Contactless rebound of elastic bodies in a viscous incompressible fluid

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, where it is now well established that collisions cannot occur in finite time under certain assumptions. In a simplified framework, we provide conditions which allow us to prove that rebound is possible even in the absence of a topological contact. Our results lead to the conjecture that a qualitative change in the shape of the solid is necessary to obtain a physically meaningful rebound in fluids. We support the conjecture by comparing numerical simulations performed for the reduced model with finite element solutions obtained for corresponding well-established partial differential equation systems describing elastic solids interacting with incompressible fluids.