Topology of Force Networks in Granular Media under Impact

We investigate the evolution of the force network in experimental systems of two-dimensional granular materials under impact. We use the first Betti number, $\beta_1$, and persistence diagrams, as measures of the topological properties of the force network. We show that the structure of the network has a complex, hysteretic dependence on both the intruder acceleration and the total force response of the granular material. $\beta_1$ can also distinguish between the nonlinear formation and relaxation of the force network. In addition, using the persistence diagram of the force network, we show that the size of the loops in the force network has a Poisson-like distribution, the characteristic size of which changes over the course of the impact

Force and Mass Dynamics in Non-Newtonian Suspensions

Above a certain solid fraction, dense granular suspensions in water exhibit non-Newtonian behavior, including impact-activated solidification. Although it has been suggested that solidification depends on boundary interactions, quantitative experiments on the boundary forces have not been reported. Using high-speed video, tracer particles, and photoelastic boundaries, we determine the impactor kinematics and the magnitude and timings of impactor-driven events in the body and at the boundaries of cornstarch suspensions. We observe mass shocks in the suspension during impact. The shockfront dynamics are strongly correlated to those of the intruder. However, the total momentum associated with this shock never approaches the initial impactor momentum. We also observe a faster second front, associated with the propagation of pressure to the boundaries of the suspension. The two fronts depend differently on the initial impactor speed, $v_0$, and the suspension packing fraction. The speed of the pressure wave is at least an order of magnitude smaller than (linear) ultrasound speeds obtained for much higher frequencies, pointing to complex amplitude and frequency response of cornstarch suspensions to compressive strains

Hydrodynamic Coupling Melts Acoustically Levitated Crystalline Rafts

The acoustic levitation of small particles provides a versatile platform to investigate the collective dynamical properties of self-assembled many-body systems in the presence of hydrodynamic coupling. However, acoustic scattering forces can only generate attractive interactions at close range in the levitation plane, limiting self-assembly to rafts where particles come into direct, dissipative, contact. Here, we overcome this limitation by using particles small enough that the viscosity of air establishes a repulsive streaming flow at close range. By tuning the size of particles relative to the characteristic length scale of the viscous flow, we control the interplay between attractive and repulsive forces. In this novel granular raft, particles form an open lattice with tunable spacing. Hydrodynamic coupling between particles gives rise to spontaneous excitations in the lattice, in turn driving intermittent particle rearrangements. Under the action of these fluctuations, the raft transitions from a predominantly quiescent, crystalline structure, to a two-dimensional liquid-like state. We show that this transition is characterized by dynamic heterogeneity and intermittency, as well as cooperative particle movements, that produce an effectively `cageless' crystal. These findings shed light on fluid-coupling driven excitations that are difficult to isolate and control in many other hydrodynamic systems

Cluster formation by acoustic forces and active fluctuations in levitated granular matter

The properties of small clusters can differ dramatically from the bulk phases of the same constituents. In equilibrium, cluster assembly has been recently explored, whereas out of equilibrium, the physical principles of clustering remain elusive. These principles underlie phenomena from molecular assembly to the formation of planets from granular matter. Here, we introduce acoustic levitation as a platform to experimentally probe the formation of nonequilibrium small structures in a controlled environment. We focus on the minimal models of cluster formation: six and seven millimetre-scale particles in two dimensions. Experiments and modelling reveal that, in contrast to thermal colloids, in non-equilibrium granular ensembles the magnitude of active fluctuations controls not only the assembly rates but also their assembly pathways and ground-state statistics. These results open up new possibilities for non-invasively manipulating macroscopic particles, tuning their interactions, and directing their assembly

Acoustically levitated lock and key grains

We present a scheme for generating shape-dependent, specific bonds between millimeter scale particles, using acoustic levitation. We levitate particles in an ultrasonic standing wave, allowing for substrate-free assembly. Secondary scattering generates shape-dependent attractive forces between particles, while driving the acoustic trap above its resonance frequency produces active fluctuations that mimic an effective temperature. We three-dimensionally (3D) print planar particles, and show that the local curvature of their binding sites controls the selectivity for attaching a matching particle. We find that the probability of a particle occupying a binding site and the time taken to leave the binding site can be independently tuned via the binding site depth and height, respectively. Finally, we show that these principles can be used to design particles that assemble into complex structures

Mechanical Properties of Acoustically Levitated Granular Rafts

We investigate a model system for the rotational dynamics of inertial many-particle clustering, in which submillimeter objects are acoustically levitated in air. Driven by scattered sound, levitated grains self-assemble into a monolayer of particles, forming mesoscopic granular rafts with both an acoustic binding energy and a bending rigidity. Detuning the acoustic trap can give rise to stochastic forces and torques that impart angular momentum to levitated objects. As the angular momentum of a quasi-two-dimensional granular raft is increased, the raft deforms from a disk to an ellipse, eventually pinching off into multiple separate rafts, in a mechanism that resembles the breakup of a liquid drop. We extract the raft effective surface tension and elastic modulus and show that nonpairwise acoustic forces give rise to effective elastic moduli that scale with the raft size. We also show that the raft size controls the microstructural basis of plastic deformation, resulting in a transition from fracture to ductile failure