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

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 , the separation between time scales characterizing the swimmer orientation dynamics (of ) and those that characterize migration across the channel (of ), allows for use of the method of multiple scales to derive a drift-diffusion equation for the swimmer concentration profile; here, is the swimming speed, is the channel half-width and is the swimmer rotary diffusivity. The steady state concentration profile is a function of the Peclet number, ( being the channel centreline velocity), and the swimmer aspect ratio . Swimmers with (with ), in the regime ( ), migrate towards the channel walls, corresponding to a high-shear trapping behaviour. For ( for ), however, swimmers migrate towards the centreline, corresponding to a low-shear trapping behaviour. Interestingly, within the low-shear trapping regime, swimmers with asymptote to a -independent concentration profile for large , while those with exhibit a ‘centreline collapse’ for . 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 plane, thereby highlighting the singular behaviour of infinite-aspect-ratio swimmers.