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Dynamics of a sphere in inertial shear flow between parallel walls

Published online by Cambridge University Press:  29 March 2021

Andrew J. Fox ,
James W. Schneider  and
Aditya S. Khair Open the ORCID record for Aditya S. Khair [Opens in a new window]
Andrew J. Fox
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA15213, USA
James W. Schneider
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA15213, USA
Aditya S. Khair*
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA15213, USA
*
†Email address for correspondence: akhair@andrew.cmu.edu
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Abstract

The motion of a rigid sphere in ambient simple shear flow of a Newtonian fluid between infinite parallel walls is calculated via the lattice Boltzmann method for various particle Reynolds numbers, ${\textit {Re}}_p=Ga^2/\nu$, where $G$ is the velocity gradient of the shear; $a$ is the particle radius; and $\nu$ is the kinematic viscosity of the fluid. For a neutrally buoyant sphere, there exists a critical ${\textit {Re}}_p$ below which the hydrodynamic lift force has a single zero crossing, driving the particle to an equilibrium position at the centre of the channel. Above the critical ${\textit {Re}}_p$, the equilibrium position of the sphere undergoes a supercritical pitchfork bifurcation; inertial lift creates three equilibrium positions: an unstable equilibrium position at the centre and two stable equilibria equidistant from the centre. The critical ${\textit {Re}}_p$ occurs below the transition to unsteady flow, and increases with increasing particle confinement ratio, $\kappa =a/H$, where $H$ is the channel height. The equilibrium position of a non-neutrally buoyant sphere shifts toward a confining wall of the channel, in a manner that is dependent on the orientation, i.e. horizontal or vertical, of the channel. In both channel alignments, the gravitational force breaks the symmetry of the particle dynamics about the centreline of the channel, resulting in an imperfect bifurcation above a critical ${\textit {Re}}_p$. However, a sufficiently strong gravitational force will break the bifurcation and produce a single off-centre equilibrium position. We finally consider a neutrally buoyant sphere under the cessation or reversal of shear flow.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Nonlinear Dynamical Systems: Bifurcation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A119
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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