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Inertial migration of a sphere in plane Couette flow

Published online by Cambridge University Press:  19 December 2023

Prateek Anand Open the ORCID record for Prateek Anand [Opens in a new window]  and
Ganesh Subramanian Open the ORCID record for Ganesh Subramanian [Opens in a new window]
Prateek Anand
Affiliation:
International Centre for Theoretical Sciences, Bengaluru 560089, India
Ganesh Subramanian*
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru 560064, India
*
†Email address for correspondence: sganesh@jncasr.ac.in
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Abstract

We study the inertial migration of a torque-free neutrally buoyant sphere in wall-bounded plane Couette flow over a wide range of channel Reynolds numbers $Re_c$ in the limit of small particle Reynolds number ($Re_p\ll 1$) and confinement ratio ($\lambda \ll 1$). Here, $Re_c = V_{wall}H/\nu$, where $H$ denotes the separation between the channel walls, $V_\text {wall}$ denotes the speed of the moving wall, and $\nu$ is the kinematic viscosity of the Newtonian suspending fluid. Also, $\lambda = a/H$, where $a$ is the sphere radius, with $Re_p=\lambda ^2 Re_c$. The channel centreline is found to be the only (stable) equilibrium below a critical $Re_c$ ($\approx 148$), consistent with the predictions of earlier small-$Re_c$ analyses. A supercritical pitchfork bifurcation at the critical $Re_c$ creates a pair of stable off-centre equilibria, located symmetrically with respect to the centreline, with the original centreline equilibrium becoming unstable simultaneously. The new equilibria migrate wall-ward with increasing $Re_c$. In contrast to the inference based on recent computations, the aforementioned bifurcation occurs for arbitrarily small $Re_p$ provided that $\lambda$ is sufficiently small. An analogous bifurcation occurs in the two-dimensional scenario, that is, for a circular cylinder suspended freely in plane Couette flow, with the critical $Re_c$ being approximately $110$.

JFM classification

Low-Reynolds-number flows: Stokesian dynamics Complex Fluids: Suspensions Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 977 , 25 December 2023 , A33
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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