Abstract

The dispersion of passive tracers in pipe/channel flows is well understood. G.I. Taylor established that the combined action of shear and diffusion causes tracers to disperse with effective diffusivity K = Pe^2 for laminar flows (K = Re/ln(Re) for turbulent flows). But how do swimmers, such as algae, disperse? Shear flow is known to significantly affect the transport of swimming algae in suspension: viscous and gravitational torques bias bottom-heavy swimmers towards regions of downwelling fluid (gyrotaxis). With Martin Bees, I recently developed an analytical theory extending Taylor’s analysis to incorporate biased swimming. The theory is general. It requires as inputs transport parameters from models of the average response to flow of the swimmer of interest. For algae, two competing models exist: (rotational) Fokker-Planck (FP) and generalized-Taylor-dispersion (GTD). I will present recent results comparing our analytical predictions and direct numerical simulations (DNS) for algae in laminar and turbulent channel flows. Our results allow us to address the old question of whether GTD is superior to FP. They also highlight how very differently swimmers disperse from passive tracers, particularly in laminar flows. I will discuss the practical implications of our findings and connect them with my current work on algal bioreactors with Kyriacos Leptos, Ray Goldstein, and Alison Smith.