Time resolved particle dynamics in granular convection

Abstract

We present an experimental study of the movement of individual particles in a layer of vertically shaken granular material. High-speed imaging allows us to investigate the motion of beads within one vibration period. This motion consists mainly of vertical jumps, and a global ordered drift. The analysis of the system movement as a whole reveals that the observed bifurcation in the flight time is not adequately described by the Inelastic Bouncing Ball Model. Near the bifurcation point, friction plays an important role, and the branches of the bifurcation do not diverge as the control parameter is increased. By fitting the grains trajectories near the wall it is possible to quantify the effective acceleration acting on them. A comparison of the mass centre flying time and the flying time determined for the grains near the wall exposes the underlying mechanism that causes the downward flow.

Convection in a vibrated granular layer

“…But if flight times are calculated by assuming that the granular layer is a perfectly inelastic body upon which only gravity is acting, then the experimental results are not recovered. The measured flight times are shorter than predicted [15]. Kroll [16] pointed out that the effect of interstitial air was likely to be the cause.…”

“…It is clear that the Gutman model correctly reproduces the flight times of the granular layer as a whole up to Γ ≈ 2.3. The disagreement between the model and the experiment for greater driving accelerations is not due to the presence of air; the finite duration of the collision (assumption (2)) is likely to be involved [15]. If Γ is increased further, the flight time τ reaches the value of the driving period T .…”

“…In fact, inside the layer the grains move differently from one place to another, and this differential motion establishes the convective patterns. Near the onset (for Γ 1) the velocity field takes the form of a toroidal roll, as depicted in [15], figure 5. This differential motion can only be understood if there are forces acting only at certain zones of the granular layer, affecting exclusively some of the grains.…”

“…This means that another force, apart from gravity and the effect due to the interstitial air, is acting on the grains near the wall so as to produce a net downward motion at each cycle. The quantification of this force by means of an effective acceleration will be presented elsewhere [15].…”

Bouncing dynamics of a spring

“…Furthermore, periodicity and chaotic behaviors have been investigated. One also reports numerous applications of the bouncing ball model in various fields such as granular media [5], nanotechnology [6], neuro-sciences [7], gambling [8] or in the bouncing droplets dynamics [9].…”