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Contactless rebound of elastic bodies in a viscous incompressible fluid

Published online by Cambridge University Press:  24 May 2022

G. Gravina
Affiliation:
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Prague, Czech Republic Department of Mathematics, Temple University, Philadelphia, PA 19122, USA
S. Schwarzacher*
Affiliation:
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Prague, Czech Republic
O. Souček
Affiliation:
Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Prague, Czech Republic
K. Tůma
Affiliation:
Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Prague, Czech Republic
*
Email address for correspondence: schwarz@karlin.mff.cuni.cz

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.

Type
JFM Papers
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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