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Particle Technology- Hindered Systems and Thickening

The third lecture in the module Particle Technology, delivered to second year students who have already studied basic fluid mechanics. Hindered systems is mainly about sedimentation of concentrated suspensions.

The way concentrated dispersions behave is also covered: buoyancy correction and viscosity for Newtonian suspensions. Industrial thickener design is included, based on incompressible settling behaviour.

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Particle Technology- Hindered Systems and Thickening

  1. 1. Hindered Systems &Thickening<br />Chapter 6 in Fundamentals<br />Watch this lecture at<br />Visit for further resources.<br />Professor Richard Holdich<br /><br />
  2. 2. Introduction<br /><ul><li>Hindered settling
  3. 3. Porosity/voidage
  4. 4. and Concentration</li></li></ul><li>Introduction<br /><ul><li>Hindered settling - thickener design</li></li></ul><li><ul><li>Hindered settling – pharma crystallisation</li></li></ul><li>Hindered Systems &Thickening<br /><ul><li>Buoyancy correction – p61
  5. 5. Viscosity correction – p61
  6. 6. Hindered settling relations – p55
  7. 7. Zones in batch sedimentation – p57
  8. 8. Kynch's analysis – p60
  9. 9. Flux theory & thickener designs – p57/8</li></li></ul><li>Buoyancy Correction<br /><ul><li>Archimede’s Principle
  10. 10. When a body is wholly, or partially, immersed in a fluid it experiences an upthrust equal to the weight of fluid displaced.
  11. 11. Buoyancy - hence buoyed weight is:</li></li></ul><li>Buoyancy Correction<br /><ul><li>However, when measuring the buoyancy in a continuum consisting of suspended particles Archimede’s Principle tells us that the buoyancy correction is the density of the continuum not fluid alone (e.g. for a hydrometer in a slurry):</li></ul>where<br />
  12. 12. Viscosity correction<br /><ul><li>When a body is moving relative to a suspension made of others (usually finer).
  13. 13. NOT appropriate for sedimentation and filtration of a homogeneous suspension.
  14. 14. Krieger’s equation:</li></ul>Kis crowding factor 1/CMAX, and equal to 1.56 for spheres<br />eta is intrinsic viscosity, which is 2.5 for spheres<br />
  15. 15. Viscosity correction<br />
  16. 16. Hindered settling relations<br /><ul><li>Free settling</li></li></ul><li>Hindered settling relations<br /><ul><li>Hindered settling</li></li></ul><li>Hindered settling relations<br /><ul><li>Hindered settling</li></li></ul><li>Hindered settling relations<br /><ul><li>Hindered settling</li></ul>U = Ut (1-C)n<br /><ul><li>Richardson and Zaki’s equations</li></li></ul><li>Zones in batch sedimentation<br /><ul><li>Hindered settling</li></li></ul><li>Zones in batch sedimentation<br />At time t:<br />Height<br />Zones:<br />Supernatant<br />Original<br />concentration<br />Co<br />Variable<br />concentration<br />Sediment<br />Time<br />t<br />
  17. 17. Zones in batch sedimentation<br />Height<br />Zones:<br />Supernatant<br />Original<br />concentration<br />Co<br />Variable<br />concentration<br />Sediment<br />Concentration<br />
  19. 19. Kynch's analysis<br /><ul><li>Material balance on thickening element:</li></li></ul><li>Kynch's analysis<br /><ul><li>Material balance on thickening element:</li></ul>Input:<br />Output:<br />Accumulation:<br />Giving:<br />
  20. 20. Kynch's analysis<br /><ul><li>Material balance on thickening element:</li></ul>Height<br />Giving:<br />The rate at which the concentration <br />propagates up the vessel is equal to the differential of the ‘solids flux’ with<br />respect to solids concentration.<br />Time<br />
  21. 21. Kynch's analysis<br /><ul><li>Experimental measurements:</li></li></ul><li>Introduction<br /><ul><li>Hindered settling - thickener design</li></li></ul><li>Flux theory & thickener design<br /><ul><li>Thickeners - hindered settling</li></li></ul><li>Flux theory & thickener design<br /><ul><li>Thickeners - hindered settling</li></ul>Picket fence rake - plunging feed<br />
  22. 22. Flux theory<br /><ul><li>Settling curves
  23. 23. Batch flux curve</li></ul>CU<br />
  24. 24. Flux theory<br /><ul><li>Flux?</li></ul>m2 v/v m s-1 kg m-3 i.e. kg s-1<br /><ul><li>or</li></ul>v/v m s-1 kg m-3 i.e. kg m-2 s-1<br />i.e. mass flow rate of solids (per unit area) - input & output.<br />Area and solid density are assumed to be constant - hence simply velocity by concentration (v/v) are used.<br />
  25. 25. Flux theory<br /><ul><li>Batch flux curve</li></li></ul><li>Flux theory<br />
  26. 26. Flux theory<br /><ul><li>Underflow withdrawal flux</li></li></ul><li>Flux theory<br /><ul><li>Composite flux</li></li></ul><li>Flux theory<br /><ul><li>Limiting flux</li></li></ul><li>Flux theory<br />F m3/s<br /><ul><li>Limiting flux</li></ul>A<br />
  27. 27. Coe and Clevenger<br /><ul><li>Flux at any point:
  28. 28. Flux in feed:</li></ul>G = F Co<br />G = (U + T) A C<br /><ul><li>Flux in underflow:</li></ul>G = (Uu + T) A Cu<br /><ul><li>Rearrange equations for T then G gives:</li></li></ul><li>Coe and Clevenger<br />WhereU(C)is Uat values ofCbetweenCoandCu. Solve the above equations for various values ofCandU(C)and select the area that is the greatest for the design.<br />
  29. 29. Thickener designs - others<br /><ul><li>Lamella settler - increased capacity:</li></li></ul><li>Thickener designs - others<br /><ul><li>Lamella settler - increased capacity:</li></li></ul><li>Thickener designs - others<br /><ul><li>Potable (drinking) water treatment - floc bed clarifier:</li></ul>Upward flow clarification, coagulation using ferric sulphate or polyectrolyte. Solids collected in the blanket are removed by cone de-sludging.<br />
  30. 30. Sedimentation<br />Recap:<br /><ul><li>Stokes law ok for small particles
  31. 31. Particles of given size settle fastest in free settling
  32. 32. Increasing concentration slows particles - hindered settling
  33. 33. If a PSD then smaller particles dragged down by the larger ones
  34. 34. Empirically relate U=f(C): U=Ut(1-C)n</li></li></ul><li>Sedimentation<br /><ul><li>On line thickener design available on the www (freely available) using Coe and Clevenger technique:
  35. 35.</li></li></ul><li>This resource was created by Loughborough University and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme.<br />© 2009 Loughborough University<br />This work is licensed under a Creative Commons Attribution 2.0 License. <br />The name of Loughborough University, and the Loughborough University logo are the name and registered marks of Loughborough University. To the fullest extent permitted by law Loughborough University reserves all its rights in its name and marks, which may not be used except with its written permission.<br />The JISC logo is licensed under the terms of the Creative Commons Attribution-Non-Commercial-No Derivative Works 2.0 UK: England & Wales Licence.  All reproductions must comply with the terms of that licence.<br />The HEA logo is owned by the Higher Education Academy Limited may be freely distributed and copied for educational purposes only, provided that appropriate acknowledgement is given to the Higher Education Academy as the copyright holder and original publisher.<br />