Time-dependent behavior of granular material in a vibrating box

Abstract

Using numerical and analytic methods, we study the time dependent behavior of granular material in a vibrating box. We find, by molecular dynamics simulation, that the temporal fluctuations of the pressure and the height expansion scale in Af , where A (f ) is the amplitude (frequency) of the vibration. On the other hand, the fluctuations of the velocity and the granular temperature do not scale in any simple combination of A and f . Using the kinetic theory of Haff, we study the temporal behaviors of the hydrodynamic quantities by perturbing about their time averaged values in the quasi-incompressible limit. The results of the kinetic theory disagree with the numerical simulations. The kinetic theory predicts that the whole material oscillates roughly as a single block. However, the numerical simulations show that the region of active particle movement is localized and moves with time, behavior very similar to the propagation of a sound wave.

A New Approach based on Langevin type Equation for Driven Granular Gas under Gravity

“…It has been used to study velocity distributions and the scaling relationships in granular fluids under external vibration [4,12,13,14,15,16]. At more macroscopic scale, hydrodynamic equations which are derived from the Boltzmann equation have been applied to driven granular systems to study local density, flow, and temperature profiles [17,18,19,20,21].…”