Anisotropy driven dynamics in vibrated granular rods

TL;DR

This study investigates how anisotropic granular rods move on a vibrated plate, revealing tilt-dependent horizontal velocities through experiments, simulations, and theoretical modeling, highlighting the role of friction during collisions.

Contribution

The paper introduces a combined experimental, simulation, and theoretical approach to understand tilt-induced horizontal motion in vibrated granular rods, emphasizing the role of friction regimes.

Findings

Horizontal velocity depends on tilt and plate acceleration.

Friction during collisions is crucial for horizontal motion.

Good agreement between experiments, simulations, and theory.

Abstract

The dynamics of a set of rods bouncing on a vertically vibrated plate is investigated using experiments, simulations, and theoretical analysis. The experiments and simulations are performed within an annulus to impose periodic boundary conditions. Rods tilted with respect to the vertical are observed to spontaneously develop a horizontal velocity depending on the acceleration of the plate. For high plate acceleration, the rods are observed to always move in the direction of tilt. However, the rods are also observed to move opposite to direction of tilt for a small range of plate acceleration and rod tilt. A phase diagram of the observed motion is presented as a function of plate acceleration and the tilt of the rods which is varied by changing the number of rods inside the annulus. Next we introduce a novel molecular dynamics method to simulate the dynamics of the rods using the dimensions and dissipation parameters from the experiments. We reproduce the observed horizontal rod speeds as a function of rod tilt and plate acceleration in the simulations. By decreasing the friction between the rods and the base plate to zero in the simulation, we identify the friction during the collision as the crucial ingredient for occurrence of the horizontal motion. Guided by the data from the experiments and the simulations, we construct a mechanical model for the dynamics of the rods in the limit of thin rods. The starting point of the analysis is the collision of a single rod with an oscillating plate. Three friction regimes are identified: slide, slip-stick, and slip reversal. A formula is derived for the observed horizontal velocity as a function of tilt angle. Good agreement for the horizontal velocity as a function of rod tilt and plate acceleration is found between experiments, simulations and theory.