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APS March 2006
- 1. Origin of Stability in Particle Sedimentation ( low Re , non-inertial : high Pe, No Brownian Motion) Phil Segre Physics Dept., Emory Univ. Jim McClymer - Physics Dept., Univ. of Maine P.N. Segre and J.P. McClymer, PRE, in preparation (2006) . P.N. Segre and J.P. McClymer, J. Phys. Cond. Matt. 16 , S4219 (2004) P.N. Segre, Phys. Rev. Lett. 89 , 254503 (2002). Fluidized Beds
- 2. Top Middle Particle Image Velocimetry x z y Pump Camera
- 3. Background – Unanswered Questions Sedimentation Experiments What is the origin of , v ? Time-Dependent behavior – Not necessarily Steady State. Uncertainty over whether the concentration is Stratified, i.e. . Fluidized Beds – This work Time-Independent, Steady state behavior observed. As in sedimentation, observed, but also . Q. Are these properties for simple universal functions, or do they depend upon system size ?? TEST: Choose one average volume fraction , and one bed height H=18.5 cm, but vary particle size a.
- 6. Correlation Lengths (z) C z (z)=exp(-z/ z ) z (z) ~ a We find an empirical scaling
- 8. Advection-Diffusion Model. (Advection Term) Expanding… Advective Term So Assume that and v are anti-correlated – Less dense regions go up –more dense regions down – Blob Model . Blob Model
- 9. Advection-Diffusion Model. (Diffusive Term)
- 10. Test of Flux Balance The fluxes are well balanced in all beds!
- 11. New Relation
- 14. Particle Flux Dense regions Fall , Dilute Regions Rise … Net Particle Flux Downward ! For fluctuations; use N 1/2 Model The flux gradient is then Velocity Fluctuations v Result from Fluctuations