Adhesive interactions of viscoelastic spheres

TL;DR

This paper presents an analytical model for the adhesive interactions of viscoelastic spheres, incorporating viscoelastic, elastic, and adhesive forces with a novel cross-term, and assesses their impact on collision outcomes.

Contribution

It introduces a new analytical framework for viscoelastic adhesive sphere interactions, including a cross-term that captures combined effects, extending existing contact theories.

Findings

Derived the total force including a cross-term for viscoelastic adhesive spheres.

Estimated the adhesive contribution to the normal coefficient of restitution.

Provided a criterion for the validity of the viscoelastic collision model.

Abstract

We develop an analytical theory of adhesive interaction of viscoelastic spheres in quasistatic approximation. Deformations and deformation rates are assumed to be small, which allows for the application of the Hertz contact theory, modified to account for viscoelastic forces. The adhesion interactions are described by the Johnson, Kendall, and Roberts theory. Using the quasistatic approximation we derive the total force between the bodies which is not sufficiently described by the superposition of elastic, viscous and adhesive contributions, but instead an additional cross-term appears, which depends on the elastic, viscous and adhesive parameters of the material. Using the derived theory we estimate the contribution of adhesive forces to the normal coefficient of restitution and derive a criterion for the validity of the viscoelastic collision model.