What buoyancy really is. A Generalized Archimedes Principle for sedimentation and ultracentrifugation

TL;DR

This paper redefines buoyancy by deriving a Generalized Archimedes Principle that explains unexpected sedimentation behaviors observed in colloidal mixtures, extending classical understanding beyond the traditional law.

Contribution

It introduces a new theoretical framework for buoyancy that accounts for complex sedimentation phenomena not explained by classical Archimedes' principle.

Findings

Standard Archimedes' principle is a limiting case.

Denser particles can float on lighter fluids.

Experimental validation of the generalized principle.

Abstract

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.