  Particle settling is a pervasive process in nature, and centrifugation is a
much 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 at 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.
