Trajectories of Swimming Micro-Organisms and Continuum Models of Bioconvection

Abstract

A random walk model has been developed to describe the motion of individual swimming cells, such as Chlamydomonas and Peridinium. These types of motile cells swim along helical paths and change their direction continuously and smoothly. They do not exhibit the run-and-tumble behaviour of bacteria like E. coli. The length scale of interest in this study is that on which the cells’ mean direction of motion changes significantly. This length is much greater than the radius of the helical trajectories so that we regard the trajectories as smooth lines. Consequently, it is the continuous limit of the random walk as the time step τ → 0 which is used in the modelling. This model has been successfully tested and is being used to provide the data for calculating the macroscopic parameters needed in continuum models of spontaneous pattern formation in suspensions of swimming micro-organisms, which is known as bioconvection. Details of the continuum models are given in the review by Pedley & Kessler (1992).