Particle Velocity Fluctuations in Steady State Sedimentation: Stratification Controlled Correlations

The structure and dynamics of steady state sedimentation of semi-concentrated ($\phi=0.10$) monodisperse spheres are studied in liquid fluidized beds. Laser turbidity and particle imaging methods are used to measure the particle velocity fluctuations and the steady state concentration profiles. Using a wide range of particle and system sizes, we find that the measured gradients $\nabla \phi$, the fluctuation magnitudes $\sigma_v$, and their spatial correlation lengths $\xi$, are not uniform in the columns - they all show strongly $z-$dependent profiles. These profiles also display a scaling in which results from different particle sizes collapse together when plotted in the forms $-a\nabla \phi(z)$, $\xi(z)/a$, and $\sigma_v(z)/v_p$, demonstrating the universality of the particle dynamics and structure in steady state sedimentation. Our results are also used to test a recently proposed model for the correlation lengths $\xi(z)$ in terms of the concentration stratification $\nabla \phi(z)$ [P.J. Mucha and M.P. Brenner, Phys. Fluids {\bf 15}, 1305 (2003)], $\xi(z)=c_0 a[\phi S(\phi)]^{1/5}[-a\nabla\phi(z)]^{-2/5}$. We find that the correlation lengths predicted by this model are in very good agreement with our measured values, showing that the origin of the fluctuation length $\xi$ lies with the concentration stratification $\nabla \phi$.