The Hindered Settling Function at Low Re Has Two Branches

We analyze hindered settling speed versus volume fraction $\phi$ for dispersions of monodisperse spherical particles sedimenting under gravity, using data from 15 different studies drawn from the literature, as well as 12 measurements of our own. We discuss and analyze the results in terms of popular empirical forms for the hindered settling function, and compare to the known limiting behaviors. A significant finding is that the data fall onto two distinct branches, both of which are well-described by a hindered settling function of the Richardson-Zaki form $H(\phi)=(1-\phi)^n$ but with different exponents: $n=5.6\pm0.1$ for Brownian systems with P\'eclet number ${\rm Pe}<{\rm Pe}_c$, and $n=4.48\pm0.04$ for non-Brownian systems with ${\rm Pe}>{\rm Pe}_c$. The crossover P\'eclet number is ${\rm Pe}_c\approx10^8$, which is surprisingly large.