The influence of boundary conditions on the contact problem in a 3D Navier-Stokes Flow

TL;DR

This paper studies how different boundary conditions affect the contact behavior of a sphere falling in a viscous fluid, showing slip conditions can prevent collision paradoxes present in no-slip scenarios.

Contribution

It demonstrates that slip boundary conditions can avoid the no-collision paradox in viscous flow contact problems, extending understanding of boundary effects in fluid-structure interactions.

Findings

Slip boundary conditions prevent collision in finite time.

No-slip conditions lead to the no-collision paradox.

Mixed boundary conditions are also analyzed.

Abstract

We consider the free fall of a sphere above a wall in a viscous incompressible fluid. We investigate the influence of boundary conditions on the finite-time occurrence of contact between the sphere and the wall. We prove that slip boundary conditions enable to circumvent the "no-collision" paradox associated with no-slip boundary conditions. We also examine the case of mixed boundary conditions.