Shock Propagation in Granular Flow Subjected to an External Impact

TL;DR

This paper investigates shock propagation in granular flow caused by an impact, combining experiments, simulations, and theory to understand the scaling behavior and dimensional crossover effects.

Contribution

It introduces a theoretical model predicting a t^{1/3} shock radius growth and explains the late-time crossover to three-dimensional behavior observed experimentally.

Findings

Shock radius grows as t^{1/3} in 2D.

Experimental data shows a late-time crossover to different scaling.

Simulations confirm the dimensional crossover and model predictions.

Abstract

We analyze a recent experiment [Phys. Rev. Lett., {\bf103}, 224501 (2009)] in which the shock, created by the impact of a steel ball on a flowing monolayer of glass beads, is quantitatively studied. We argue that radial momentum is conserved in the process, and hence show that in two dimensions the shock radius increases in time $t$ as a power law $t^{1/3}$. This is confirmed in event driven simulations of an inelastic hard sphere system. The experimental data are compared with the theoretical prediction, and is shown to compare well at intermediate times. At late times, the experimental data exhibit a crossover to a different scaling behavior. We attribute this to the problem becoming effectively three dimensional due to accumulation of particles at the shock front, and propose a simple hard sphere model which incorporates this effect. Simulations of this model capture the crossover seen in the experimental data.