Diatom sinking speeds: Improved predictions and insight from a modified Stokes' law

Accurately predicting the size-dependant sinking rate of diatoms is necessary to fully understand the cycling of oceanic carbon and silicon. Stokes' law predicts that sinking velocity should be proportional to the square of a diatom's radius (a scaling exponent of 2), which does not agree with empirically measured sinking speeds (scaling exponents of 1.2-1.6). We offer an alternative model for sinking speed that separately accounts for the different densities of a diatom's frustule (its siliceous cell armor) and its cytoplasm. The ratio of frustule to cytoplasm volume changes with size and, thereby, affects the scaling relationship between velocity and radius. The resulting model predicts a scaling exponent between 1 and 2 depending on the size and shape of the diatom, more accurately predicting the upper bound of measured sinking speeds and offering an analytical formula for the prediction of the maximum sinking speed of diatoms.