Droplet and cluster formation in freely falling granular streams

The pendant drop experiment for aggregates of cohesive granular particles

The pendant drop experiment can be used to study the interfacial tension of a liquid. Here we perform a similar experiment for a granular system. When a dense aggregate of cohesive particles extrudes from an orifice, a cluster of particles detaches, similar to the detachment of a liquid drop. We investigate the volume of the clusters formed from close-packed cohesive oil droplets in an aqueous solution. Our findings reveal that the volume of the clusters depends on the size of the orifice as well as the cohesion strength. Interestingly, we observe that the droplet size does not significantly impact the average cluster volume. We establish a simple scaling law that governs the size of a granular cluster which differs from that of a classic pendant drop. We propose that the key difference between continuum and granular systems is the constraints on rearrangements within the cohesive particles that prevent the clusters from adopting a minimal surface structure, as is the case for a classic pendant drop.

Granular flow-solid wall interaction: investigation of the teapot effect

The evolution of granular flows generally involves solid boundaries, which add complexity to their dynamics and pose challenges to understand relevant natural and industrial phenomena. While an interesting "teapot effect" has been observed for liquid flowing over the solid surface of a teapot's spout, a similar phenomenon for discrete particles receives far less attention. In this work, we experimentally investigated the interactions between granular flows and a wedge-shaped solid edge (spout), showing that the trailing edge of the solid boundary plays a key role in causing velocity non-uniformity and splitting the flow into "dispersed" and "uniform" regions. Tuning the parameters (inclination angle, particle diameter, radii and surface roughness of the trailing edge) of the granular flow, a dimensionless number was summarized and successfully predicted the dispersion of the granular flows. Moreover, we also proved that introducing stronger cohesive forces between particles could harness the granular flows from heterogenous structures to grain clusters, which can be employed to switch between different flow regimes and regulate the dispersion behavior of particle flows. This study reveals the interaction of granular flow over complex solid boundaries, potentially offering new insights into particle-dominated flow dynamics.

Axisymmetric Compression of a Circular Particle Raft Driven by the Diffusion of Surfactant

Particle rafts are a new kind of soft matter formed by self-organization on the interface, which possesses mechanical properties between fluid and solid, and they have been widely used in many industrial fields. In the present study, the compression experiment of a circular particle raft is first performed, where an SDS (sodium dodecyl sulfate)-coated metal ring is placed around its periphery. When the surfactant diffuses, the particle raft shrinks, and its shrinkage ratio increases with the increase in the surfactant concentration, where the experimental results are consistent with the numerical simulation. Next, the relationship between the initial surface tension difference of SDS and the radius shrinkage of the particle raft is obtained by dimensional analysis. In what follows, the diffusion model is built to quantify the diffusion process of SDS at the liquid-gas interface, and then the analytical concentration solution of the concentration of SDS at the periphery of particle raft is given. The particle raft is viewed as an elastic circular plate under the action of the radial pressure, which originates from the surface tension difference, which has been verified by the experimental result. These explorations cast a new light on how to apply loads to measure mechanical properties of soft matter, which also provide some inspirations on the design of microsensors and microfluidics.

Arctic soil patterns analogous to fluid instabilities

Slow-moving arctic soils commonly organize into striking large-scale spatial patterns called solifluction terraces and lobes. Although these features impact hillslope stability, carbon storage and release, and landscape response to climate change, no mechanistic explanation exists for their formation. Everyday fluids-such as paint dripping down walls-produce markedly similar fingering patterns resulting from competition between viscous and cohesive forces. Here we use a scaling analysis to show that soil cohesion and hydrostatic effects can lead to similar large-scale patterns in arctic soils. A large dataset of high-resolution solifluction lobe spacing and morphology across Norway supports theoretical predictions and indicates a newly observed climatic control on solifluction dynamics and patterns. Our findings provide a quantitative explanation of a common pattern on Earth and other planets, illuminating the importance of cohesive forces in landscape dynamics. These patterns operate at length and time scales previously unrecognized, with implications toward understanding fluid-solid dynamics in particulate systems with complex rheology.

Packing fraction of clusters formed in free-falling granular streams based on flash x-ray radiography

We study the packing fraction of clusters in free-falling streams of spherical and irregularly shaped particles using flash x-ray radiography. The estimated packing fraction of clusters is low enough to correspond to coordination numbers less than 6. Such coordination numbers in numerical simulations correspond to aggregates that collide and grow without bouncing. Moreover, the streams of irregular particles evolved faster and formed clusters of larger sizes with lower packing fraction. This result on granular streams suggests that particle shape has a significant effect on the agglomeration process of granular materials.

Cluster-Induced Deagglomeration in Dilute Gravity-Driven Gas-Solid Flows of Cohesive Grains

Clustering is often presumed to lead to enhanced agglomeration between cohesive grains due to the reduced relative velocities of particles within a cluster. Our discrete-particle simulations on gravity-driven, gas-solid flows of cohesive grains exhibit the opposite trend, revealing a new mechanism we coin "cluster-induced deagglomeration." Specifically, we examine relatively dilute gas-solid flows and isolate agglomerates of cohesive origin from overall heterogeneities in the system, i.e., agglomerates of cohesive origin and clusters of hydrodynamic origin. We observe enhanced clustering with an increasing system size (as is the norm for noncohesive systems) as well as reduced agglomeration. The reduced agglomeration is traced to the increased collisional impact velocities of particles at the surface of a cluster; i.e., higher levels of clustering lead to larger relative velocities between the clustered and nonclustered regions, thereby serving as an additional source of granular temperature. This physical picture is further evidenced by a theoretical model based on a balance between the generation and breakage rates of agglomerates. Finally, cluster-induced deagglomeration also provides an explanation for a surprising saturation of agglomeration levels in gravity-driven, gas-solid systems with increasing levels of cohesion, as opposed to the monotonically increasing behavior seen in free-evolving or driven granular systems in the absence of gravity. Namely, higher cohesion leads to more energy dissipation, which is associated with competing effects: enhanced agglomeration and enhanced clustering, the latter of which results in more cluster-induced deagglomeration.

Penetration in bimodal, polydisperse granular material

We investigate the impact penetration of spheres into granular media which are compositions of two discrete size ranges, thus creating a polydisperse bimodal material. We examine the penetration depth as a function of the composition (volume fractions of the respective sizes) and impact speed. Penetration depths were found to vary between δ=0.5D_{0} and δ=7D_{0}, which, for mono-modal media only, could be correlated in terms of the total drop height, H=h+δ, as in previous studies, by incorporating correction factors for the packing fraction. Bimodal data can only be collapsed by deriving a critical packing fraction for each mass fraction. The data for the mixed grains exhibit a surprising lubricating effect, which was most significant when the finest grains [d_{s}∼O(30) μm] were added to the larger particles [d_{l}∼O(200-500) μm], with a size ratio, ε=d_{l}/d_{s}, larger than 3 and mass fractions over 25%, despite the increased packing fraction. We postulate that the small grains get between the large grains and reduce their intergrain friction, only when their mass fraction is sufficiently large to prevent them from simply rattling in the voids between the large particles. This is supported by our experimental observations of the largest lubrication effect produced by adding small glass beads to a bed of large sand particles with rough surfaces.

Kinetic theory for dilute cohesive granular gases with a square well potential

We develop the kinetic theory of dilute cohesive granular gases in which the attractive part is described by a square well potential. We derive the hydrodynamic equations from the kinetic theory with the microscopic expressions for the dissipation rate and the transport coefficients. We check the validity of our theory by performing the direct simulation Monte Carlo.

Cluster statistics and quasisoliton dynamics in microscopic optimal-velocity models

Using the non-linear optimal velocity models as an example, we show that there exists an emergent intrinsic scale that characterizes the interaction strength between multiple clusters appearing in the solutions of such models. The interaction characterizes the dynamics of the localized quasisoliton structures given by the time derivative of the headways, and the intrinsic scale is analogous to the "charge" of the quasisolitons, leading to non-trivial cluster statistics from the random perturbations to the initial steady states of uniform headways. The cluster statistics depend both on the quasisoliton charge and the density of the traffic. The intrinsic scale is also related to an emergent quantity that gives the extremum headways in the cluster formation, as well as the coexistence curve separating the absolute stable phase from the metastable phase. The relationship is qualitatively universal for general optimal velocity models.

Anomalous energy cascades in dense granular materials yielding under simple shear deformations

By using molecular dynamics (MD) simulations of dense granular particles in two dimensions, we study turbulent-like structures of their non-affine velocities under simple shear deformations. We find that the spectrum of non-affine velocities, introduced as an analog of the energy spectrum for turbulent flows, exhibits the power-law decay if the system is yielding in a quasi-static regime, where large-scale collective motions and inelastic interactions of granular particles are crucial for the anomalous cascade of kinetic energy. Based on hydrodynamic equations of dense granular materials, which include both kinetic and contact contributions in constitutive relations, we derive a theoretical expression for the spectrum, where a good agreement between the result of MD simulations and theoretical prediction is established over a wide range of length scales.

Hydrodynamic instabilities in shear flows of dry cohesive granular particles

We extend the dynamic van der Waals model introduced by A. Onuki [Phys. Rev. Lett., 2005, 94, 054501] to the description of cohesive granular flows under a plane shear to study their hydrodynamic instabilities. By numerically solving the dynamic van der Waals model, we observed various heterogeneous structures of density fields in steady states, where the viscous heating is balanced with the energy dissipation caused by inelastic collisions. Based on the linear stability analysis, we found that the spatial structures are determined by the mean volume fraction, the applied shear rate, and the inelasticity, where the instability is triggered if the system is thermodynamically unstable, i.e. the pressure, p, and the volume fraction, ϕ, satisfy ∂p/∂ϕ < 0.

Effect of elastic vibrations on normal head-on collisions of isothermal spheres

We numerically investigate head-on collisions of isothermal viscoelastic spheres. We find that the restitution coefficient oscillates against the impact speed if the solid viscosity inside the sphere is small enough. We confirm that the oscillation arises from the resonance between the duration of contact and the eigenfrequencies of the sphere. This oscillation disappears if there exists the strong solid viscosity in spheres. We also find that a sinusoidal behavior of the restitution coefficient against the initial phase in the eigenmodes for collisions between a thermally activated sphere and a flat wall. As a result, the restitution coefficient can exceed unity if the impact speed of the colliding sphere is nearly equal to or slower than the thermal speed. We have confirmed the existence of the fluctuation theorem for impact processes through our simulation.

Sedimentation of granular columns in the viscous and weakly inertial regimes

We investigate the dynamics of granular columns of point particles that interact via long-range hydrodynamic interactions and fall under the action of gravity. We investigate the influence of inertia using the Green's function for the Oseen equation. The initial conditions (density and aspect ratio) are systematically varied. Our results suggest that universal self-similar laws may be sufficient to characterize the temporal and structural evolution of the granular columns. A characteristic time above which an instability is triggered (which may enable the formation of clusters) is also retrieved and discussed.

Penetration of projectiles into granular targets

Energetic collisions of subatomic particles with fixed or moving targets have been very valuable to penetrate into the mysteries of nature. But the mysteries are quite intriguing when projectiles and targets are macroscopically immense. We know that countless debris wandering in space impacted (and still do) large asteroids, moons and planets; and that millions of craters on their surfaces are traces of such collisions. By classifying and studying the morphology of such craters, geologists and astrophysicists obtain important clues to understand the origin and evolution of the Solar System. This review surveys knowledge about crater phenomena in the planetary science context, avoiding detailed descriptions already found in excellent papers on the subject. Then, it examines the most important results reported in the literature related to impact and penetration phenomena in granular targets obtained by doing simple experiments. The main goal is to discern whether both schools, one that takes into account the right ingredients (planetary bodies and very high energies) but cannot physically reproduce the collisions, and the other that easily carries out the collisions but uses laboratory ingredients (small projectiles and low energies), can arrive at a synergistic intersection point.

In situ granular charge measurement by free-fall videography

We present the design and performance characterization of a new experimental technique for measuring individual particle charges in large ensembles of macroscopic grains. The measurement principle is qualitatively similar to that used in determining the elementary charge by Millikan in that it follows individual particle trajectories. However, by taking advantage of new technology we are able to work with macroscopic grains and achieve several orders of magnitude better resolution in charge to mass ratios. By observing freely falling grains accelerated in a horizontal electric field with a co-falling, high-speed video camera, we dramatically increase particle tracking time and measurement precision. Keeping the granular medium under vacuum, we eliminate air drag, leaving the electrostatic force as the primary source of particle accelerations in the co-moving frame. Because the technique is based on direct imaging, we can distinguish between different particle types during the experiment, opening up the possibility of studying charge transfer processes between different particle species. For the ∼300 μm diameter grains reported here, we achieve an average acceleration resolution of ∼0.008 m/s(2), a force resolution of ∼500 pN, and a median charge resolution ∼6× 10(4) elementary charges per grain (corresponding to surface charge densities ∼1 elementary charges per μm(2)). The primary source of error is indeterminacy in the grain mass, but with higher resolution cameras and better optics this can be further improved. The high degree of resolution and the ability to visually identify particles of different species or sizes with direct imaging make this a powerful new tool to characterize charging processes in granular media.

Stability of freely falling granular streams

A freely falling stream of weakly cohesive granular particles is modeled and analyzed with the help of event driven simulations and continuum hydrodynamics. The former show a breakup of the stream into droplets, whose size is measured as a function of cohesive energy. Extensional flow is an exact solution of the one-dimensional Navier-Stokes equation, corresponding to a strain rate, decaying like t(-1) from its initial value, γ[over ˙](0). Expanding around this basic state, we show that the flow is stable for short times, γ[over ˙](0)t<<1, whereas for long times, γ[over ˙](0)t>>1, perturbations of all wavelengths grow. The growth rate of a given wavelength depends on the instant of time when the fluctuation occurs, so that the observable patterns can vary considerably.

Droplet formation and scaling in dense suspensions

When a dense suspension is squeezed from a nozzle, droplet detachment can occur similar to that of pure liquids. While in pure liquids the process of droplet detachment is well characterized through self-similar profiles and known scaling laws, we show here the simple presence of particles causes suspensions to break up in a new fashion. Using high-speed imaging, we find that detachment of a suspension drop is described by a power law; specifically we find the neck minimum radius, r(m), scales like near breakup at time τ = 0. We demonstrate data collapse in a variety of particle/liquid combinations, packing fractions, solvent viscosities, and initial conditions. We argue that this scaling is a consequence of particles deforming the neck surface, thereby creating a pressure that is balanced by inertia, and show how it emerges from topological constraints that relate particle configurations with macroscopic Gaussian curvature. This new type of scaling, uniquely enforced by geometry and regulated by the particles, displays memory of its initial conditions, fails to be self-similar, and has implications for the pressure given at generic suspension interfaces.