Dispersion of swimming algae in laminar and turbulent channel flows: consequences for photobioreactors

TL;DR

This study investigates how shear flows influence the dispersion of gyrotactic algae in laminar and turbulent channel flows, combining DNS and analytical theory to inform photobioreactor design.

Contribution

It provides a detailed comparison of algae dispersion in shear flows using DNS and analytical models, highlighting the effects of flow type and Peclet number.

Findings

In laminar downwelling flow, algae drift exceeds mean flow, increasing with Peclet number.

Effective axial diffusivity of algae varies non-monotonically with Peclet number.

Gyrotactic effects are weaker but detectable in turbulent flows.

Abstract

Shear flow significantly affects the transport of swimming algae in suspension. For example, viscous and gravitational torques bias bottom-heavy cells to swim towards regions of downwelling fluid (gyrotaxis). It is necessary to understand how such biases affect algal dispersion in natural and industrial flows, especially in view of growing interest in algal photobioreactors. Motivated by this, we here study the dispersion of gyrotactic algae in laminar and turbulent channel flows using direct numerical simulation (DNS) and the analytical swimming dispersion theory of Bees and Croze (2010). Time-resolved dispersion measures are evaluated as functions of the Peclet and Reynolds numbers in upwelling and downwelling flows. For laminar flows, DNS results are compared with theory using competing descriptions of biased swimming cells in shear flow. Excellent agreement is found for predictions that employ generalized-Taylor-dispersion. The results highlight peculiarities of gyrotactic swimmer dispersion relative to passive tracers. In laminar downwelling flow the cell distribution drifts in excess of the mean flow, increasing in magnitude with Peclet number. The cell effective axial diffusivity increases and decreases with Peclet number (for tracers it merely increases). In turbulent flows, gyrotactic effects are weaker, but discernable and manifested as non-zero drift. These results should significantly impact photobioreactor design.