Swimming droplets driven by a surface wave

Liquid Surfaces with Chaotic Capillary Waves Exhibit an Effective Surface Tension

The influence of chaotic capillary waves on the time-averaged shape of a liquid volume is studied experimentally and theoretically. In that context, a liquid film containing a stable hole is subjected to Faraday waves. The waves induce a shrinkage of the hole compared to the static film, which can be described using the Young-Laplace equation by incorporating an effective capillary length. In the regime of chaotic Faraday waves, the presented theoretical model explains the hole shrinkage quantitatively, linking the effective capillary length to the wave energy. The effect of chaotic Faraday waves can be interpreted as a dynamic surface force that acts against surface tension.

Reversed spin of a ratchet motor on a vibrating water bed

A ratchet gear on a vibrating water bed exhibits a one-way spin. However, the spinning direction is opposite to that of the gear placed on the granular bed. The one-way spin is caused by the surface waves of water. Surface deformation causes transportation of the water element to rotate the gear. The spatial symmetry of the surface wave and gear geometry regulates the rotational torque. In this study, the same ratchet shows reversed motion between the granular and water beds, and the direction is not determined only by the ratchet geometry. The self-organization of the fluid medium caused by small agitation induces a nontrivial inversion of the spinning direction.

Active colloid with externally induced periodic bipolar motility and its cooperative motion

Active matter physics has been developed with various types of self-propelled particles, including those with polar and bipolar motility and beyond. However, the bipolar motions experimentally realized so far have been either random along the axis or periodic at intrinsic frequencies. Here we report another kind of bipolar active particles, whose periodic bipolar self-propulsion is set externally at a controllable frequency. We used Quincke rollers-dielectric particles suspended in a conducting liquid driven by an electric field-under an AC electric field instead of the usually used DC field. Reciprocating motion of a single particle at the external frequency was observed experimentally and characterized theoretically as stable periodic motion. Experimentally, we observed not only the reciprocating motion but also non-trivial active Brownian particle (ABP)-like persistent motion in a long time scale. This resulted in a Lorentzian spectrum around zero frequency, which is not accounted for by a simple extension of the conventional model of Quincke rollers to the AC field. It was found that ABP-like motion can be reproduced by considering the top-bottom asymmetry in the experimental system. Moreover, we found a rotational diffusion coefficient much larger than the thermal one, as also reported in previous experiments, which may have resulted from roughness of the electrode surface. We also found self-organized formation of small clusters, such as doublets and triplets, and characterized cooperative motion of particles therein. The AC Quincke rollers reported here may serve as a model experimental system of bipolar active matter, which appears to deserve further investigations.

Acoustic, Phononic, Brillouin Light Scattering and Faraday Wave-Based Frequency Combs: Physical Foundations and Applications

Frequency combs (FCs)-spectra containing equidistant coherent peaks-have enabled researchers and engineers to measure the frequencies of complex signals with high precision, thereby revolutionising the areas of sensing, metrology and communications and also benefiting the fundamental science. Although mostly optical FCs have found widespread applications thus far, in general FCs can be generated using waves other than light. Here, we review and summarise recent achievements in the emergent field of acoustic frequency combs (AFCs), including phononic FCs and relevant acousto-optical, Brillouin light scattering and Faraday wave-based techniques that have enabled the development of phonon lasers, quantum computers and advanced vibration sensors. In particular, our discussion is centred around potential applications of AFCs in precision measurements in various physical, chemical and biological systems in conditions where using light, and hence optical FCs, faces technical and fundamental limitations, which is, for example, the case in underwater distance measurements and biomedical imaging applications. This review article will also be of interest to readers seeking a discussion of specific theoretical aspects of different classes of AFCs. To that end, we support the mainstream discussion by the results of our original analysis and numerical simulations that can be used to design the spectra of AFCs generated using oscillations of gas bubbles in liquids, vibrations of liquid drops and plasmonic enhancement of Brillouin light scattering in metal nanostructures. We also discuss the application of non-toxic room-temperature liquid-metal alloys in the field of AFC generation.

Self-Propulsion of a Volatile Drop on the Surface of an Immiscible Liquid Bath

We demonstrate the self-propulsion of a volatile drop on the surface of a bath of an immiscible liquid. Evaporative heat pumping is converted into directed motion through thermocapillary stresses, which arise from the coupling between surface-tension-driven flows and temperature advection. A propulsive force arises from convection-sustained temperature gradients along the drop interface, resulting in a warmer pool of liquid being advected by the hydrodynamic flow in the underlying bath toward the back of the drop. The dependence of the drop speed on the activity source, i.e., the evaporation flux, is derived with scaling arguments and captures the experimental data.

Diffusion of active particles with angular velocity reversal

Biological and synthetic microswimmers display a wide range of swimming trajectories depending on driving forces and torques. In this paper we consider a simple overdamped model of self-propelled particles with a constant self-propulsion speed but an angular velocity that varies in time. Specifically, we consider the case of both deterministic and stochastic angular velocity reversals, mimicking several synthetic active matter systems, such as propelled droplets. The orientational correlation function and effective diffusivity is studied using Langevin dynamics simulations and perturbative methods.

On a simple model that explains inversion of a self-propelled rotor under periodic stop-and-release-operations

We propose a simple mathematical model that describes the time evolution of a self-propelled object on a liquid surface using variables such as object location, surface concentration of active molecules, and hydrodynamic surface flow. The model is applied to simulate the time evolution of a rotor composed of a polygonal plate with camphor pills at its corners. We have qualitatively reproduced results of experiments, in which the inversion of rotational direction under periodic stop-and-release-operations was investigated. The model correctly describes the probability of the inversion as a function of the duration of the phase when the rotor is stopped. Moreover, the model allows to introduce the rotor asymmetry unavoidable in real experiments and study its influence on the studied phenomenon. Our numerical simulations have revealed that the probability of the inversion of rotational direction is determined by the competition among the transport of the camphor molecules by the flow, the intrinsic asymmetry of the rotor, and the noise amplitude.

Friction on water sliders

A body in motion tends to stay in motion but is often slowed by friction. Here we investigate the friction experienced by centimeter-sized bodies sliding on water. We show that their motion is dominated by skin friction due to the boundary layer that forms in the fluid beneath the body. We develop a simple model that considers the boundary layer as quasi-steady, and is able to capture the experimental behaviour for a range of body sizes, masses, shapes and fluid viscosities. Furthermore, we demonstrate that friction can be reduced by modification of the body's shape or bottom topography. Our results are significant for understanding natural and artificial bodies moving at the air-water interface, and can inform the design of aerial-aquatic microrobots for environmental exploration and monitoring.

Bifurcation in the angular velocity of a circular disk propelled by symmetrically distributed camphor pills

We studied rotation of a disk propelled by a number of camphor pills symmetrically distributed at its edge. The disk was put on a water surface so that it could rotate around a vertical axis located at the disk center. In such a system, the driving torque originates from surface tension difference resulting from inhomogeneous surface concentration of camphor molecules released from the pills. Here, we investigated the dependence of the stationary angular velocity on the disk radius and on the number of pills. The work extends our previous study on a linear rotor propelled by two camphor pills [Y. Koyano et al., Phys. Rev. E 96, 012609 (2017)]. It was observed that the angular velocity dropped to zero after a critical number of pills was exceeded. Such behavior was confirmed by a numerical model of time evolution of the rotor. The model predicts that, for a fixed friction coefficient, the speed of pills can be accurately represented by a function of the linear number density of pills. We also present bifurcation analysis of the conditions at which the transition between a standing and a rotating disk appears.

Surface swimmers, harnessing the interface to self-propel

In the study of microscopic flows, self-propulsion has been particularly topical in recent years, with the rise of miniature artificial swimmers as a new tool for flow control, low Reynolds number mixing, micromanipulation or even drug delivery. It is possible to take advantage of interfacial physics to propel these microrobots, as demonstrated by recent experiments using the proximity of an interface, or the interface itself, to generate propulsion at low Reynolds number. This paper discusses how a nearby interface can provide the symmetry breaking necessary for propulsion. An overview of recent experiments illustrates how forces at the interface can be used to generate locomotion. Surface swimmers ranging from the microscopic scale to typically the capillary length are covered. Two systems are then discussed in greater detail. The first is composed of floating ferromagnetic spheres that assemble through capillarity into swimming structures. Two previously studied configurations, triangular and collinear, are discussed and contrasted. A new interpretation for the triangular swimmer is presented. Then, the non-monotonic influence of surface tension and viscosity is evidenced in the collinear case. Finally, a new system is introduced. It is a magnetically powered, centimeter-sized piece that swims similarly to water striders.

Pilot-wave dynamics of two identical, in-phase bouncing droplets

A droplet bouncing on the surface of a vibrating liquid bath can move horizontally guided by the wave it produces on impacting the bath. The wave itself is modified by the environment, and thus, the interactions of the moving droplet with the surroundings are mediated through the wave. This forms an example of a pilot-wave system. Taking the Oza-Rosales-Bush description for walking droplets as a theoretical pilot-wave model, we investigate the dynamics of two interacting identical, in-phase bouncing droplets theoretically and numerically. A remarkably rich range of behaviors is encountered as a function of the two system parameters, the ratio of inertia to drag, κ , and the ratio of wave forcing to drag, β . The droplets typically travel together in a tightly bound pair, although they unbind when the wave forcing is large and inertia is small or inertia is moderately large and wave forcing is moderately small. Bound pairs can exhibit a range of trajectories depending on parameter values, including straight lines, sub-diffusive random walks, and closed loops. The droplets themselves may maintain their relative positions, oscillate toward and away from one another, or interchange positions regularly or chaotically as they travel. We explore these regimes and others and the bifurcations between them through analytic and numerical linear stability analyses and through fully nonlinear numerical simulation.

Persistent random deformation model of cells crawling on a gel surface

In general, cells move on a substrate through extension and contraction of the cell body. Though cell movement should be explained by taking into account the effect of such shape fluctuations, past approaches to formulate cell-crawling have not sufficiently quantified the relationship between cell movement (velocity and trajectory) and shape fluctuations based on experimental data regarding actual shaping dynamics. To clarify this relationship, we experimentally characterized cell-crawling in terms of shape fluctuations, especially extension and contraction, by using an elasticity-tunable gel substrate to modulate cell shape. As a result, an amoeboid swimmer-like relation was found to arise between the cell velocity and cell-shape dynamics. To formulate this experimentally-obtained relationship between cell movement and shaping dynamics, we established a persistent random deformation (PRD) model based on equations of a deformable self-propelled particle adopting an amoeboid swimmer-like velocity-shape relationship. The PRD model successfully explains the statistical properties of velocity, trajectory and shaping dynamics of the cells including back-and-forth motion, because the velocity equation exhibits time-reverse symmetry, which is essentially different from previous models. We discuss the possible application of this model to classify the phenotype of cell migration based on the characteristic relation between movement and shaping dynamics.

Active colloids with collective mobility status and research opportunities

The collective mobility of active matter (self-propelled objects that transduce energy into mechanical work to drive their motion, most commonly through fluids) constitutes a new frontier in science and achievable technology. This review surveys the current status of the research field, what kinds of new scientific problems can be tackled in the short term, and what long-term directions are envisioned. We focus on: (1) attempts to formulate design principles to tailor active particles; (2) attempts to design principles according to which active particles interact under circumstances where particle-particle interactions of traditional colloid science are augmented by a family of nonequilibrium effects discussed here; (3) attempts to design intended patterns of collective behavior and dynamic assembly; (4) speculative links to equilibrium thermodynamics. In each aspect, we assess achievements, limitations, and research opportunities.

Theoretical model of chirality-induced helical self-propulsion

We recently reported the experimental realization of a chiral artificial microswimmer exhibiting helical self-propulsion [T. Yamamoto and M. Sano, Soft Matter 13, 3328 (2017)1744-683X10.1039/C7SM00337D]. In the experiment, cholesteric liquid crystal (CLC) droplets dispersed in surfactant solutions swam spontaneously, driven by the Marangoni flow, in helical paths whose handedness is determined by the chirality of the component molecules of CLC. To study the mechanism of the emergence of the helical self-propelled motion, we propose a phenomenological model of the self-propelled helical motion of the CLC droplets. Our model is constructed by symmetry argument in chiral systems, and it describes the dynamics of CLC droplets with coupled time-evolution equations in terms of a velocity, an angular velocity, and a tensor variable representing the symmetry of the helical director field of the droplet. We found that helical motions as well as other chiral motions appear in our model. By investigating bifurcation behaviors between each chiral motion, we found that the chiral coupling terms between the velocity and the angular velocity, the structural anisotropy of the CLC droplet, and the nonlinearity of model equations play a crucial role in the emergence of the helical motion of the CLC droplet.

Swinging motion of active deformable particles in Poiseuille flow

Dynamics of active deformable particles in an external Poiseuille flow is investigated. To make the analysis general, we employ time-evolution equations derived from symmetry considerations that take into account an elliptical shape deformation. First, we clarify the relation of our model to that of rigid active particles. Then, we study the dynamical modes that active deformable particles exhibit by changing the strength of the external flow. We emphasize the difference between the active particles that tend to self-propel parallel to the elliptical shape deformation and those self-propelling perpendicularly. In particular, a swinging motion around the centerline far from the channel walls is discussed in detail.