Hydrodynamic attraction of swimming microorganisms by surfaces

Cells swimming in confined environments are attracted by surfaces. We measure the steady-state distribution of smooth-swimming bacteria (Escherichia coli) between two glass plates. In agreement with earlier studies, we find a strong increase of the cell concentration at the boundaries. We demonstrate theoretically that hydrodynamic interactions of the swimming cells with solid surfaces lead to their reorientation in the direction parallel to the surfaces, as well as their attraction by the closest wall. A model is derived for the steady-state distribution of swimming cells, which compares favorably with our measurements. We exploit our data to estimate the flagellar propulsive force in swimming E. coli.     

Theory of swimming filaments in viscoelastic media

Motivated by our desire to understand the biophysical mechanisms underlying the swimming of sperm in the non-Newtonian fluids of the female mammalian reproductive tract, we examine the swimming of filaments in the nonlinear viscoelastic upper convected Maxwell model. We obtain the swimming velocity and hydrodynamic force exerted on an infinitely long cylinder with prescribed beating pattern. We use these results to examine the swimming of a simplified sliding-filament model for a sperm flagellum. Viscoelasticity tends to decrease swimming speed, and changes in the beating patterns due to viscoelasticity can reverse swimming direction.     

Trypanosomes – versatile microswimmers

Evolution has generated a plethora of flagellate microswimmers. They populate all natural waters, from the deep sea to the ponds in our neighbourhood. But flagellates also thrive in the bodies of higher organisms, where they mostly remain undetected, but can also become pathogenic. Trypanosomes comprise a large group of mostly parasitic flagellates that cause many diseases, such as human sleeping sickness or the cattle plague nagana. We consider African trypanosomes as extremely versatile microswimmers, as they have to adapt to very diverse microenvironments. They swim efficiently in the blood of their mammalian hosts, but also in various tissue spaces and even in the human brain. Furthermore, in the transmitting tsetse fly, trypanosomes undergo characteristic morphological changes that are accompanied by amazing transitions between solitary and collective types of motion. In this review, we provide a basic introduction to trypanosome biology and then focus on the complex type of rotational movement that trypanosomes display. We relate their swimming performance to morphological parameters and the respective microenvironment, developing a contemporary view on the physics of trypanosome motility. The genetically programmed successions of life style-dependent motion patterns provide challenges and opportunities for interdisciplinary studies of microswimmers.     

Effective swimming strategies in low Reynolds number flows

The optimal strategy for a microscopic swimmer to migrate across a linear shear flow is discussed. The two cases, in which the swimmer is located at large distance, and in the proximity of a solid wall, are taken into account. It is shown that migration can be achieved by means of a combination of sailing through the flow and swimming, where the swimming strokes are induced by the external flow without need of internal energy sources or external drives. The structural dynamics required for the swimmer to move in the desired direction is discussed and two simple models, based respectively on the presence of an elastic structure, and on an orientation dependent friction, to control the deformations induced by the external flow, are analyzed. In all cases, the deformation sequence is a generalization of the tank-treading motion regimes observed in vesicles in shear flows. Analytic expressions for the migration velocity as a function of the deformation pattern and amplitude are provided. The effects of thermal fluctuations on propulsion have been discussed and the possibility that noise be exploited to overcome the limitations imposed on the microswimmer by the scallop theorem have been discussed.     

Swimming with an image

The hydrodynamic interactions of a swimming bacterium with a neighboring surface can cause it to swim in circles. For example, when E. coli is above a solid surface it had been observed to swim in a clockwise direction. By contrast we observe that, when swimming near a liquid-air interface, the sense of rotation is reversed. We quantitatively account for this through the hydrodynamic interaction of the bacterium with its own mirror image swimming on the opposite side of a perfect-slip boundary. The strength of the coupling is reduced for longer cells, where the torque is spread over a larger length, resulting in longer bacteria swimming in larger circles. We confirm this through precise video measurements of bacterial trajectories and orientations.     

Active Brownian motion tunable by light

Active Brownian particles are capable of taking up energy from their environment and converting it into directed motion; examples range from chemotactic cells and bacteria to artificial micro-swimmers. We have recently demonstrated that Janus particles, i.e.?gold-capped colloidal spheres, suspended in a critical binary liquid mixture perform active Brownian motion when illuminated by light. In this paper, we investigate in more detail their swimming mechanism, leading to active Brownian motion. We show that the illumination-borne heating induces a local asymmetric demixing of the binary mixture, generating a spatial chemical concentration gradient which is responsible for the particle's self-diffusiophoretic motion. We study this effect as a function of the functionalization of the gold cap, the particle size and the illumination intensity: the functionalization determines what component of the binary mixture is preferentially adsorbed at the cap and the swimming direction (towards or away from the cap); the particle size determines the rotational diffusion and, therefore, the random reorientation of the particle; and the intensity tunes the strength of the heating and, therefore, of the motion. Finally, we harness this dependence of the swimming strength on the illumination intensity to investigate the behavior of a micro-swimmer in a spatial light gradient, where its swimming properties are space-dependent.     

Rectification of swimming bacteria and self-driven particle systems by arrays of asymmetric barriers

We show that the recent experimental observation of the rectification of swimming bacteria in a system with an array of asymmetric barriers occurs due to the ballistic component of the bacteria trajectories introduced by the bacterial "motor." Each bacterium selects a random direction for motion and then moves in this direction for a fixed period of time before randomly changing its orientation and moving in a new direction. In the limit where the bacteria undergo only Brownian motion on the size scale of the barriers, rectification does not occur. We examine the effects of steric interactions between the bacteria and observe a clogging effect upon increasing the bacteria density.     

Two-Dimensional Self-Propelled Fish Motion in Medium： An Integrated Method for Deforming Body Dynamics and Unsteady Fluid Dynamics

We present （1） the dynamical equations of deforming body and （2） an integrated method for deforming body dynamics and unsteady fluid dynamics, to investigate a modelled freely self-propelled fish. The theoretical model and practical method is applicable for studies on the general mechanics of animal locomotion such as flying in air and swimming in water, particularly of free self-propulsion. The present results behave more credibly than the previous numerical studies and are close to the experimental results, and the aligned vortices pattern is discovered in cruising swimming.     

Quantifying the sorting efficiency of self-propelled run-and-tumble swimmers by geometrical ratchets

Suitable asymmetric microstructures can be used to control the direction of motion in microorganism populations. This rectification process makes it possible to accumulate swimmers in a region of space or to sort different swimmers. Here we study numerically how the separation process depends on the specific motility strategies of the microorganisms involved. Crucial properties such as the separation efficiency and the separation time for two bacterial strains are precisely defined and evaluated. In particular, the sorting of two bacterial populations inoculated in a box consisting of a series of chambers separated by columns of asymmetric obstacles is investigated. We show how the sorting efficiency is enhanced by these obstacles and conclude that this kind of sorting can be efficiently used even when the involved populations differ only in one aspect of their swimming strategy.     

Quantitative measurement of dynamic flow induced by <Emphasis Type="Italic">Tetrahymena pyriformis</Emphasis> (<Emphasis Type="Italic">T. pyriformis</Emphasis>) using micro-particle image velocimetry

Abstract  

In-depth quantitative visualization studies are required to understand the flow induced by swimming micro-organisms and find potential applications. The present study visualized the flow induced by Tetrahymena pyriformis of size 45–50 μm, which swam freely and via stimulation by galvanotaxis in a PDMS micro-chamber using a micro-particle image velocimetry system. The results showed that the maximum velocity of the induced flow was around 430 μm/s for free swimming and 700 μm/s for galvanotactic-controlled swimming. Due to the applied electric field, the electro-osmosis flow led to increased velocity of roughly 135 μm/s at 3 V/mm. The increased velocity stems from the increased motility of the cell under the electric field. Therefore, it was demonstrated that galvanotaxis can control the swimming direction and increase the induced velocity.     

Swimming strategy of settling elongated micro-swimmers by reinforcement learning

Particular types of plankton in aquatic ecosystems can coordinate their motion depending on the local flow environment to reach regions conducive to their growth or reproduction. Investigating their swimming strategies with regard to the local environment is important to obtain in-depth understanding of their behavior in the aquatic environment. In the present research, to examine an impact of the shape and gravity on a swimming strategy, plankton is considered as settling swimming particles of ellipsoidal shape. The Q-learning approach is adopted to obtain swimming strategies for smart particles with a goal of efficiently moving upwards in a two-dimensional steady flow. Strategies obtained from reinforcement learning are compared to those of naive gyrotactic particles that are modeled considering the behavior of realistic plankton. It is found that the elongation of particles improves the performance of upward swimming by facilitating particles' resistance to the perturbation of vortex. In the case when the settling velocity is included, the strategy obtained by reinforcement learning has similar performance to that of the naive gyrotactic one, and they both align swimmers in upward direction. The similarity between the strategy obtained from machine learning and the biological gyrotactic strategy indicates the relationship between the aspherical shape and settling effect of realistic plankton and their gyrotactic feature.     

Computation of three-dimensional Brinkman flows using regularized methods

The Brinkman equations of fluid motion are a model of flows in a porous medium. We develop the exact solution of the Brinkman equations for three-dimensional incompressible flow driven by regularized forces. Two different approaches to the regularization are discussed and compared on test problems. The regularized Brinkman model is also applied to the unsteady Stokes equation for oscillatory flows since the latter leads to the Brinkman equations with complex permeability parameter. We provide validation studies of the method based on the flow and drag of a solid sphere translating in a Brinkman medium and the flow inside a cylindrical channel of circular cross-section. We present a numerical example of a swimming organism in a Brinkman flow which shows that the maximum swimming speed is obtained with a small but non-zero value of the porosity. We also demonstrate that unsteady Stokes flows with oscillatory forcing fall within the same framework and are computed with the same method by applying it to the motion of the oscillating feeding appendage of a copepod.     

Stirring by swimming bodies

We consider the stirring of an inviscid fluid caused by the locomotion of bodies through it. The swimmers are approximated by non-interacting cylinders or spheres moving steadily along straight lines. We find the displacement of fluid particles caused by the nearby passage of a swimmer as a function of an impact parameter. We use this to compute the effective diffusion coefficient from the random walk of a fluid particle under the influence of a distribution of swimming bodies. We compare with the results of simulations. For typical sizes, densities and swimming velocities of schools of krill, the effective diffusivity in this model is five times the thermal diffusivity. However, we estimate that viscosity increases this value by two orders of magnitude.     

Classical solutions and pattern formation for a volume filling chemotaxis model

We establish the global existence of classical solutions to a generalized chemotaxis model, which includes the volume filling effect expressed through a nonlinear squeezing probability. This novel choice of squeezing probability reflects the elastic properties of cells. Necessary and sufficient conditions for spatial pattern formation are given and the underlying bifurcations are analyzed. In numerical simulations, the complex dynamics of merging and emerging patterns are shown for zero cell kinetics and nonzero cell kinetics, respectively. We conclude that the emerging process of pattern formation is due to cell growth.     

Topology Optimization of the Caudal Fin of the Three-Dimensional Self-Propelled Swimming Fish

Based on the boundary vorticity-flux theory, topology optimization of the caudal fin of the three-dimensional self-propelled swimming fish is investigated by combining unsteady computational fluid dynamics with moving boundary and topology optimization algorithms in this study. The objective functional of topology optimization is the function of swimming efficiency, swimming speed and motion direction control. The optimal caudal fin, whose topology is different from that of the natural fish caudal fin, makes the 3D bionic fish achieve higher swimming efficiency, faster swimming speed and better maneuverability. The boundary vorticity-flux on the body surface of the 3D fish before and after optimization reveals the mechanism of high performance swimming of the topology optimization bionic fish. The comparative analysis between the swimming performance of the 3D topology optimization bionic fish and the 3D lunate tail bionic fish is also carried out, and the wake structures of two types of bionic fish show the physical nature that the swimming performance of the 3D topology optimization bionic fish is significantly better than the 3D lunate tail bionic fish.     

Spiral breakup in an array of coupled cells: the role of the intercellular conductance

We study numerically how the intercellular conductance affects the process of spiral breakup in an array of coupled excitable cells. The cell dynamics are described by the Aliev-Panfilov model, and the intercellular connection is made via Ohmic elements. We find that decreasing intercellular conductance can prevent the breaking up of a spiral wave into a complex spatiotemporal pattern. We study the mechanism of this effect and show that the breakup disappears because of increasing the diastolic interval of an initial spiral wave.     

Spectral Anomalies in the Fraunhofer Diffraction Pattern

We study the spectral characteristics theoretically and experimentally in the Fraunhofer diffraction pattern formed by the diffraction of a spatially coherent, polychromatic light through a slit. It is found that the spectrum in some diffraction directions close to the singular direction is redshifted, compared to the spectrum of the incident polychromatic light, and blueshifted in other directions, and splits into two lines at the singular direction. We show that the experimental results are consistent with the theoretical expectations.     

Unexpected bipolar flagellar arrangements and long-range flows driven by bacteria near solid boundaries

Experiments and mathematical modeling show that complex flows driven by unexpected flagellar arrangements are induced when peritrichously flagellated bacteria are confined in a thin layer of fluid, between asymmetric boundaries. The flagella apparently form a dynamic bipolar assembly rather than the single bundle characteristic of free swimming bacteria, and the resulting flow is observed to circulate around the cell body. It ranges over several cell diameters, in contrast to the small extent of the flows surrounding free swimmers. Results also suggest that flagellar bundles on bacteria that lie flat on a solid substrate have an effective rotation rate slower than "free" flagella. This discovery extends our knowledge of the dynamic geometry of bacteria and their flagella, and reveals new mechanisms for motility-associated molecular transport and intercellular communication.     

Self-propelled particles with fluctuating speed and direction of motion in two dimensions

We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion, and assume that both processes can be described by independent characteristic time scales. We show the occurrence of a complex transient that can exhibit a series of alternating regimes of motion, for two different angular dynamics which correspond to persistent and directed random walks. We also show additive corrections to the diffusion coefficient. The characteristic time scales are also exposed in the velocity autocorrelation, which is a sum of exponential forms.