Dispersion of biased swimming microorganisms in a fluid flowing through a tube

TL;DR

This paper extends classical dispersion theory to account for the transport of self-propelled microorganisms in a tubular flow, providing exact expressions for drift and diffusion, with applications to bioreactors and swimming algae.

Contribution

It introduces a generalized dispersion framework for biased swimming microorganisms in flow, including exact formulas and comparisons with traditional Taylor-Aris approximations.

Findings

Exact expressions for mean drift and diffusivity derived

Skewness of distribution vanishes at long times

Application to gyrotactic algae in bioreactors

Abstract

Classical Taylor-Aris dispersion theory is extended to describe the transport of suspensions of self-propelled dipolar cells in a tubular flow. General expressions for the mean drift and effective diffusivity are determined exactly in terms of axial moments, and compared with an approximation a la Taylor. As in the Taylor-Aris case, the skewness of a finite distribution of biased swimming cells vanishes at long times. The general expressions can be applied to particular models of swimming microorganisms, and thus be used to predict swimming drift and diffusion in tubular bioreactors, and to elucidate competing unbounded swimming drift and diffusion descriptions. Here, specific examples are presented for gyrotactic swimming algae.