Collision of Adhesive Viscoelastic Particles

TL;DR

This paper models the collision of convex viscoelastic particles considering adhesion, deriving conditions under which particles stick or rebound, and estimating the impact velocity threshold for these outcomes.

Contribution

It introduces a combined viscoelastic and adhesive contact model for small-impact collisions of convex bodies, extending previous purely viscoelastic models.

Findings

Derived a threshold impact velocity for sticking versus restitution.

Showed adhesion effects become significant at low impact velocities.

Provided a quasi-static approximation for the contact problem.

Abstract

The collision of convex bodies is considered for small impact velocity, when plastic deformation and fragmentation may be disregarded. In this regime the contact is governed by forces according to viscoelastic deformation and by adhesion. The viscoelastic interaction is described by a modified Hertz law, while for the adhesive interactions, the model by Johnson, Kendall and Roberts (JKR) is adopted. We solve the general contact problem of convex viscoelastic bodies in quasi-static approximation, which implies that the impact velocity is much smaller than the speed of sound in the material and that the viscosity relaxation time is much smaller than the duration of a collision. We estimate the threshold impact velocity which discriminates restitutive and sticking collisions. If the impact velocity is not large as compared with the threshold velocity, adhesive interaction becomes important, thus limiting the validity of the pure viscoelastic collision model.