Sinking rates of phytoplankton filaments orientated at different angles: theory and physical model

Abstract

Measurements of phytoplankton sinking rates are usually performed on samples of randomly oriented cells or colonies and yet the theoretical analyses of results are usually based on formulae restricted to objects oriented either vertically or horizontally. Formulae first published in 1965 but unknown in the phytoplankton literature can be used to calculate sinking rates of prolate ellipsoids and cylinders, shapes commonly encountered in phytoplankton, sinking at a range of angles between vertical and horizontal. The formulae predict a curvilinear decrease in speed from the maximum when oriented at 0° to the vertical, and a horizontal component in the trajectories of cylindrical particles oriented at angles of >0° and <90°, with filaments with an axial ratio of 100 drifting sideways at up to 25% of the speed of vertical drift. All of these predictions were verified with a physical model of graphite cylinders (pencil leads) sinking in an oil-filled sedimentation column, after corrections for column wall effects were applied. The mean vertical sinking rate of a disperse, randomly oriented population of filaments was also calculated, from the probability of orientation at each angle, and the theoretical speed at that angle.