Sedimentation equilibrium and the Generalized Archimedes' Principle

The buoyancy concept is critically re-examined for applications to dispersions of nano-particles, such as colloids, proteins, or macromolecules. It is shown that when the size of the buoyant particle is not too different (say, at most a factor of ten) from the size of the dispersed particles, new intriguing phenomena emerge, leading to the violation of the Archimedes' principle. The resulting buoyancy force depends not only on the volume of the particle and on the mass density of the dispersion, but also on the relative size of the particles, on their geometry, and on the interactions between the buoyant particle and the fluid. Explicit expressions for such a generalized Archimedes' principle are obtained and the results are tested against targeted experiments in colloidal dispersions.