Migration of gyrotactic micro-organisms in water

Abstract

Understanding the swimming characteristics of micro-organisms is significant for modelling the migration of motile cells and corresponding ecological risk assessments associated with harmful algae in oceans and estuaries. Presented in this paper is an experimental and numerical investigation of swimming characteristics of a typical gyrotactic micro-organism, Heterosigma akashiwo (H. akashiwo) in water, based on the technology of planar laser-induced fluorescence and the finite volume method. Two-dimensional swimming velocity of algal cells are obtained by analyzing cells' trajectories in the vertical plane, and three-dimensional swimming velocity is reconstructed based on the assumption that cells' swimming is isotropic in the horizontal plane. Four important parameters are given to reflect the swimming characteristics of gyrotactic cells in still water, including the mean swimming speed (Vs = 146 μm/s), the relative strength of reorientation by gravitational torque to rotational diffusion (λ = 1.96), the time scale of reorientation (B = 5.6 s), and rotational diffusivity (Dr = 0.046 rad2/s). A database of the ambient vorticity, mean swimming velocity and diffusivity tensor is established, by solving Fokker-Planck equation for the probability density function of cells' swimming under the combined action of gravity, rotational diffusion, and the ambient vorticity. The mean swimming velocity and translational diffusion tensor of H. akashiwo are found to change with the horizontal and vertical vorticity. It is also shown that gyrotactic cells swim in a given direction for a weak horizontal vorticity, in contrast to cells' tumbling and being trapped for a strong horizontal vorticity.