Scaling of the normal coefficient of restitution for wet impacts

TL;DR

This paper investigates how the coefficient of restitution in wet impacts varies with impact velocity and liquid film properties, using experimental measurements and a scaling model based on the Stokes number.

Contribution

It introduces a scaling approach for the COR in wet impacts, linking it to the Stokes number and providing a model for high-velocity limits.

Findings

COR decreases with impact velocity for fixed film-to-particle ratio

The scaling model accurately predicts the COR behavior across different conditions

The model explains energy dissipation due to liquid inertia at high impact velocities

Abstract

A thorough understanding of the energy dissipation in the dynamics of wet granular matter is essential for a continuum description of natural phenomena such as debris flow, and the development of various industrial applications such as the granulation process. The coefficient of restitution (COR), defined as the ratio between the relative rebound and impact velocities of a binary impact, is frequently used to characterize the amount of energy dissipation associated. We measure the COR by tracing a freely falling sphere bouncing on a wet surface with the liquid film thickness monitored optically. For fixed ratio between the film thickness and the particle size, the dependence of the COR on the impact velocity and various properties of the liquid film can be characterized with the Stokes number, defined as the ratio between the inertia of the particle and the viscosity of the liquid. Moreover, the COR for infinitely large impact velocities derived from the scaling can be analyzed by a model considering the energy dissipation from the inertia of the liquid film.