Scalings and Stability in Monodisperse Fluidized Beds

We have measured the concentration and fluctuation profiles to investigate steady state sedimentation of nearly monodisperse ($\sigma_a/a\le 1.6\%$) fluidized beds over a wide range of particle sizes $a$. In terms of the normalized particle column height $H^*\equiv H/a$, we find that taller columns are more stratified, and exhibit larger fluctuations, than shorter columns. Operating at a single average volume fraction $\phi_0$, we find scaling relations for the concentration at the top interface, $\phi_{top}=\phi_0e^{-H^*/3711}$, the velocity fluctuations, $\sigma_v(z)/v_0=\sqrt{H^*}\alpha(z)$, and the correlation lengths, $\xi(z)=a\beta(z)$. Finally, we develop a new advection-diffusion model that describes the observed bed stability.