Abstract

The key to quantify phenomena such as gyrotactic plume formation and bioconvection requires a macroscopic view of their collective behaviour. Instead of modelling micro-swimmers individually, one can model the collective as a continuum using an advection-diffusion-typed equation. Using the gyrotactic swimmer, Dunaliella salina, in a downflowing pipe (Kessler, 1986 JFM ) as an example setup, I am going to discuss the success and challenges in developing the continuum model. The advantage of the continuum equation is that one can couple swimmers with non-linear flow pattern like bioconvection with the full Navier-Stokes equation for the flow. However, the challenge lies in the lack of an accurate model for the effective diffusivity of these swimmers. The earlier model by Prof. Pedley (Pedley & Kessler, 1990 JFM ) is not as accurate at high shear, while the recent model using Generalised Taylor Dispersion (GTD), although accurate in some cases (Croze et al., 2017 JFM ), fails at strain-dominant region (Bearon et al., 2011 JFM ). Lastly, I am going to present a roadmap towards a Direct Numerical Simulation of the suspension of swimmers.