Estimation of sinking velocity using free-falling dynamically scaled models: Foraminifera as a test case

Abstract

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 adapted dynamic scaling, borrowed from engineering, to determine settling velocity. 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 flow around objects with known velocities. Our novel application uses free-falling models to determine the unknown sinking velocity 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 predicted sinking velocity of real tests in seawater. This method can be applied to study other settling particles such as plankton, spores or seeds.