Spreading of a granular droplet

TL;DR

This study investigates how horizontal vibrations influence the spreading behavior of a thin granular film, deriving a nonlinear diffusion model that accurately predicts the shape and dynamics of the resulting granular droplet.

Contribution

The paper introduces a theoretical nonlinear diffusion equation for granular spreading under vibrations and provides an empirical friction law linking external parameters to layer behavior.

Findings

Self-similar parabolic shape of granular droplet observed

Quantitative agreement between theory and experiment

Effective dynamic friction coefficients derived

Abstract

The influence of controlled vibrations on the granular rheology is investigated in a specifically designed experiment. We study experimentally a thin granular film spreading under the action of horizontal vibrations. A nonlinear diffusion equation is derived theoretically that describes the evolution of the deposit shape. A self-similar parabolic shape (the``granular droplet'') and a spreading dynamics are predicted that both agree quantitatively with the experimental results. The theoretical analysis is used to extract effective dynamic friction coefficients between the base and the granular layer under sustained and controlled vibrations. We derive an empirical friction law involving external driving parameters and the layer height to represent our data.