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

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 a previously published analytical swimming dispersion theory. Time-resolved dispersion measures are evaluated as functions of the Péclet 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 Péclet number. The cell effective axial diffusivity increases and decreases with Péclet number (for tracers it merely increases). In turbulent flows, gyrotactic effects are weaker, but discernable and manifested as non-zero drift. These results should have a significant impact on photobioreactor design.

Accumulation of motile elongated micro-organisms in turbulence

“…These type of swimmers are known to accumulate in regions of negative vertical velocity, in downwelling flows, also in the turbulent regime when spherical (Kessler 1985;Durham 2012;DeLillo et al 2012;Croze et al 2013). The main findings of this work are reported in figure 3: For gyrotactic swimmers of different shape clustering decreases when the aspect ratio of swimmers is increasing.…”

“…In the first case they are advected as passive tracers, whereas in the second case the swimming orientations are uniformly distributed. Large swimming velocities are able to counteract the dispersive effect of turbulence (Croze et al 2013) and more elongated particles are associated to a potentially compressible velocity field, being sensitive to the background shear. In summary, the accumulation is very weak and from our observations we can conclude that in three-dimensional turbulence patchiness exceeds that of a Poisson distribution only for elongated cells, not for spherical ones.…”

“…They found that accumulation in downwelling regions is the dominant means of aggregation also in turbulent flow and shows that patchiness is not significantly affected by the Taylor Reynolds number Re λ . Croze et al (2013) studied dispersion of gyrotactic algae in turbulent channel flow and quantify the increased diffusivity induced by the turbulent fluctuations.…”

Stability of downflowing gyrotactic microorganism suspensions in a two-dimensional vertical channel

“…The generalised Taylor dispersion theory would be a good starting point in this regard as it has recently been shown to provide a reliable prediction for self-propelling particles with a constant rotational diffusivity (e.g. Bearon et al 2011;Croze et al 2013). However, it is not evident yet whether it would also provide a good description for the dispersion of 'real' cells.…”

“…The assumption of a constant τ may not be a reasonable description particularly if the local vorticity (or the flow rate) is large (see also e.g. Bearon et al 2012;Croze et al 2013). It can be improved by the generalised Taylor dispersion theory as recently addressed (Hill & Bees 2002;Malena & Frankel 2003;Bearon et al 2011).…”