Fluidized Beds

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  