Estimation of sinking velocities using free-falling dynamically scaled models: foraminifera as a test case

The velocity of settling particles is an important determinant of distribution in extinct and extant species with passive dispersal mechanisms, such as plants, corals, and phytoplankton. Here we adapt dynamic scaling, borrowed from engineering, to determine settling velocities. Dynamic scaling leverages physical models with relevant dimensionless numbers matched to achieve similar dynamics to the original object. Previous studies have used flumes, wind tunnels, or towed models to examine fluid flows around objects with known velocities. Our novel application uses free-falling models to determine the unknown sinking velocities of planktonic foraminifera - organisms important to our understanding of the Earth's current and historic climate. Using enlarged 3D printed models of microscopic foraminifera tests, sunk in viscous mineral oil to match their Reynolds numbers and drag coefficients, we predict sinking velocities of real tests in seawater. This method can be applied to study other settling particles such as plankton, spores, or seeds.