Nutrient exposure of chemotactic organisms in small-scale turbulent flows

Micro-organisms living in a turbulent fluid environment often use directed motility to locate regions of higher than average nutrient concentrations. Here, we consider a simple continuum model for the distribution of such chemotactic particles when the particles and the chemoattractant are both advected by a turbulent flow. The influence of chemotactic sensitivity on the spatial distribution of the particles is characterized for different types of advected chemical fields. Using an effective diffusion approximation, we obtain an analytical expression for the nutrient exposure resulting from the chemotactic activity of the particles, generalizing previous results obtained for the case of phototaxis in flows. We show that the biological advantage of chemotaxis in such systems is determined by the spatial variability of the averaged chemoattractant field and the effective diffusivity of the turbulent flow.