Driven granular gas with van der Waals interaction

Abstract

Granular matter is a collection of solid particles which inelastically collide with each other with possible size range from 1 $\mu$m (like clays) to $1$ km (like some asteroids). Due to the characteristic of dissipation, a myriad of interesting phenomena are observed in granular system, such as pattern formation, ``Brazil nut effect'', and phase separations. Most of them find a direct connection to our daily life or industrial processes. Additional cohesive forces between grains may significantly change the behavior of the system. For granular particles with sizes smaller than $100$ $\mu$m, one adhesive interaction, the van der Waals force, starts to play a role. It has been recognized that van der Waals interaction plays an important role in the generation of asteroids. However, detailed explorations of the influence by van der Waals interactions on granular materials are still lacking. In this thesis we try to fill this gap and numerically study how van der Waals interactions affect the collective behavior of excited granular gas. We perform time-driven molecular dynamics simulations. The system we simulate is composed of monodisperse spherical particles with a diameter of $70$ $\mu$m, which are confined by two parallel walls separated by a fixed distance. The restitution coefficient $\epsilon$ quantifies the dissipation, and the Hamaker constant sets the strength of the van der Waals interaction. The whole system is vibrated sinusoidally in the direction perpendicular to the walls, and the particles gain energy via collisions with the two walls. Particles will feel conservative attractive forces when they approach each other (modeled by the Hamaker theory) and inelastically collide with each other when they touch (modeled by the spring-dashpot model). We map the phase diagram of shaking amplitude $A$ and average filling fraction $\bar{\phi}$, and a new solid-like and gas coexistence regime is found, together with cluster and homogeneous states. We characterize the different granular phases by means of a set of order parameters, such as bond orientational order parameter, coordination number, and connection number. The solid-like part of the coexistence part could transform from a random close packing state (with local filling fraction $0.64$) to a poly-crystalline state (with hcp or fcc local structures) with $A$ increasing. The boundary line of the transition can be modulated by the restitution coefficient $\epsilon$ and the Hamaker constant, but is independent of $\bar{\phi}$. We show that the transition is due to different quenching speeds, a combined effect of the energy dissipation during collisions and energy injection through the walls.