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

3. 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

4. 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

5. 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

6. 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

7. 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

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

9. 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- fine powders that cannot be fluidized without bubbling(even more cohesive) Group D- large powders that form spouting beds(coarse powders, may have low cohesivity)

10. 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)

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

12. 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 *

13. 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

14. 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

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

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

17. 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=