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

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.

💡 Research Summary

This paper investigates how gyrotactic swimming algae disperse in both laminar and turbulent channel flows, a problem of particular relevance to the design of algal photobioreactors and to natural aquatic environments where shear flows are common. Gyrotaxis arises because bottom‑heavy cells experience a torque balance between viscous shear and gravity, causing them to preferentially orient and swim toward downwelling regions. Understanding how this bias interacts with advection and diffusion is essential for predicting cell distribution, light exposure, and nutrient uptake in engineered systems.

The authors employ two complementary approaches. First, they perform direct numerical simulations (DNS) of the coupled Navier–Stokes equations and the equations of motion for individual gyrotactic cells in a planar channel. By varying the Peclet number (Pe = UH/D, where U is the mean flow speed, H the channel half‑height, and D the cell’s swimming diffusivity) and the Reynolds number (Re = UH/ν), they explore a wide range of flow regimes, including upwelling (flow toward the wall) and downwelling (flow away from the wall) configurations. Second, they apply the analytical swimming‑dispersion framework developed by Bees and Croze (2010), which extends classical Taylor‑dispersion theory to include biased swimming. Two competing models for the biased swimming term are examined: a simple biased‑random‑walk description and a more sophisticated shear‑induced orientation model.

In laminar flow, the DNS results reveal several striking departures from passive‑tracer behavior. In downwelling flow, gyrotactic cells accumulate near the wall and acquire a mean axial drift that exceeds the bulk fluid velocity. This drift grows roughly linearly with Pe, indicating that stronger advection amplifies the gyrotactic focusing effect. The effective axial diffusivity, however, shows a non‑monotonic dependence on Pe: it initially rises as shear‑induced cross‑stream mixing enhances dispersion, but beyond a critical Pe it declines because the concentrated cell layer suppresses longitudinal spreading. The generalized‑Taylor‑dispersion model that incorporates the shear‑induced orientation term reproduces both the drift and diffusivity trends with remarkable accuracy, whereas the simpler biased‑random‑walk model fails to capture the magnitude of the drift and the diffusivity peak.

In turbulent flow, the random fluctuations of the velocity field partially disrupt the alignment of cells, weakening gyrotactic focusing. Nevertheless, the DNS still detects a small but measurable positive drift (≈10–20 % of the laminar value) and a modest increase in effective diffusivity relative to passive tracers. The turbulent results suggest that even in highly mixed environments, gyrotaxis does not vanish completely; it manifests as a subtle bias that could influence long‑term cell residence times and light exposure.

The authors discuss the practical implications of these findings for photobioreactor design. In reactors that rely on laminar shear (e.g., thin‑film or flat‑panel systems), downwelling flow can cause cells to concentrate near the illuminated surface, potentially leading to self‑shading and reduced photosynthetic efficiency. Conversely, upwelling flow or the intentional introduction of moderate turbulence can promote a more homogeneous cell distribution, improving light utilization and mass transfer. By tuning Pe (through flow rate or channel geometry) and Re (through pump power or channel roughness), engineers can manipulate both the mean drift and the effective diffusivity to achieve desired residence‑time distributions.

Finally, the paper highlights the broader significance of integrating DNS with generalized dispersion theory. It provides the first quantitative validation of the Bees‑Croze model for gyrotactic swimmers in realistic shear flows and establishes a framework that can be extended to more complex geometries, multi‑species suspensions, and reactors with gas‑liquid interfaces. The insights gained here are directly applicable to the scaling up of algal biofuel production, CO₂ sequestration, and high‑value bioproduct synthesis, where precise control over cell positioning and mixing is paramount.