underwater swimmers since it is differentiable and can naturally interpolate between bio-inspired base shapes via optimal transport. By combining this design space with differentiable simulation and control, we can efficiently optimize a soft underwater swimmer's performance with fewer simulations than baseline methods. We demonstrate the efficacy of our method on various design problems such as fast, stable, and energy-efficient swimming and demonstrate applicability to multi-objective design.

Hydraulic design criteria of the modified meander C-type fishway using the combined experimental and CFD models

Fishways' structure has been developed to mitigate the harmful effects of human-made structures such as dams and weirs on the migratory fish process as an essential part of the environmental cycle. In this study, a Modified Meander C-type Fishway (MMCF) was designed and analyzed based on a fish species movement capability. The proposed fishways' structural design follows the key features of the vertical slot fishways (VSF) structure and consists of eleven successive cylindrical pools connected through vertical slots. In the present study, physical and computational fluid dynamics were used to investigate the flow characteristics inside the cylindrical pools with designed radius (R) and vertical slots as the system's connectors. Different geometry scenarios were applied to the model, such as the slots' various dimensionless opening ratios (s/R = 0.1, 0.2, 0.3) with varying bed slope scenarios (5%, 10%, and 20%). The obtained results illustrated the dimensionless hydraulic design diagrams based on the dimensionless discharge parameter (Q⁎) as a critical parameter for designing and operating the fishways. Horizontal and vertical flow velocity distribution graphs were presented, which could be used to estimate a potential low-velocity field for each specific fish species. As a geometrical improvement scenario, the pool's average-depth parameter (d) was increased for each scenario using the designed vertical baffles adjusted at the pools' opening gate with different vertical slot's height scenarios (hb/R = 0, 0.1, 0.2). Studying the radial and tangential fluctuations of the turbulent flow inside the proposed fishway demonstrated the structure's performance to make a more stable swimming path for the fishes toward the upstream movement.

Magnetic Soft Robot With the Triangular Head–Tail Morphology Inspired By Lateral Undulation

In this article, extend the uses of a deformable structure of magnetic elastomer to develop a bio-inspired locomotion system for millimeter-scaled robots. As proposed in other researches, this material allows a possibility of the motor-less mechanism powered by magnetic field. The actuating mechanism of the robot mainly relies on the body deformation due to magnetic alignment. On the other hand, herein, the magnetic soft robot with the triangular head-tail morphology and sine-based magnetization utilizes a high degree of freedom provided by magnetic compliance for mobility in a form of lateral undulation. Under the oscillating magnetic field, dynamic torque primarily acts to the head, the tail passively waves, and the whole body propagates a series of lateral body-waves for self-propulsion in fluid, instead of pushing out surrounding fluid to make a swimming gait. We achieve the independent control of the laterally undulating robot in force-free swimming, and demonstrate its tunable body deformation to swim in various diameters of the fluid-filled tubes. A by-product of the undulation can transfer a force rate to swim through the fabric-media. By the increase of the actuating frequency, the undulating robot propels faster to retain a stable swimming in the flow. The versatilities of the robot with the proposed mechanism can be applied to serve the diverse purposes as a reliable and effective locomotion system with a minimal control. Particularly in biomedical applications, miniature soft robots with a potential mechanism for self-propulsion can contribute the great results to pursue minimally invasive treatments.

Fluid dynamics of a self-propelled biomimetic underwater vehicle with pectoral fins

Fluid dynamics of a self-propelled biomimetic underwater vehicle (BUV) with pectoral fins is investigated by an immersed boundary (IB) method. Typically, the BUV with a pair of pectoral fins starts from rest and attains a constant mean velocity as the mean longitudinal force is zero. The capability and accuracy of the IB method to deal with the interaction between the fluid and complex moving body are firstly validated. Then we carry out a parametric study to understand the effect of key governing parameters on the dynamic response of the BUV. It is found that with the increase of motion frequency or rolling amplitude, the pectoral fin propulsors can induce larger forward velocity so that the BUV takes less time to attain its stable periodic swimming state. Although the pectoral fin is a very complicated lifting surface, a linear relationship between forward Reynolds number (final swimming velocity is used as velocity scale) and frequency Reynolds number (product of motion frequency and fin chord length is used as velocity scale) can be established when the frequency Reynolds number is above a critical value. A linear relationship between forward Reynolds number and rolling amplitude is also found within the studied range of rolling amplitude. Furthermore, a small-density-ratio BUV is sensitive to the surrounding flow with more rapid evolution process of self-propulsion. Whereas, BUV with a large density ratio is more stable. The implications of the hydrodynamic analysis on the bio-inspired engineering design of BUV with pectoral fins are also discussed.

A transition to stable one-dimensional swimming enhances E. coli motility through narrow channels

Living organisms often display adaptive strategies that allow them to move efficiently even in strong confinement. With one single degree of freedom, the angle of a rotating bundle of flagella, bacteria provide one of the simplest examples of locomotion in the living world. Here we show that a purely physical mechanism, depending on a hydrodynamic stability condition, is responsible for a confinement induced transition between two swimming states in E. coli. While in large channels bacteria always crash onto confining walls, when the cross section falls below a threshold, they leave the walls to move swiftly on a stable swimming trajectory along the channel axis. We investigate this phenomenon for individual cells that are guided through a sequence of micro-fabricated tunnels of decreasing cross section. Our results challenge current theoretical predictions and suggest effective design principles for microrobots by showing that motility based on helical propellers provides a robust swimming strategy for exploring narrow spaces.

Biofilms at interfaces: microbial distribution in floating films.

Cellular motility is a key function guiding microbial adhesion to interfaces, which is the first step in the formation of biofilms. The close association of biofilms and bioremediation has prompted extensive research aimed at comprehending the physics of microbial locomotion near interfaces. We study the dynamics and statistics of microorganisms in a 'floating biofilm', i.e., a confinement with an air-liquid interface on one side and a liquid-liquid interface on the other. We use a very general mathematical model, based on a multipole representation and probabilistic simulations, to ascertain the spatial distribution of microorganisms in films of different viscosities. Our results reveal that microorganisms can be distributed symmetrically or asymmetrically across the height of the film, depending on their morphology and the ratio of the film's viscosity to that of the fluid substrate. Long-flagellated, elongated bacteria exhibit stable swimming parallel to the liquid-liquid interface when the bacterial film is less viscous than the underlying fluid. Bacteria with shorter flagella on the other hand, swim away from the liquid-liquid interface and accumulate at the free surface. We also analyze microorganism dynamics in a flowing film and show how a microorganism's ability to resist 'flow-induced-erosion' from interfaces is affected by its elongation and mode of propulsion. Our study generalizes past efforts on understanding microorganism dynamics under confinement by interfaces and provides key insights on biofilm initiation at liquid-liquid interfaces.

3-D Path Following of Helical Microswimmers With an Adaptive Orientation Compensation Model

Controlling magnetic microswimmers toward 3-D manipulation tasks has received considerable attention. Although related studies on manipulating helical microswimmers have been developed, stable closed-loop controls and accuracy swimming models should be still investigated. This article addresses the problem of 3-D path following for magnetically driven helical microswimmers with an adaptive-compensation scheme. The orientation-compensation model in the global coordinate frame is learned by radial basis function (RBF) networks trained with backpropagation algorithms, which is used to express the motion of the helical microswimmer in the presence of the weight of the swimmer and lateral disturbances from the boundary effects. A proxy-based sliding-mode control (PSMC) approach is developed to design stable controllers based on the kinematic error model. The effects of variable parameters and boundary effects are also considered. Experimental results including different paths in 3-D space validated the path following with submillimeter accuracy using the helical microswimmer. Note to Practitioners —This article is motivated by the issue of the following predefined paths for magnetically driven helical microswimmers in 3-D space. The proposed closed-loop controller employs the error model in 3-D space to formulate the control law according to an orientation-compensation model learned by neural networks. It is demonstrated that the helical microswimmer is able to follow different paths in 3-D space with submillimeter accuracy using the proposed control scheme.