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Shear-induced migration of microswimmers in pressure-driven channel flow

Published online by Cambridge University Press:  12 March 2020

Laxminarsimharao Vennamneni Open the ORCID record for Laxminarsimharao Vennamneni [Opens in a new window] ,
Sankalp Nambiar  and
Ganesh Subramanian Open the ORCID record for Ganesh Subramanian [Opens in a new window]
Laxminarsimharao Vennamneni
Affiliation:
Engineering Mechanics Unit, JNCASR, Jakkur, Bangalore560064, India
Sankalp Nambiar
Affiliation:
Engineering Mechanics Unit, JNCASR, Jakkur, Bangalore560064, India
Ganesh Subramanian*
Affiliation:
Engineering Mechanics Unit, JNCASR, Jakkur, Bangalore560064, India
*
†Email address for correspondence: [email protected]
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Abstract

We study shear-induced migration in a dilute suspension of microswimmers (modelled as active Brownian particles or ABPs) subject to plane Poiseuille flow. For wide channels characterized by $U_{s}/HD_{r}\ll 1$, the separation between time scales characterizing the swimmer orientation dynamics (of $O(D_{r}^{-1})$) and those that characterize migration across the channel (of $O(H^{2}D_{r}/U_{s}^{2})$), allows for use of the method of multiple scales to derive a drift-diffusion equation for the swimmer concentration profile; here, $U_{s}$ is the swimming speed, $H$ is the channel half-width and $D_{r}$ is the swimmer rotary diffusivity. The steady state concentration profile is a function of the Péclet number, $Pe=U_{f}/(D_{r}H)$ ($U_{f}$ being the channel centreline velocity), and the swimmer aspect ratio $\unicode[STIX]{x1D705}$. Swimmers with $\unicode[STIX]{x1D705}\gg 1$ (with $\unicode[STIX]{x1D705}\sim O(1)$), in the regime $1\ll \text{Pe}\ll \unicode[STIX]{x1D705}^{3}$ ($Pe\sim O(1)$), migrate towards the channel walls, corresponding to a high-shear trapping behaviour. For $Pe\gg \unicode[STIX]{x1D705}^{3}$ ($Pe\gg 1$ for $\unicode[STIX]{x1D705}\sim O(1)$), however, swimmers migrate towards the centreline, corresponding to a low-shear trapping behaviour. Interestingly, within the low-shear trapping regime, swimmers with $\unicode[STIX]{x1D705}<2$ asymptote to a $Pe$-independent concentration profile for large $Pe$, while those with $\unicode[STIX]{x1D705}\geqslant 2$ exhibit a ‘centreline collapse’ for $Pe\rightarrow \infty$. The prediction of low-shear trapping, validated by Langevin simulations, is the first explanation of recent experimental observations (Barry et al., J. R. Soc. Interface, vol. 12 (112), 2015, 20150791). We organize the high-shear and low-shear trapping regimes on a $Pe{-}\unicode[STIX]{x1D705}$ plane, thereby highlighting the singular behaviour of infinite-aspect-ratio swimmers.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 890 , 10 May 2020 , A15
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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