Gyrotactic swimmer dispersion in pipe flow: testing the theory

Abstract

Suspensions of microswimmers are a rich source of fascinating new fluid mechanics. Recently we predicted the active pipe flow dispersion of gyrotactic microalgae, whose orientation is biased by gravity and flow shear. Analytical theory predicts that these active swimmers disperse in a markedly distinct manner from passive tracers (Taylor dispersion). Dispersing swimmers display nonzero drift and effective diffusivity that is non-monotonic with Péclet number. Such predictions agree with numerical simulations, but hitherto have not been tested experimentally. Here, to facilitate comparison, we obtain new solutions of the axial dispersion theory accounting both for swimmer negative buoyancy and a local nonlinear response of swimmers to shear, provided by two alternative microscopic stochastic descriptions. We obtain new predictions for suspensions of the model swimming alga Dunaliella salina, whose motility and buoyant mass we parametrise using tracking video microscopy. We then present a new experimental method to measure gyrotactic dispersion using fluorescently stained D. salina and provide a preliminary comparison with predictions of a nonzero drift above the mean flow for each microscopic stochastic description. Finally, we propose further experiments for a full experimental characterisation of gyrotactic dispersion measures and discuss implications of our results for algal dispersion in industrial photobioreactors.Key words: Authors should not enter keywords on the manuscript, as these must be chosen by the author during the online submission process and will then be added during the typesetting process (see http://journals.cambridge.org/data/relatedlink/jfmkeywords.pdf for the full list)

Diurnal variations in the motility of algal populations

“…The bias parameter has not been previously measured before for C. reinhardtii, and, across the diurnal variations, is measured to be smaller than that quantified for other gravitactic species, e.g. = 0.21 for D. salina (17) and = 2.2 for Chlamydomonas augustae (25).…”

“…In previous studies, e.g. (14,17,25), these parameters have been considered fixed and independent of the growth illumination. Here, instead, we account for their diurnal variation and evaluate the length l with parameters measured in the light and dark phases of a diurnal cycle.…”

“…Aside from mean speed and flagellar frequency, we measured other motility and hydrodynamic parameters important for the transport and dispersion of suspensions. These measurements are important to allow the parameterisation of mathematical models of cell suspensions, as has been done for other species, but ignoring diurnal variations (17). The parameters measured include the gravitactic reorientation time B, and rotational di usivity D r , and the bias parameter = 1/(2BD r ), which quantifies the ratio of rotational di usive and gravitational reorientation times.…”

“…Tracking settling heat-immobilised cells, we were also able to quantify the mean mass density ⇢ of cells, an important parameter for the analysis of suspension bioconvective instabilities (26) and for coupling the gyrotactic dynamics of cells to flow, e.g. in pipe flows (17). As shown in Figure S4, the density appears 10% larger than the surrounding fluid, with a slight reduction in its value during the light period.…”

“…Similar considerations apply to quantitative measurements of motility in other microalgal species. For example, swimming speed, rotational di usivity and gravitatic reorientation time (the time it takes a cell to gravitactically reorient to the vertical) have recently been measured for the marine species Dunaliella salina (17) and Heterosigma akashiwo (18,19). However, like in the studies of C. reinhardtii, these microalgae were not synchronised to diurnal cycles.…”