Particle Velocity Fluctuations in Steady State Sedimentation: Stratification Controlled Correlations

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dc.creatorSegrè, P. N.
dc.creatorDavidheiser, J. E.
dc.date2007-09-08
dc.date.accessioned2026-07-07T08:28:23Z
dc.date.available2026-07-07T08:28:23Z
dc.descriptionThe 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 $\nabla ϕ$.
dc.description13 pages, 16 figures
dc.identifierhttps://arxiv.org/abs/0709.1188
dc.identifierhttp://arxiv.org/abs/0709.1188
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137598
dc.subjectFluid Dynamics
dc.titleParticle Velocity Fluctuations in Steady State Sedimentation: Stratification Controlled Correlations
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