Particle settling is a pervasive process in nature, and centrifugation is a versatile separation technique. Yet, the results of settling and ultracentrifugation experiments often appear to contradict the very law on which they are based: Archimedes' principle - arguably, the oldest physical law. The purpose of this paper is delving into the very roots of the concept of buoyancy by means of a combined experimental-theoretical study on sedimentation profiles in colloidal mixtures. Our analysis shows that the standard Archimedes' principle is only a limiting approximation, valid for mesoscopic particles settling in a molecular fluid, and we provide a general expression for the actual buoyancy force. This "Generalized Archimedes' Principle" accounts for unexpected effects, such as denser particles floating on top of a lighter fluid, which in fact we observe in our experiments
