How inertial lift affects the dynamics of a microswimmer in Poiseuille flow

Akash Choudhary,Subhechchha Paul,Felix Rühle,Holger Stark

doi:10.1038/s42005-021-00794-y

Abstract

The transport of motile microorganisms is strongly influenced by fluid flows that are ubiquitous in biological environments. Here we demonstrate the impact of fluid inertia. We analyze the dynamics of a microswimmer in pressure-driven Poiseuille flow, where fluid inertia is small but non-negligible. Using perturbation theory and the reciprocal theorem, we show that in addition to the classical inertial lift of passive particles, the active nature generates a ‘swimming lift’, which we evaluate for neutral and pusher/puller-type swimmers. Accounting for fluid inertia engenders a rich spectrum of complex dynamics including bistable states, where tumbling coexists with stable centerline swimming or swinging. The dynamics is sensitive to the swimmer’s hydrodynamic signature and goes well beyond the findings at vanishing fluid inertia. Our work will have non-trivial implications on the transport and dispersion of active suspensions in microchannels.

Highlights

The transport of motile microorganisms is strongly influenced by fluid flows that are ubiquitous in biological environments
In combination with the passive inertial lift, this gives rise to rich complex dynamics in channel flow, which goes well beyond the findings in refs. 16,17
The inertial lift profile of Eq 5 causes a complex dynamics of the microswimmer governed by Eq 1, which we explore step by step

Summary

Introduction

The transport of motile microorganisms is strongly influenced by fluid flows that are ubiquitous in biological environments. 1234567890():,; Self-propelling microswimmers often experience dynamic fluid environments and confinements, for example, pathogens in lung mucus[1], microorganisms in laminar flow through porous matrix[2], and sperm cells in the Fallopian tubes[3] Often these swimmers interact with micro-scale flows and boundaries[4] to enhance survival probability[5] and biofilm formation[6] or cause intriguing collective patterns[7]. Inertial lift forces cause cross-stream migration and eventually focus particles roughly halfway between channel center and walls This effect has initiated major advances in cell-sorting and flow cytometry techniques in the newly developing field of inertial microfluidics[34,35]. The disturbance interacts with the curvature of the background flow and the channel walls, which in the presence of fluid inertia results in counter-acting shear-gradient and wall-induced lift forces that cause inertial focusing[37]

Methods

Results

Conclusion