Particle Velocity Fluctuations in Steady State Sedimentation: Stratification Controlled Correlations

TL;DR

This study investigates particle velocity fluctuations and stratification in steady state sedimentation of monodisperse spheres, revealing universal scaling laws and confirming a model linking correlation lengths to concentration stratification.

Contribution

It demonstrates the universality of particle dynamics in sedimentation and validates a model connecting correlation lengths with concentration stratification.

Findings

Fluctuation magnitudes and correlation lengths vary with height in the column.

Results from different particle sizes collapse onto universal scaling laws.

The model predicting correlation lengths from stratification matches experimental data.

Abstract

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 $\nabla \phi$.