Interaction of spheres in oscillatory fluid flows

Acoustic manipulation of multi-body structures and dynamics

Sound can exert forces on objects of any material and shape. This has made the contactless manipulation of objects by intense ultrasound a fascinating area of research with wide-ranging applications. While much is understood for acoustic forcing of individual objects, sound-mediated interactions among multiple objects at close range gives rise to a rich set of structures and dynamics that are less explored and have been emerging as a frontier for research. We introduce the basic mechanisms giving rise to sound-mediated interactions among rigid as well as deformable particles, focusing on the regime where the particles' size and spacing are much smaller than the sound wavelength. The interplay of secondary acoustic scattering, Bjerknes forces, and micro-streaming is discussed and the role of particle shape is highlighted. Furthermore, we present recent advances in characterizing non-conservative and non-pairwise additive contributions to the particle interactions, along with instabilities and active fluctuations. These excitations emerge at sufficiently strong sound energy density and can act as an effective temperature in otherwise athermal systems.

Pattern formation of spherical particles in an oscillating flow

We study the self-organization of spherical particles in an oscillating flow through experiments inside an oscillating box. The interactions between the particles and the time-averaged (steady streaming) flow lead to the formation of either one-particle-thick chains or multiple-particle-wide bands, depending on the oscillatory conditions. Both the chains and the bands are oriented perpendicular to the direction of oscillation with a regular spacing between them. For all our experiments, this spacing is only a function of the relative particle-fluid excursion length normalized by the particle diameter, A_{r}/D, implying that it is an intrinsic quantity that is established only by the hydrodynamics. In contrast, the width of the bands depends on both A_{r}/D and the confinement, characterized by the particle coverage fraction ϕ. Using the relation for the chain spacing, we accurately predict the transition from one-particle-thick chains to wider bands as a function of ϕ and A_{r}/D. Our experimental results are complemented with numerical simulations in which the flow around the particles is fully resolved. These simulations show that the regular chain spacing arises from the balance between long-range attractive and short-range repulsive hydrodynamic interactions, caused by the vortices in the steady streaming flow. We further show that these vortices induce an additional attractive interaction at very short range when A_{r}/D≳0.7, which stabilizes the multiple-particle-wide bands. Finally, we give a comprehensive overview of the parameter space where we illustrate the different regions using our experimental data.

Dynamics of a bubble in oscillating viscous liquid

This article is devoted to the investigation of gaseous bubble dynamics in oscillating viscous liquids of different density values. The study is conducted numerically using the level-set method with a non-stationary approach. The bubble is initially located near the upper wall of the container. The effects of the inclusion and host liquid viscosities on interaction of the bubble with the wall are analysed. The calculations show that in the absence of gravity, for low-viscosity fluids the bubble is attracted to the nearest wall, which is consistent with previous analytical and experimental results. With increasing viscosity, the vibrational attraction to the wall becomes weaker and is then replaced by repulsion, which can be explained by the decelerative effect of viscosity in the boundary layer near the rigid surface, where the average flow becomes less intensive. The dependencies of the repulsion force on the parameter values are obtained by using the balance method (investigation of the gravity level needed to attain the quasi-equilibrium state at a certain distance between the bubble and the wall). The calculations show that the repulsion force grows with decreasing Reynolds number (increase of the viscosity). This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.

As above, so below, and also in between: mesoscale active matter in fluids

Living matter, such as biological tissue, can be viewed as a nonequilibrium hierarchical assembly, where at each scale self-driven components come together by consuming energy in order to form increasingly complex structures. The remarkable properties of living or "active-matter" systems, as they are generally known, such as versatility, self-healing, and self-replicating, have prompted the following questions: (1) do we understand the biology and biophysics that give rise to these properties? (2) can we achieve similar functionality with synthetic active materials? In this perspective we specifically focus on why it is important to study active matter in fluids with finite inertia. Finite inertia is relevant for mesoscale organisms that swim or fly covering at least three orders of magnitude in size (≈0.5 mm-50 cm) and their collective behavior is generally unknown. As a result, we are limited both in our understanding of the biology of mesoscale swarms and processes but also in our design of self-powered machines and robots at those scales. We expect interesting collective behavior to emerge because with finite inertia, come nonlinearities and the many-body hydrodynamic interactions between the organisms/particles can become quite complex, potentially leading to phenomena, such as novel flocking states and nonequilibrium phase transitions that have not been observed before and which could have great impact in materials applications.

Microstreaming and Its Role in Applications: A Mini-Review

Acoustic streaming is the steady flow of a fluid that is caused by the propagation of sound through that fluid. The fluid flow in acoustic streaming is generated by a nonlinear, time-averaged effect that results from the spatial and temporal variations in a pressure field. When there is an oscillating body submerged in the fluid, such as a cavitation bubble, vorticity is generated on the boundary layer on its surface, resulting in microstreaming. Although the effects are generated at the microscale, microstreaming can have a profound influence on the fluid mechanics of ultrasound/acoustic processing systems, which are of high interest to sonochemistry, sonoprocessing, and acoustophoretic applications. The effects of microstreaming have been evaluated over the years using carefully controlled experiments that identify and quantify the fluid motion at a small scale. This mini-review article overviews the historical development of acoustic streaming, shows how microstreaming behaves, and provides an update on new numerical and experimental studies that seek to explore and improve our understanding of microstreaming.

Magnetic Levitation Stabilized by Streaming Fluid Flows

We demonstrate that the ubiquitous laboratory magnetic stirrer provides a simple passive method of magnetic levitation, in which the so-called "flea" levitates indefinitely. We study the onset of levitation and quantify the flea's motion (a combination of vertical oscillation, spinning and "waggling"), finding excellent agreement with a mechanical analytical model. The waggling motion drives recirculating flow, producing a centripetal reaction force that stabilized the flea. Our findings have implications for the locomotion of artificial swimmers and the development of bidirectional microfluidic pumps, and they provide an alternative to sophisticated commercial levitators.

Propulsion of a Two-Sphere Swimmer

We describe experiments and simulations demonstrating the propulsion of a neutrally buoyant swimmer that consists of a pair of spheres attached by a spring, immersed in a vibrating fluid. The vibration of the fluid induces relative motion of the spheres which, for sufficiently large amplitudes, can lead to motion of the center of mass of the two spheres. We find that the swimming speed obtained from both experiment and simulation agree and collapse onto a single curve if plotted as a function of the streaming Reynolds number, suggesting that the propulsion is related to streaming flows. There appears to be a critical onset value of the streaming Reynolds number for swimming to occur. We observe a change in the streaming flows as the Reynolds number increases, from that generated by two independent oscillating spheres to a collective flow pattern around the swimmer as a whole. The mechanism for swimming is traced to a strengthening of a jet of fluid in the wake of the swimmer.

Vortex-mediated bouncing drops on an oscillating liquid

We have investigated the behavior of bouncing drops on a liquid surface by using particle image velocimetry analysis. A drop on an oscillating liquid surface is observed to not coalesce with the liquid and to travel along the surface if the oscillation is strong enough. A streaming vortex pair, induced by the alternatively distorted liquid surface, shows up below a bouncing drop. The time-averaged flow fields of the vortices are measured. In our quasi-one-dimensional setup, there are three stable distances for the drops, which can be characterized by the Faraday wavelength. The interactions of the vortex-mediated bouncing drops are deduced from the streamlines in the liquid bulk. We further show that a three-dimensional vortex ring is induced by a bouncing drop in a square cell.

Mechanism of vibration-induced repulsion force on a particle in a viscous fluid cell

Space platforms such as the Space Shuttle and International Space Station have been considered an ideal environment for production of protein and semiconductor crystals of superior quality due to the negligible gravity-induced convection. Although it was believed that under microgravity environment diffusive mass transport would dominate the growth of the crystals, some related experiments have not shown satisfactory results possibly due to the movement of the growing crystals in fluid cells caused by small vibrations present in the space platforms called g-jitter. In ground-based experiments, there have been clear observations of attraction and repulsion of a solid particle with respect to a nearby wall of the fluid cell due to small vibrations. The present work is a numerical investigation on the physical mechanisms responsible for the repulsion force, which has been predicted to increase with the cell vibration frequency and amplitude, as well as the fluid viscosity. Moreover, the simulations have revealed that the repulsion force occurs mostly due to the increased pressure in the narrow gap between the particle and the nearest wall.

Spontaneous orbiting of two spheres levitated in a vibrated liquid

In the absence of gravity, particles can form a suspension in a liquid irrespective of the difference in density between the solid and the liquid. If such a suspension is subjected to vibration, there is relative motion between the particles and the fluid which can lead to self-organization and pattern formation. Here, we describe experiments carried out to investigate the behavior of two identical spheres suspended magnetically in a fluid, mimicking weightless conditions. Under vibration, the spheres mutually attract and, for sufficiently large vibration amplitudes, the spheres are observed to spontaneously orbit each other. The collapse of the experimental data onto a single curve indicates that the instability occurs at a critical value of the streaming Reynolds number. Simulations reproduce the observed behavior qualitatively and quantitatively, and are used to identify the features of the flow that are responsible for this instability.

Assembly of vorticity-aligned hard-sphere colloidal strings in a simple shear flow

Colloidal suspensions self-assemble into equilibrium structures ranging from face- and body-centered cubic crystals to binary ionic crystals, and even kagome lattices. When driven out of equilibrium by hydrodynamic interactions, even more diverse structures can be accessed. However, mechanisms underlying out-of-equilibrium assembly are much less understood, though such processes are clearly relevant in many natural and industrial systems. Even in the simple case of hard-sphere colloidal particles under shear, there are conflicting predictions about whether particles link up into string-like structures along the shear flow direction. Here, using confocal microscopy, we measure the shear-induced suspension structure. Surprisingly, rather than flow-aligned strings, we observe log-rolling strings of particles normal to the plane of shear. By employing Stokesian dynamics simulations, we address the mechanism leading to this out-of-equilibrium structure and show that it emerges from a delicate balance between hydrodynamic and interparticle interactions. These results demonstrate a method for assembling large-scale particle structures using shear flows.

Chain formation of spheres in oscillatory fluid flows

A collection of spherical particles subjected to horizontal oscillatory fluid flow is known to form chains perpendicular to the direction of the oscillation. We have developed computer simulations to model such a system and have validated them against experiments carried out in a small fluid-filled cell. In both experiment and simulation we find that the particles go through the same stages of evolution from a dispersed initial configuration to an ordered chain structure. We then use our computer simulations to investigate in detail the interactions responsible for chain formation and the interaction between fully formed chains.

Migration of an asymmetric dimer in oscillatory fluid flow

We describe the motion of an asymmetric dimer across a horizontal surface when exposed to an oscillatory fluid flow. The dimer consists of two spheres of distinct sizes, rigidly attached to each other. The dimer is found to move in a direction perpendicular to the fluid flow, with the smaller sphere foremost. We have determined how the speed depends upon the vibratory conditions, on the fluid viscosity, and on the dimer size and aspect ratio. Computer simulations are used to give an insight into the mechanism responsible for the motion. We use a scaling argument based on the asymmetry of the streaming flow to predict the approximate dependence of the migration speed on the system parameters.