On the general concept of buoyancy in sedimentation and ultracentrifugation

Gravity or ultracentrifuge settling of colloidal particles and macromolecules usually involves several disperse species, either because natural and industrial colloids display a large size polydispersity, or because additives are put in on purpose to allow for density-based fractionation of the suspension. Such 'macromolecular crowding', however, may have surprising effects on sedimentation, for it strongly affects the buoyant force felt by a settling particle. Here we show that, as a matter of fact, the standard Archimedes' principle is just a limiting law, valid only for mesoscopic particles settling in a molecular fluid, and we obtain a fully general expression for the actual buoyancy force providing a microscopic basis to the general thermodynamic analysis of sedimentation in multi-component mixtures. The effective buoyancy also depends on the particle shape, being much more pronounced for thin rods and discs. Our model is successfully tested on simple colloidal mixtures, and used to predict rather unexpected effects, such as denser particles floating on top of a lighter fluid, which we actually observe in targeted experiments. This 'generalized Archimedes principle' may provide a tool to devise novel separation methods sensitive to particle size and shape.