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# Particle Technology- Dilute Particle Systems

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The second lecture in the module Particle Technology, delivered to second year students who have already studied basic fluid mechanics.

Dilute particle systems is mainly about sedimentation of single particles and dilute suspensions. The Particle Reynolds number determines the degree of turbulence in the fluid and techniques are provided for settling in laminar and turbulent systems. Industrial clarification is included.

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### Particle Technology- Dilute Particle Systems

1. 1. Dilute Particulate Systems<br />Chapter 5 in Fundamentals<br />Watch this lecture at http://www.vimeo.com/10200970<br />Visit http://www.midlandit.co.uk/particletechnology.htm for further resources.<br />Professor Richard Holdich<br />R.G.Holdich@Lboro.ac.uk<br />
2. 2. Dilute Particulate Systems<br /><ul><li>field force(s) and drag
3. 3. Stokes’s settling equation
4. 4. Particle Reynolds number
5. 5. Drag coefficient/Friction factor plot
6. 6. what to do when Re'>0.2
7. 7. (Heywood tables)
8. 8. industrial clarification</li></li></ul><li>Forces<br /><ul><li>Newton:</li></li></ul><li>Weight Force<br /><ul><li>Tedious to weigh small particles, hence we use the particle diameter and convert to mass, then weight.</li></li></ul><li>Archimede’s Principle<br /><ul><li>When a body is wholly, or partially, immersed in a fluid it experiences an upthrust equal to the weight of fluid displaced.
9. 9. Discovered in his bath?
10. 10. Buoyancy - hence buoyed weight is:</li></li></ul><li>Stokes’s Drag Expression<br /><ul><li>Solution to Navier-Stokes equation
11. 11. valid for no inertia</li></li></ul><li>Inertia<br /><ul><li>Rate of change of momentum</li></li></ul><li>Centrifugal Force<br /><ul><li>Note the weight is:
12. 12. The centrifugal force is:</li></ul>where r is radial position and omega is the angular speed (s-1).<br />
13. 13. Electro- and Thermo-phoretic<br /><ul><li>Due to electric field or temperature gradients
14. 14. Mainly applicable to small particles (less than 10 microns) is gases
15. 15. See gas cleaning notes</li></li></ul><li>Gases<br /><ul><li>Small particles can ‘slip’ between the molecules of gases - hence there is a slip correction due to Cunningham applicable to particles less than 2 microns and based on the mean free path of the gas.
16. 16. The settling velocity will be…?</li></li></ul><li>Liquids<br /><ul><li>Small particles are subject to bombardment by liquid molecules giving rise to Brownian motion. Hence they might not settle at all!
17. 17. Significant with particles 1 micron in diameter and less.
18. 18. N.B. they will still settle in a centrifuge.</li></li></ul><li>Stokes’s settling equation<br />Single particle settling<br />Utis terminal settling velocity.<br />
19. 19. Stokes’s settling equation<br />The Stokes settling equation:<br />Stokes law valid for no inertia present<br />AND a low concentration/single particle. Note that bigger particles settle faster - Galileo and that tower in Pisa?<br />
20. 20. Stokes’s settling equation<br /><ul><li>Free settling</li></li></ul><li>Stokes’s settling equation<br />Stokes’s settling equation:<br />Note that bigger particles settle faster. Industrially we often enhance settling rates by causing the particles to coagulate or flocculate together.<br />
21. 21. Stokes’s settling equation<br /><ul><li>Colloid stability important in filtration and sedimentation.
22. 22. Often assessed by the Zeta potential
23. 23. Surface forces can predominate at iso-electric point.</li></li></ul><li>Particle Reynolds number<br />Particle Reynolds number:<br />still a ratio of inertial to viscous forces - note it is based on the FLUID properties of density and viscosity.<br />Must be less than 0.2 for Stokes’s law<br />AND a low concentration/single particle<br />
24. 24. Particle Reynolds number<br />
25. 25. Drag coefficient/Friction factor plot<br />
26. 26. What to do when Re'>0.2<br />Drag force = RAp<br />cf Friction factor: shear stress over density and velocity2<br />Weight =<br />Drag force =<br />
27. 27. What to do when Re'>0.2<br />Drag force = RAp<br />Weight =<br />Drag force =<br />…check that this reduces to Stokes law in laminar region.<br />
28. 28. What to do when Re'>0.2<br /><ul><li>Numerous correlations between friction factor and Reynolds number @ Re’>0.2
29. 29. Above can be used to give settling velocity =f(diameter) or vice-versa.
30. 30. Recommend a simple Tabular scheme developed by Heywood - now fully automated on the www (freely available): http://www.filtration-and-separation.com</li></li></ul><li>Industrial Clarification<br /><ul><li>field force(s) and drag
31. 31. Stokes’s settling equation
32. 32. Particle Reynolds number
33. 33. Drag coefficient/Friction factor plot
34. 34. what to do when Re'>0.2
35. 35. (Heywood tables)
36. 36. industrial clarification</li></li></ul><li>Industrial Clarification<br />Simple Camp-Hazen clarification model<br />or<br />
37. 37. Industrial Clarification - long tube test<br />
38. 38. Summary<br /><ul><li>field force(s) and drag
39. 39. Stokes’s settling equation
40. 40. Particle Reynolds number
41. 41. Drag coefficient/Friction factor plot
42. 42. what to do when Re'>0.2