Simple heuristic for the viscosity of polydisperse hard spheres

A fast and simple way to measure how polydisperse spheres crowd around each other, termed the packing fraction, agrees well with rheological data.

Journal of Chemical Physics 141, 214503 (2014)

R. Farr

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Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"
Image for the paper "Simple heuristic for the viscosity of polydisperse hard spheres"

We build on the work of Mooney [Colloids Sci. 6, 162 (1951)] to obtain an heuristic analytic approximation to the viscosity of a suspension any size distribution of hard spheres in a Newtonian solvent. The result agrees reasonably well with rheological data on monodispserse and bidisperse hard spheres, and also provides an approximation to the random close packing fraction of polydisperse spheres. The implied packing fraction is less accurate than that obtained by Farr and Groot [J. Chem. Phys. 131(24), 244104 (2009)], but has the advantage of being quick and simple to evaluate.