Turbulence and the diffusive layers around small organisms

Abstract

We consider whether the diffusion of substances to and from a small spherical organism that is motionless relative to the surrounding water is significantly affected by the turbulent motions in the water. Viscosity, by smoothing out turbulent eddies less than a few millimeters across, dictates that the flow of nutrients and wastes to and from a very small organism must occur by molecular diffusion through a thin surrounding boundary layer. Motion of the organism relative to the water through sinking or swimming distorts this boundary layer. This alters the gradients and causes a fairly well understood increase in diffusive flux. The effect of turbulent motion on the flux, however, is less well understood. We first clarify the relationship between the size of the smallest turbulent eddies and the Kolmogorov or viscous length and go on to contend that turbulent motion over the small distances near small organisms is manifested as a linear velocity gradient whose magnitude is determined by the rate of turbulent energy dissipation. Knowing the shear enables us to calculate, from the experimental results of Purcel (1978, Journal of Fluid Mechanics, 84, 551-559), the quantitative effect of the turbulence on the diffusive flux to and from an idealized spherical organism. For motionless cells 100 μm in diameter, high levels of turbulence (dissipation rate 10-6 W kg-1_ produce a {reversed tilde equals}2% increase in flux. This escalates to a 100% increase for cells {reversed tilde equals}1 mm in diameter. Our results also lead to the conclusion that the microzones of increased nutrient levels surrounding small organisms, proposed by Mitchell et al. (1985, Nature, 316, 58-59), are much more robust than they suggested. © 1989.