Ordered clusters and dynamical states of particles in a vibrated fluid

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.

Hydrodynamic coupling melts acoustically levitated crystalline rafts

Going beyond the manipulation of individual particles, first steps have recently been undertaken with acoustic levitation in air to investigate the collective dynamical properties of many-body systems self-assembled within the levitation plane. However, these assemblies have been limited to two-dimensional, close-packed rafts where forces due to scattered sound pull particles into direct frictional contact. Here, we overcome this restriction using particles small enough that the viscosity of air establishes a repulsive streaming flow at close range. By tuning the particle size relative to the characteristic length scale for viscous streaming, we control the interplay between attractive and repulsive forces and show how particles can be assembled into monolayer lattices with tunable spacing. While the strength of the levitating sound field does not affect the particles' steady-state separation, it controls the emergence of spontaneous excitations that can drive particle rearrangements in an effectively dissipationless, underdamped environment. Under the action of these excitations, a quiescent particle lattice transitions from a predominantly crystalline structure to a two-dimensional liquid-like state. We find that this transition is characterized by dynamic heterogeneity and intermittency, involving cooperative particle movements that remove the timescale associated with caging for the crystalline lattice. These results shed light on the nature of athermal excitations and instabilities that can arise from strong hydrodynamic coupling among interacting particles.

Annealing and melting of active two-dimensional soliton lattices in chiral nematic films

In this work, thousands of electrically driven dissipative solitons, called directrons, are generated in a chiral nematic liquid crystal. The directrons start with random motions but soon synchronize their motions and self-organize into a two-dimensional hexagonal lattice. The directron lattice moves collectively and forms a hexatic phase. By increasing the applied voltage, the lattice exhibits a first-order hexatic-to-liquid phase transition.

Searching for structural predictors of plasticity in dense active packings

In amorphous solids subject to shear or thermal excitation, so-called structural indicators have been developed that predict locations of future plasticity or particle rearrangements. An open question is whether similar tools can be used in dense active materials, but a challenge is that under most circumstances, active systems do not possess well-defined solid reference configurations. We develop a computational model for a dense active crowd attracted to a point of interest, which does permit a mechanically stable reference state in the limit of infinitely persistent motion. Previous work on a similar system suggested that the collective motion of crowds could be predicted by inverting a matrix of time-averaged two-particle correlation functions. Seeking a first-principles understanding of this result, we demonstrate that this active matter system maps directly onto a granular packing in the presence of an external potential, and extend an existing structural indicator based on linear response to predict plasticity in the presence of noisy dynamics. We find that the strong pressure gradient necessitated by the directed activity, as well as a self-generated free boundary, strongly impact the linear response of the system. In low-pressure regions the linear-response-based indicator is predictive, but it does not work well in the high-pressure interior of our active packings. Our findings motivate and inform future work that could better formulate structure-dynamics predictions in systems with strong pressure gradients.

Unveiling of the mechanisms of acoustic streaming induced by sharp edges

Acoustic waves can generate steady streaming within a fluid owing to the generation of viscous boundary layers near walls of typical thickness δ. In microchannels, the acoustic wavelength λ is adjusted to twice the channel width w to ensure a resonance condition, which implies the use of MHz transducers. Recently, though, intense acoustic streaming was generated by acoustic waves of a few kHz (hence with λ≫w), owing to the presence of sharp-tipped structures of curvature radius at the tip r_{c} smaller than δ. The present study quantitatively investigates this sharp-edge acoustic streaming via the direct resolution of the full Navier-Stokes equation using the finite element method. The influence of δ,r_{c}, and viscosity ν on the acoustic streaming performance is quantified. Our results suggest choices of operating conditions and geometrical parameters, in particular the dimensionless tip radius of curvature r_{c}/δ and the liquid viscosity.

Acoustic Streaming Generated by Sharp Edges: The Coupled Influences of Liquid Viscosity and Acoustic Frequency

Acoustic streaming can be generated around sharp structures, even when the acoustic wavelength is much larger than the vessel size. This sharp-edge streaming can be relatively intense, owing to the strongly focused inertial effect experienced by the acoustic flow near the tip. We conducted experiments with particle image velocimetry to quantify this streaming flow through the influence of liquid viscosity ν , from 1 mm 2 /s to 30 mm 2 /s, and acoustic frequency f from 500 Hz to 3500 Hz. Both quantities supposedly influence the thickness of the viscous boundary layer δ = ν π f 1 / 2 . For all situations, the streaming flow appears as a main central jet from the tip, generating two lateral vortices beside the tip and outside the boundary layer. As a characteristic streaming velocity, the maximal velocity is located at a distance of δ from the tip, and it increases as the square of the acoustic velocity. We then provide empirical scaling laws to quantify the influence of ν and f on the streaming velocity. Globally, the streaming velocity is dramatically weakened by a higher viscosity, whereas the flow pattern and the disturbance distance remain similar regardless of viscosity. Besides viscosity, the frequency also strongly influences the maximal streaming velocity.

Mechanisms of spontaneous chain formation and subsequent microstructural evolution in shear-driven strongly confined drop monolayers

It was experimentally demonstrated by Migler and his collaborators [Phys. Rev. Lett., 2001, 86, 1023; Langmuir, 2003, 19, 8667] that a strongly confined drop monolayer sheared between two parallel plates can spontaneously develop a flow-oriented drop-chain morphology. Here we show that the formation of the chain-like microstructure is driven by far-field Hele-Shaw quadrupolar interactions between drops, and that drop spacing within chains is controlled by the effective drop repulsion associated with the existence of confinement-induced reversing streamlines, i.e., the swapping trajectory effect. Using direct numerical simulations and an accurate quasi-2D model that incorporates quadrupolar and swapping-trajectory contributions, we analyze microstructural evolution in a monodisperse drop monolayer. Consistent with experimental observations, we find that drop spacing within individual chains is usually uniform. Further analysis shows that at low area fractions all chains have the same spacing, but at higher area fractions there is a large spacing variation from chain to chain. These findings are explained in terms of uncompressed and compressed chains. At low area fractions most chains are uncompressed (spacing equals lst, which is the stable separation of an isolated pair). At higher area fractions compressed chains (with tighter spacing) are formed in a process of chain zipping along y-shaped structural defects. We also discuss the relevance of our findings to other shear-driven systems, such as suspensions of spheres in non-Newtonian fluids.

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.

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.

Acoustically bound microfluidic bubble crystals

Bubbles confined in microchannels self-organize without directly contacting one another when excited by an external acoustic field. The bubbles tend to form periodic "crystal"-like lattices with a finite interbubble distance. This equilibrium distance can be adjusted by simply tuning the acoustic frequency. This new type of crystal is purely mediated by acoustic surface waves emitted by the pulsating bubbles. Because these waves are reflected at the channel boundaries, the bubbles interact with their own images across the boundary.

Dynamic self-assembly and control of microfluidic particle crystals

Engineered two-phase microfluidic systems have recently shown promise for computation, encryption, and biological processing. For many of these systems, complex control of dispersed-phase frequency and switching is enabled by nonlinearities associated with interfacial stresses. Introducing nonlinearity associated with fluid inertia has recently been identified as an easy to implement strategy to control two-phase (solid-liquid) microscale flows. By taking advantage of inertial effects we demonstrate controllable self-assembling particle systems, uncover dynamics suggesting a unique mechanism of dynamic self-assembly, and establish a framework for engineering microfluidic structures with the possibility of spatial frequency filtering. Focusing on the dynamics of the particle-particle interactions reveals a mechanism for the dynamic self-assembly process; inertial lift forces and a parabolic flow field act together to stabilize interparticle spacings that otherwise would diverge to infinity due to viscous disturbance flows. The interplay of the repulsive viscous interaction and inertial lift also allow us to design and implement microfluidic structures that irreversibly change interparticle spacing, similar to a low-pass filter. Although often not considered at the microscale, nonlinearity due to inertia can provide a platform for high-throughput passive control of particle positions in all directions, which will be useful for applications in flow cytometry, tissue engineering, and metamaterial synthesis.

Liquid film coating a fiber as a model system for the formation of bound states in active dispersive-dissipative nonlinear media

We analyze the coherent-structure interaction and the formation of bound states in active dispersive-dissipative nonlinear media using a viscous film coating a vertical fiber as a prototype. The coherent structures in this case are droplike pulses that dominate the evolution of the film. We study experimentally the interaction dynamics and show evidence for formation of bound states. A theoretical explanation is provided through a coherent-structures theory of a simple model for the flow.

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.

Something old, something new

Some thoughts on the development of theoretical fluid dynamics in this century and some reflections on the developments of the past century were provided as an introduction to a broad-ranging conference. A written synopsis of these remarks is provided here.

Violation of the action-reaction principle and self-forces induced by nonequilibrium fluctuations

We show that the extension of Casimir-like forces to fluctuating fluids driven out of equilibrium can exhibit two interrelated phenomena forbidden at equilibrium: self-forces can be induced on single asymmetric objects and the action-reaction principle between two objects can be violated. These effects originate in asymmetric restrictions imposed by the objects' boundaries on the fluid's fluctuations. They are not ruled out by the second law of thermodynamics since the fluid is in a nonequilibrium state. Considering a simple reaction-diffusion model for the fluid, we explicitly calculate the self-force induced on a deformed circle. We also show that the action-reaction principle does not apply for the internal Casimir forces between a circle and a plate. Their sum, instead of vanishing, provides the self-force on the circle-plate assembly.

Hydrodynamic crystals: collective dynamics of regular arrays of spherical particles in a parallel-wall channel

Simulations of over 10;{3} hydrodynamically coupled solid spheres are performed to investigate collective motion of linear trains and regular square arrays of particles suspended in a fluid bounded by two parallel walls. Our novel accelerated Stokesian-dynamics algorithm relies on simplifications associated with the Hele-Shaw asymptotic far-field form of the flow scattered by the particles. The simulations reveal propagation of particle-displacement waves, deformation, and rearrangements of a particle lattice, propagation of dislocation defects in ordered arrays, and long-lasting coexistence of ordered and disordered regions.

Interaction of spheres in oscillatory fluid flows

Rigid spherical particles in oscillating fluid flows form interesting structures as a result of fluid mediated interactions. Here we show that spheres under horizontal vibration align themselves at right angles to the oscillation and sit with a gap between them. The details of this behavior have been investigated through experiments and simulations. We have carried out experiments in which a pair of stainless steel spheres is shaken horizontally in a cell filled with glycerol-water fluid mixtures of three different viscosities, at various frequencies and amplitudes of oscillation. There is an equilibrium gap between the particles resulting from a long-range attraction and a short-range repulsion. The size of the gap was found to depend on the fluid viscosity and the vibratory parameters, and we have identified two distinct scaling regimes for the dependence of the gap on the system parameters. Using a Navier-Stokes solver the same system was simulated. The interaction force between the spheres was measured and the streaming flows induced by the motion were determined.

Analysis of the electromeniscus phenomenon using a different interpretation of the Maxwell model applied to three-dimensional molecular orientations

An electrohydrodynamic phenomenon called the electromeniscus is analyzed. This phenomenon is closely related to the oscillation of a microscale liquid and is analyzed using an interpretation of the Maxwell model coupled with a variational principle. The analysis clearly shows that the electromeniscus phenomenon is generated as a result of mass transformation of the oscillating liquid in order to transform the electric energy at the electrode to kinetic energy of the liquid most efficiently through their resonance. Mass transformation is a characteristic phenomenon of a liquid, and control of this phenomenon demonstrates great potential for self-aligning nanoscale materials and production of functional polymers characterized by specific molecular orientations.

Surface wave assisted self-assembly of multidomain magnetic structures

An ensemble of magnetic microparticles at the liquid surface displays novel snakelike self-assembled structures induced by an alternating magnetic field. We demonstrate that these structures are directly related to surface waves in the liquid generated by the collective response of magnetic microparticles to the alternating magnetic field. The segments of the "snake" exhibit long-range antiferromagnetic ordering, while each segment is composed of ferromagnetically aligned chains of microparticles. The structures exhibit magnetic hysteretic behavior with respect to an external in-plane magnetic field and logarithmic relaxation of the remanent magnetic moment.

Chaos and threshold for irreversibility in sheared suspensions

Systems governed by time reversible equations of motion often give rise to irreversible behaviour. The transition from reversible to irreversible behaviour is fundamental to statistical physics, but has not been observed experimentally in many-body systems. The flow of a newtonian fluid at low Reynolds number can be reversible: for example, if the fluid between concentric cylinders is sheared by boundary motion that is subsequently reversed, then all fluid elements return to their starting positions. Similarly, slowly sheared suspensions of solid particles, which occur widely in nature and science, are governed by time reversible equations of motion. Here we report an experiment showing precisely how time reversibility fails for slowly sheared suspensions. We find that there is a concentration dependent threshold for the deformation or strain beyond which particles do not return to their starting configurations after one or more cycles. Instead, their displacements follow the statistics of an anisotropic random walk. By comparing the experimental results with numerical simulations, we demonstrate that the threshold strain is associated with a pronounced growth in the Lyapunov exponent (a measure of the strength of chaotic particle interactions). The comparison illuminates the connections between chaos, reversibility and predictability.

Structures and chaotic fluctuations of granular clusters in a vibrated fluid layer

Particles that oscillate with respect to a background fluid experience a long-range attraction and a short-range repulsion that give rise to clustering at a preferred separation. We have studied the structure and dynamics of these clusters for both small (2<N<7) and large (N=25 or 48) clusters. For small clusters, the particles often form well-defined structures with chaotic fluctuations about the mean particle positions. However, for a given N , there are generally several different structures, e.g., both isosceles and equilateral triangles. The nearest neighbor spacings grow systematically with the dimensionless driving acceleration Gamma. Large clusters are less rigid, and show much larger velocity fluctuations than do small clusters, for sufficiently large Gamma. The fluctuation amplitude grows systematically with Gamma for large clusters, but not for small ones. The instantaneous particle velocity is typically largest when a particle moves through a region where its probability density is low. Some of the observed phenomena suggest a variational model in which particles seek minima in an effective potential, and are perturbed by dynamically generated noise arising from the nonlinear interactions between particles. However, pairwise forces cannot account for all of the results. We discuss the nature of the fluctuations, including the low apparent dimension of the occupied set in configuration space for clusters of modest size.

A bubble-driven microfluidic transport element for bioengineering

Microfluidics typically uses channels to transport small objects by actuation forces such as an applied pressure difference or thermocapillarity. We propose that acoustic streaming is an alternative means of directional transport at small scales. Microbubbles on a substrate establish well controlled fluid motion on very small scales; combinations ("doublets") of bubbles and microparticles break the symmetry of the motion and constitute flow transport elements. We demonstrate the principle of doublet streaming and describe the ensuing transport. Devices based on doublet flow elements work without microchannels and are thus potentially cheap and highly parallelizable.

Effective interactions between inclusions in complex fluids driven out of equilibrium

The concept of fluctuation-induced effective interactions is extended to systems driven out of equilibrium. We compute the forces experienced by macroscopic objects immersed in a soft material driven by external shaking sources. We show that, in contrast with equilibrium Casimir forces induced by thermal fluctuations, their sign, range, and amplitude depend on specifics of the shaking and can thus be tuned. We also comment on the dispersion of these shaking-induced forces, and discuss their potential application to phase ordering in soft materials.

Dynamic self-assembly and patterns in electrostatically driven granular media

We show that granular media, consisting of metallic microparticles immersed in a poorly conducting liquid in a strong dc electric field, self-assemble into a rich variety of novel phases. These phases include static precipitates: honeycombs and Wigner crystals; and novel dynamic condensates: toroidal vortices and pulsating rings. The observed structures are explained by the interplay between charged granular gas and electrohydrodynamic convective flows in the liquid.