Contactless rebound of elastic bodies in a viscous incompressible fluid

TL;DR

This study explores how elastic bodies can rebound in a viscous incompressible fluid without physical contact, challenging classical assumptions and introducing a reduced model to analyze fluid-structure interactions.

Contribution

We propose a simplified reduced model for elastic body rebound in viscous fluids and demonstrate conditions under which rebound occurs without topological contact.

Findings

Rebound can occur without physical contact under certain conditions.

A shape change in the solid is likely necessary for rebound.

Numerical simulations support the theoretical conjecture.

Abstract

In this paper, we investigate the phenomenon of particle rebound in a viscous incompressible fluid environment. We focus on the important case of no-slip boundary conditions, for which it is by now classical that, under certain assumptions, collisions cannot occur in finite time. Motivated by the desire to understand this fascinating yet counterintuitive fluid-structure interaction, we introduce a reduced model which we study both analytically and numerically. In this simplified framework, we provide conditions which allow to prove that rebound is possible even in the absence of a topological contact. Our results lead to conjecture that a qualitative change in the shape of the solid is necessary for obtaining a physically meaningful rebound. We support the conjecture by also comparing numerical simulations performed for the reduced model with the finite element solutions obtained for the corresponding well-established PDE system.