Early-stage aggregation in three-dimensional charged granular gas

Single-Collision Statistics Reveal a Global Mechanism Driven by Sample History for Contact Electrification in Granular Media

Models for same-material contact electrification in granular media often rely on a local charge-driving parameter whose spatial variations lead to a stochastic origin for charge exchange. Measuring the charge transfer from individual granular spheres after contacts with substrates of the same material, we find instead a "global" charging behavior, coherent over the sample's whole surface. Cleaning and baking samples fully resets charging magnitude and direction, which indicates the underlying global parameter is not intrinsic to the material, but acquired from its history. Charging behavior is randomly and irreversibly affected by changes in relative humidity, hinting at a mechanism where adsorbates, in particular, water, are fundamental to the charge-transfer process.

Accurate determination of the shapes of granular charge distributions

Experiments have shown that charge distributions of granular materials are non-Gaussian, with broad tails that indicate many particles with high charge. This observation has consequences for the behavior of granular materials in many settings, and may bear relevance to the underlying charge transfer mechanism. However, there is the unaddressed possibility that broad tails arise due to experimental uncertainties, as determining the shapes of tails is nontrivial. Here we show that measurement uncertainties can indeed account for most of the tail broadening previously observed. The clue that reveals this is that distributions are sensitive to the electric field at which they are measured; ones measured at low (high) fields have larger (smaller) tails. Accounting for sources of uncertainty, we reproduce this broadening in silico. Finally, we use our results to back out the true charge distribution without broadening, which we find is still non-Guassian, though with substantially different behavior at the tails and indicating significantly fewer highly charged particles. These results have implications in many natural settings where electrostatic interactions, especially among highly charged particles, strongly affect granular behavior.

Anomalous aggregation regimes of temperature-dependent Smoluchowski equations

Temperature-dependent Smoluchowski equations describe the ballistic agglomeration. In contrast to the standard Smoluchowski equations for the evolution of cluster densities, with constant rate coefficients, the temperature-dependent equations describe both-the evolution of the densities as well as cluster temperatures, which determine the agglomeration rates. To solve these equations, we develop a Monte Carlo technique based on the low-rank approximation for the aggregation kernel. Using this highly effective approach, we perform a comprehensive study of the kinetic phase diagram of the system and reveal a few surprising regimes, including permanent temperature growth and "density separation" regime, with a large gap in the size distribution for middle-size clusters. We perform scaling analysis and classify the aggregation kernels for the temperature-dependent equations. Furthermore, we conjecture the lack of gelation in such systems. The results of the scaling theory agree well with the simulation data.

Role of energy in ballistic agglomeration

We study a ballistic agglomeration process in the reaction-controlled limit. Cluster densities obey an infinite set of Smoluchowski rate equations, with rates dependent on the average particle energy. The latter is the same for all cluster species in the reaction-controlled limit and obeys an equation depending on densities. We express the average energy through the total cluster density that allows us to reduce the governing equations to the standard Smoluchowski equations. We derive basic asymptotic behaviors and verify them numerically. We also apply our formalism to the agglomeration of dark matter.

Plastic instabilities in charged granular systems: Competition between elasticity and electrostatics

Electrostatic theory preserves charges, but allows dipolar excitations. Elasticity theory preserves dipoles, but allows quadrupolar (Eshelby-like) plastic events. Charged amorphous granular systems are interesting in their own right; here we focus on their plastic instabilities and examine their mechanical response to external strain and to an external electric field, to expose the competition between elasticity and electrostatics. In this paper a generic model is offered, its mechanical instabilities are examined, and a theoretical analysis is presented. Plastic instabilities are discussed as saddle-node bifurcations that can be fully understood in terms of eigenvalues and eigenfunctions of the relevant Hessian matrix. This system exhibits moduli that describe how electric polarization and stress are influenced by strain and the electric field. Theoretical expression for these moduli are offered and compared to the measurements in numerical simulations.

Electrification in granular gases leads to constrained fractal growth

The empirical observation of aggregation of dielectric particles under the influence of electrostatic forces lies at the origin of the theory of electricity. The growth of clusters formed of small grains underpins a range of phenomena from the early stages of planetesimal formation to aerosols. However, the collective effects of Coulomb forces on the nonequilibrium dynamics and aggregation process in a granular gas - a model representative of the above physical processes - have so far evaded theoretical scrutiny. Here, we establish a hydrodynamic description of aggregating granular gases that exchange charges upon collisions and interact via the long-ranged Coulomb forces. We analytically derive the governing equations for the evolution of granular temperature, charge variance, and number density for homogeneous and quasi-monodisperse aggregation. We find that, once the aggregates are formed, the granular temperature of the cluster population, the charge variance of the cluster population and the number density of the cluster population evolve in such a way that their non-dimensional combination obeys a physical constraint of nearly constant dimensionless ratio of characteristic electrostatic to kinetic energy. This constraint on the collective evolution of charged clusters is confirmed both by  our theory and our detailed molecular dynamics simulations. The inhomogeneous aggregation of monomers and clusters in their mutual electrostatic field proceeds in a fractal manner. Our theoretical framework is extendable to more precise charge exchange mechanisms, a current focus of extensive experimentation. Furthermore, it illustrates the collective role of long-ranged interactions in dissipative gases and can lead to novel designing principles in particulate systems.

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.