We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study.

A simplified model has previously described the inductive charging of colliding identical grains in the presence of an external electric field. Here we extend that model by including heterogeneous surface charge distributions, grain rotations and electrostatic interactions between grains. We find from this more realistic model that strong heterogeneities in charging can occur in agitated granular beds, and we predict that shielding due to these heterogeneities can dramatically alter the charging rate in such beds.

We study segregation of a binary mixture of similarly charged particles under shear using particlebased simulations. We simulate particle dynamics using a discrete-element model including electrostatic interactions and find that particles segregate according to their net charge. Particles that are charged twice as strong as other particles of the same electrical sign are seen more at insulating boundaries with which we shear the system. Weakly charged particles, on the other hand, stay more in the center of the sheared bed. We propose a simple model based on electrostatic potential energy to understand this segregation. The model shows that the segregated system we observe in our simulations is indeed the most favorable configuration in terms of electrostatic potential energy. Our simulations further show that for a given packing fraction there is an optimal shear velocity where the segregation maximally intensifies. We show that this maximum results from a competition between diffusional and Coulomb fluxes. For a larger shear velocity, diffusion suppresses segregation. * ryutay@phys.ethz.ch

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