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.     

Three-sphere low-Reynolds-number swimmer with a cargo container

A recently introduced model for an autonomous swimmer at low Reynolds number that is comprised of three spheres connected by two arms is considered when one of the spheres has a large radius. The Stokes hydrodynamic flow associated with the swimming strokes and net motion of this system can be studied analytically using the Stokes Green's function of a point force in front of a sphere of arbitrary radius R provided by Oseen. The swimming velocity is calculated, and shown to scale as 1/R ³ with the radius of the sphere.     

Hydrodynamic interaction between two swimmers at low Reynolds number

We investigate the hydrodynamic interactions between micro-organisms swimming at low Reynolds number. By considering simple model swimmers, and combining analytic and numerical approaches, we investigate the time-averaged flow field around a swimmer. At short distances the swimmer behaves like a pump. At large distances the velocity field depends on whether the swimming stroke is invariant under a combined time-reversal and parity transformation. We then consider two swimmers and find that the interaction between them consists of two parts: a passive term, independent of the motion of the second swimmer, and an active term resulting from the simultaneous swimming action of both swimmers. The swimmer-swimmer interaction is a complicated function of their relative displacement, orientation, and phase, leading to motion that can be attractive, repulsive, or oscillatory.     

The equation of motion for the trajectory of a circling particle with an overdamped circle center

Inspired by biological microorganisms swimming in circles in liquid with low Reynolds number, I developed the dynamic theory for computing the helical trajectory of a circling particle with an overdamped circle center. The equation of motion for the circling particle is a hybrid equation of deterministic terms and stochastic terms. Observing the motion of a swimming microorganism, I found the strength of stochastic fluctuations should be much smaller than that governs deterministic dynamics. This dynamic theory predicts a nonlinear transverse motion perpendicular to the direction of external force. Both the living microorganism and artificial circling particle are applicable for an experimental check of this prediction. For the convenience of easy theoretical research, I further derived the probability conservation equations based on this dynamic theory both in two-dimensional and three-dimensional space.     

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.     

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.     

The equations of motion of initially stressed Timoshenko tubular beams conveying fluid

In this paper the equations of motion of an initially stressed Timoshenko tubular beam subjected to a tensile follower load and conveying fluid are derived by using the appropriate statement of Hamilton's principle. This latter is obtained first for “open” systems, the instantaneous total mass of which does not necessarily remain constant in the course of deformation—“open” denoting that there is momentum transport in and out of the system. The equations of motion are derived separately for a cantilevered system and for one with both extremities of the tube clamped. Yet another derivation for the cantilevered tube is presented with the system considered to be quasi-closed, where all flow-induced effects are incorporated through the virtual work, as if they were “external” forces. All three sets of equations are found to be identical. These equations are then compared with those obtained, more simply, by the Newtonian force-balance approach. Some differences between them are found to exist, the principal of which are associated with the follower or other tensile forces; these are discussed at some length, and the equations of motion obtained here are compared to those obtained by other researchers for Timoshenko beams subjected to follower or tensile forces.     

Hot microswimmers

Hot microswimmers are self-propelled Brownian particles that exploit local heating for their directed self-thermophoretic motion. We provide a pedagogical overview of the key physical mechanisms underlying this promising new technology. It covers the hydrodynamics of swimming, thermophoresis and -osmosis, hot Brownian motion, force-free steering, and dedicated experimental and simulation tools to analyze hot Brownian swimmers.     

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.     

Purcell’s “rotator”: mechanical rotation at low Reynolds number

An object consisting of three spheres, linked like the spokes on a wheel, can undergo a net rotational movement when the relative positions of the spheres proceed through a four-step cycle. This rotational motion is the analogue of the two-hinged swimmer originally proposed by Purcell (1977), which has served as a prototype for mechanical implementations of swimming. We also note that the rotational motion analysed here may be useful in the design of micromachines and has similarities to molecular-scale rotational motors that have been identified recently.     

Langevin dynamics deciphers the motility pattern of swimming parasites

The parasite African trypanosome swims in the bloodstream of mammals and causes the highly dangerous human sleeping sickness. Cell motility is essential for the parasite's survival within the mammalian host. We present an analysis of the random-walk pattern of a swimming trypanosome. From experimental time-autocorrelation functions for the direction of motion we identify two relaxation times that differ by an order of magnitude. They originate from the rapid deformations of the cell body and a slower rotational diffusion of the average swimming direction. Velocity fluctuations are athermal and increase for faster cells whose trajectories are also straighter. We demonstrate that such a complex dynamics is captured by two decoupled Langevin equations that decipher the complex trajectory pattern by referring it to the microscopic details of cell behavior.     

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 ≤ Re_s ≤ 2.0, flow Reynolds number 40 ≤ Re_p ≤ 160, blocking rate 0.2 ≤ κ ≤ 0.5. Some results are validated by comparing with available other results. The effects of Re_s, Re_p 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 Re_s 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 Re_s will induce the squirmer to make periodic and stable motion at a specific distance from the wall. Increasing Re_p 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.     

Motion and mixing for multiple ferromagnetic microswimmers

This paper concerns the interaction of several ferromagnetic microswimmers, their motion and the resulting fluid mixing. Each swimmer consists of two ferromagnetic beads joined by an elastic link, and is driven by an external, time-dependent magnetic field. The external field provides a torque on a swimmer and, together with the varying attraction between the magnetic beads, generates a time-irreversible motion leading to persistent swimming in a low Reynolds number environment. The aim of the present paper is to consider the interactions between several swimmers. A regime is considered in which identical swimmers move in the same overall direction, and their motion is synchronised because of driving by the external field. It is found that two swimmers tend to encircle one another while three undergo more complicated motion that may involve the braiding of swimmer trajectories. By means of approximations it is established that the interaction between pairs of swimmers gives circulatory motion which falls off with an inverse square law and is linked to their overall speed of motion through the fluid. As groups of two or more swimmers move through the fluid they process fluid, leaving behind a trail of fluid that has undergone mixing: this is investigated by following streak lines numerically.     

Coherent structures in monolayers of swimming particles

We report various types of coherent structures in suspensions of spherical particles swimming in a monolayer. We solve the fluid dynamics precisely from far-field hydrodynamic interactions to lubrication between two near-contact surfaces. The simulation results clearly illustrate that coherent structures, such as aggregation, mesoscale spatiotemporal motion, and band formation, can be generated by purely hydrodynamic interactions.     

The flow induced by a jellyfish

The purpose of this study is to understand the propulsion mechanism of a jellyfish during its swimming. We observed the motion of a jellyfish (Aurelia aurita) by a motion-capture camera, and measured the vector field of flow around a jellyfish by using a PIV (Particle Image Velocimetry) measurement. A jellyfish is considered to be principally propelled by a jet at the contracting phase of its motion. If that is true, it is interesting that a jellyfish never stops traveling even at the expanding phase. We found that a vortex ring with the opposite vorticity to shed vortex ring was inside a jellyfish body in the expanding phase. We discussed a cause of an increase in thrust force and keeping constant speed in the expanding phase.     

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.     

Chemotaxis driven instability of a confined bacterial suspension

A suspension of bacteria in a thin channel or film subject to a gradient in the concentration of a chemoattractant, will develop, in the absence of an imposed fluid flow, a steady bacteria concentration field that depends exponentially on cross-stream position. Above a critical bacteria concentration, this quiescent base state is unstable to a steady convective motion driven by the active stresses induced by the bacteria's swimming. Unlike previously identified long-wavelength instabilities of active fluids, this instability results from coupling of the bacteria concentration field with the disturbance flow.     

Settling and swimming of flexible fluid-lubricated foils

We study the dynamics of a flexible foil immersed in a fluid and moving close to a rigid wall. Lubrication theory allows us to derive equations of motion for the foil and thus examine the passive settling and the active swimming of a foil. This also allows us to partly answer the long-standing question in cartoon physics--can carpets fly? Our analysis suggests a region in parameter space where one may realize this dream and move the virtual towards reality.