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Behavior of Powders - Outline

Behavior of Powders - Outline. Interparticle Forces Van der Waals Forces Adsorbed Liquid Layers & Liquid bridges Electrostatic Solid Forces General Classifications for Fluidized Beds. R. y. y. van der Waals. Weakest force exists between solids; is of molecular origin

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Behavior of Powders - Outline

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

  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 • Pendular-looks like bridge, but particles not immersed in liquid • Funicular-thicker bridges but not completely filled • Capillary-particles at edge of cluster not completely wetted by liquid • Droplet-all particles completely wet

  5. Pendular- a closer look Pc: pressure inside capillary liquid • When Pc<PA, 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

  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- 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)

  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 (xsv=surface-volume mean diameter) • xsv=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 laminar turbulent logf* f* constant! Log Re

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

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

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

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

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