The settling velocity of mineral, biomineral, and biological particles and aggregates in water

Abstract

A new equation was developed to relate the size and settling velocity of particulate matter commonly recurring in aqueous ecosystems. This equation explicitly balanced the gravitational, buoyancy, viscous, and inertial forces as in Rubey () but was amended to describe in one instance both individual particles and granular aggregates with an internal fractal architecture. This approach allowed for an algebraic solution of the settling velocity, thus overcoming earlier approaches that required iterative numerical solutions. The equation was tested with mineral, biomineral, and biological suspended particles and granular aggregates from 52 existing experimental data sets, and resulted in average correlation coefficients R between 71% and 93.9%, and normilized residuals between 14.3% and 24.8% over Reynolds numbers ranging within 10−7 and 102. Accuracy of these results was generally better than for the Stokes' law, the Stokes' law modified with the Schiller‐Naumann drag coefficient, and Rubey's equation. Estimated parameters ranged within observed ones, thus suggesting that the equation was robust. An analysis of the drag showed that inertial force was negligible only for biological cells (isolated cysts), whereas it contributed by not less than 5% to the drag on large mineral particles and up to 20% for biomineral and biological aggregates. Finally, a correlation was found between the organic matter content and fractal properties of granular aggregates, which were described by empirical equations proposed here for the first time. The hypothesis that the settling velocity is a function of linear and nonlinear drag, and is ultimately determined by physical characteristics as much as biological composition and internal aggregate geometry, is supported here by quantitative analyses.