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arXiv · 0709.1188

Particle Velocity Fluctuations in Steady State Sedimentation: Stratification Controlled Correlations

P. N. Segrè·J. E. Davidheiser
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Abstract

The structure and dynamics of steady state sedimentation of semi-concentrated ($ϕ=0.10$) 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 $\nabla ϕ$, the fluctuation magnitudes $σ_v$, and their spatial correlation lengths $ξ$, 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 $-a\nabla ϕ(z)$, $ξ(z)/a$, and $σ_v(z)/v_p$, 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 $ξ(z)$ in terms of the concentration stratification $\nabla ϕ(z)$ [P.J. Mucha and M.P. Brenner, Phys. Fluids {\bf 15}, 1305 (2003)], $ξ(z)=c_0 a[ϕS(ϕ)]^{1/5}[-a\nablaϕ(z)]^{-2/5}$. 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 $ξ$ lies with the concentration stratification $\nabla ϕ$.

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P. N. Segrè, J. E. Davidheiser. 2007-09-08. Particle Velocity Fluctuations in Steady State Sedimentation: Stratification Controlled Correlations. https://arxiv.org/abs/0709.1188

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