Simple models of the chemical field around swimming plankton

Abstract

The chemical field around swimming plankton depends on the swimming style and speed of the organism and the processes affecting uptake or exudation of chemicals by the organism. Here, we present a simple model for the flow field around a neutrally buoyant self-propelled organism at low Reynolds number and numerically calculate the chemical field around the organism. We show how the concentration field close to the organism and the mass-transfer rates vary with the swimming speed and style for Dirichlet (diffusion-limited transport) boundary conditions. We calculate how the length of the chemical wake, defined as being the distance at which the chemical field drops to 10% of the surface concentration of the organism when stationary, varies with the swimming speed and style for both Dirichlet and Neumann (production limited) boundary conditions. For Dirichlet boundary conditions, the length of the chemical wake increases with increasing swimming speed, and the self-propelled organism displays a significantly longer wake than the towed-body model. For Neumann boundary conditions, the converse is true; because swimming enhances the transport of the chemical away from the organism, the surface concentration of chemical is reduced and thus the wake length is reduced.