1. Behavior of Powders - Outline Interparticle Forces –Van der Waals Forces –Adsorbed Liquid Layers & Liquid bridges –Electrostatic –Solid Forces General Classifications for Fluidized Beds

2. van der Waals Weakest force exists between solids; is of molecular origin For the case of a sphere near a wall y R K H : Hamaker constant (varies with material) Between two flat surfaces y

3. Particles & Liquids If particles are present with a condensable vapor, the surface may have a layer of condensed vapor on it Adsorbed liquid can smooth over defects increasing contact area More liquid leads to liquid bridges This bond may be stronger than bare surface van der Waals forces

4. Types of Liquid Bonding a)Pendular-looks like bridge, but particles not immersed in liquid b)Funicular-thicker bridges but not completely filled c)Capillary-particles at edge of cluster not completely wetted by liquid d)Droplet-all particles completely wet

5. Pendular- a closer look When P c <P A, particles will want to come together Surface tension forces always pull particles together This arrangement creates strongest interparticle bond With more liquid, particles can move more freely P c : pressure inside capillary liquid

6. Electrostatic & solid Bridges Same as for aerosols, charged powders can repel each other Solid bridges-imagine liquid above was NaCl/water If powder in dried crystallites of salt would remain holding particles together Other compounds called binders (liq. or solid form) can be used by dissolving in liquid & drying Solid binders –another type, dry powders that react with liquid to form solid bridges

7. Interparticle Forces are functions of: Particle size Liquid concentration Humidity Temperature Interrelationship of above variables

8. Behavior of Particles in Fluidized Beds Depending on particle characteristics and inter- particle forces, fluidization behavior differs Group A- can be fluidized by air at ambient con- ditions(least cohesiveness) over a range of fluid- ization velocity Group B- powders that bubble under some con- ditions where Group A would not bubble (more cohesive) Group C- powders that can not be fluidized without bubbling(even more cohesive) Group D- large powders that form spouting beds(coarse powders, may have low cohesivity)

9. Flow in Packed Beds (not fluidized) Darcy’s rule for laminar flow u: superficial velocity through bed H: bed thickness  P: pressure drop More exactly for case of randomly packed bed of monosized particles (diameter=x), where  =void fraction,  =fluid viscosity For turbulent flow (  f =fluid density)

10. Criteria & overall expression Packed Bed Reynolds # –Laminar Re * <10 –Turbulent Re * >2000 General eq’n.=Ergun eq’n

11. Pressure drop for non spherical Particles For laminar flow (x sv =surface-volume mean diameter) –x sv =sphere having same surface to volume ratio as particles need mean if particles are not uniform For entire range of Re *

12. Friction Factors-Packed Beds f * =friction factor= In terms of Re * f * =150/Re * +1.75 Three regimes Laminar f * =150/Re * Turbulent f * =1.75 logf * laminarturbulent f * constant! Log Re

13. Fluidization: backwards packed bed When upwards drag exceeds apparent weight of particles bed becomes fluidized  F=gravity-upthrust This eq’n ignores interparticle forces gravity Upwards drag u

14. Fluidization-Relationship between  P & u  P ip =related to extra forces needed to overcome interparticle forces  P ip Minimum fluidizatio nvelocity Fluidized bed region

15. Dimensionless numbers Ar=Archimedes # Gravity & buoyancy vs. viscous forces Re mf =Reynolds# at incipient fluidization

16. Fluidized Bed vocabulary Mass of particles in bed=M B =(1-  )  P AH A:area (cross section) of bed H: bed height  P :particle density  :void fraction Absolute density= Bed density= Bulk density=

17. What gas velocities are required? For particles larger than 100  m –Wen&Yu correlation Re mf =33.7[(1+3.59*10 -5 Ar) 0.5 -1] –Valid for spheres in the range 0.01< Re mf 1000 For particles less than 100  m(x P =particle diameter) For fluidized beds-harmonic mean of mass distribution used as mean

18. Bubbles vs. No Bubbles u mb =superficial velocity at which bubbles first appear u mb (Abrahamsen &Fieldart,1980) for For groups B&D powders, they only bubble, u mf = u mb For group C, bubbles never form (cohesive force too high) & channeling occurs

19. Slugging When size of bubbles is greater than 1/3 of diam. of bed, rise velocity is controlled by equipment Slugging leads to large pressure fluctuations & vibrations Don’t want slugging! Yagi&Muchi(1952) criteria to avoid slugging (H mf :bed height at onset of fluidization, D:diameter of bed)

20. Expansion of a fluidized bed For non bubbling, there’s a region where u increases, particle separation increases but  P/H remains constant u is related to u T –single particle terminal velocity in general u= u T  n,  =voidage of the bed u= u T  4.65 Re P > 500 u= u T  2.4 Between - Khan & Richardson, 1989

21. More Bed Stuff Expansion for bubbling beds Simple theory-any gas excess of that needed for fluidization could form bubbles (not perfect since for low cohesive powders, much increase in gas velocity can occur before bubbling & increase leads to lower density,bigger bed volume) Relationship between gas as bubbles & gas doing fluidization depends on type of powder Entrainment Removal of particles from bed by fluidizing gas Rate of entrainment & size distribution of entrained particles will depend on particle size & density, gas density & viscosity, gas velocity & fluctuations, gas flow regime, radial position, vessel diameter

22. Entrainment All particles are carried up & particle flux+suspension concentration are constant with height Disengagement zone-upward flux and suspension concentration of fine particles decreases with increasing height Coarse particles fall back down

23. Applications for fluidized beds Drying – minerals, sand, polymers, pharma- ceuticals, fertilizers Mixing – all kinds of materials Granulation – process of making particles cluster by adding a binder Coating Heating/cooling – provides uniform temp- erature and good heat transport

24. Gas distribution Erosion – solid, hard particles may cause wear in bed Loss of fines- reduces quality of fluidization lowers g as-solid contact area, reduces catalytic activity Cyclones – can be used to separate entrained fines for recycle Issues to consider screen

25. Feeding the bed May need to feed fluidized bed Important for drying, granulation, recycle of fines Methods of solids feeding –Screw conveyors –Pneumatic conveying