Archimedes principle, generalized

The fate of an object in a homogeneous fluid suspension is simple. If it weighs more than the fluid it displaces, it sinks; otherwise, it floats, just as Archimedes predicted 23 centuries ago. In both natural and industrial settings, though, the suspending fluid is often complex, filled with several other dispersed species in a variety of sizes and densities. What’s the effect of such crowding on the particle’s buoyancy? Physicists Roberto Piazza (Polytechnic University of Milan), Alberto Parola (University of Insubria), and their colleagues have now answered that question. Their key argument is that when the surrounding fluid is a colloidal suspension, the weight of displaced fluid is substantially modified from Archimedes’s prediction by density perturbations induced by the central particle itself on the surrounding colloids. In particular, there exists a region close to the particle from which the colloids, modeled as hard spheres, are excluded. The physical effect of that exclusion zone is to increase the particle’s buoyancy and thus lower its effective density. The analysis led to a generalized equation for buoyancy. Its predictions, which depend both on the particle size and on the specific interactions with the surrounding fluid, may be counterintuitive. In one of their experiments, small gold particles settled atop a suspension of much less dense but larger polymer colloids under them. (R. Piazza et al., Soft Matter, in press, doi:10.1039/C2SM26120K.)–R. Mark Wilson