Wall Drag on Free-Moving Ciliated Micro-Organisms

Abstract

It is generally assumed that wall drag on free-moving, self-propelled or passively moving micro-organisms is not significant under normal observation conditions. Yet the point at which such drag becomes significant has not been determined quantitatively. By comparing the relative velocities of sinking as well as swimming ciliates in tubes of various bore widths it has been determined that wall drag on sinking cells is about 8% significant at 108-132 body radii (or minor semi-axes) from the cell surface while the corresponding range for swimming cells is less than 1-4·2 body radii. These results are compared with the mathematical approximations for Stokes radius R_8 and depth of penetration of diffusing vorticity δ which characterize steady and quasi-steady Stokes flow respectively around a solid body. It is found that the asymptotic nature of the velocity profile of steady flow is reflected in the lack of agreement between R_8 and the measured distance for 8% drag. Conversely, the sharp gradient (or propulsive envelope) of the quasi-steady velocity profile is reflected in the substantial agreement between δ and the measured distance for > 0% drag. It is suggested that the given formula for δ which includes allowance for a propagated wave is a valid measure of the thickness of the quasi-steady region and that observations on motile ciliates be restricted to organisms at least 4 cell radii from the nearest wall if measurements free of wall-drag effects are to be obtained.