Anisotropic Energy Distribution in Three-Dimensional Vibrofluidized Granular Systems

TL;DR

This study investigates how energy is distributed and dissipated in a 3D vibrofluidized granular system, revealing directional dissipation patterns and the effects of system parameters on energy transfer.

Contribution

It introduces spatially resolved partial dissipations and fractional energy transfer metrics to analyze energy flow in granular systems under vibration.

Findings

Total dissipation is negative in the parallel direction and positive in perpendicular directions.

Energy supplied to perpendicular directions is dissipated by wall collisions.

Fractional energy transfer depends on particle number, vibration velocity, and restitution coefficients.

Abstract

We examine the energy distribution in a three-dimensional model granular system contained in an open cylinder under the influence of gravity. Energy is supplied to the system by a vibrating base. We introduce spatially resolved, partial particle-particle ``dissipations'' for directions parallel and perpendicular to the energy input, respectively. Energy balances show that the total (integrated) ``dissipation'' is less than zero in the parallel direction while greater than zero in the perpendicular directions. The energy supplied to the perpendicular directions is dissipated by particle-wall collisions. We further define a fractional energy transfer, which in the steady state represents the fraction of the power supplied by the vibrating base that is dissipated at the wall. We examine the dependence of the fractional energy transfer on the number of particles, the velocity of the vibrating base, the particle-particle restitution coefficient, and the particle-wall restitution coefficient. We also explore the influence of the system parameters on the spatially dependent partial dissipations.