Unsteady and inertial dynamics of an active particle in a fluid

TL;DR

This paper explores how unsteady and inertial effects influence the movement of active microorganisms in fluids, providing a method to calculate these effects based on known inertial corrections for passive particles.

Contribution

It introduces a novel approach to extend inertial correction methods from passive to active particles, enhancing understanding of microorganism dynamics in flow.

Findings

Method to compute inertial effects on motile organisms

Application to unsteady fluid accelerations and steady shear flow

Explanation of limitations in describing convective inertia effects

Abstract

It is well known that the reversibility of Stokes flow makes it difficult for small microorganisms to swim. Inertial effects break this reversibility, allowing new mechanisms of propulsion and feeding. Therefore it is important to understand the effects of unsteady and fluid inertia on the dynamics of microorganisms in flow. In this work, we show how to translate known inertial effects for non-motile organisms to motile ones, from passive to active particles. The method relies on a principle used earlier by Legendre and Magnaudet (1997) to deduce inertial corrections to the lift force on a bubble from the inertial drag on a solid sphere, using the fact that small inertial effects are determined by the far field of the disturbance flow. The method allows for example to compute the inertial effect of unsteady fluid accelerations on motile organisms, and the inertial forces such organisms experience in steady shear flow. We explain why the method fails to describe the effect of convective fluid inertia.