The fifth lecture in the module Particle Technology, delivered to second year students who have already studied basic fluid mechanics. Filtration covers the modification of Darcys law to predictive filtration design equations as well as ones used for test data analysis. Examples of industrial equipment for filtration are included.

1. Filtration Chapter 4 in Fundamentals Watch this lecture at http://www.vimeo.com/10201620 Visit http://www.midlandit.co.uk/particletechnology.htm for further resources. Course details: Particle Technology, module code: CGB019 and CGB919, 2nd year of study. Professor Richard Holdich R.G.Holdich@Lboro.ac.uk

3. Cake filtration mechanism

4. Modification of Darcy's law

5. Constant pressure filtration

6. Constant rate filtration

7. Variable rate & pressure filtration

9. Types - membrane Clarification on filtering membranes

10. Types - Clarification Cartridge and candle filtration

12. Cake filtration mechanism – reality p 41 Why can’t we simply measure Rm for each medium? i.e. Rm = f(material to be filtered)

15. Modification of Darcy's law Volume liquid Flow rate Darcy’s law/Kozeny: Pressure/L Time What do the graphs tell us about these equations? How will this vary for filtration? Think about a given material and filter in these equations – what is constant, what varies, look at the graph… What are the independent and dependent variables?

16. Modification of Darcy's law – p.29 At constant pressure drop: Q is constant - permeation Darcy’s law: Filtrate volume Q decreases - filtration Time

17. Modification of Darcy's law – p. 32 Build up of incompressible filter cake: Filter cake formation Filter medium

18. Modification of Darcy's law

19. Modification of Darcy's law Pressure drops are additive: Pcake Pmedium

20. Modification of Darcy's law Pressure drops are additive: P Ratio: cake volume:filtrate = constant = 

21. Modification of Darcy's law Ratio: cake volume:filtrate = constant =  What does Represent – in English, see the graph… What does Represent – in English

22. Modification of Darcy's law – p.36 where cis the dry cake mass per unit volume of filtrate: sis feed slurry mass fraction andmis the moisture ratio of the cake (mass cake wet/mass cake dry - or sample). In some instances one can assume m=1; i.e. neglect liquid in cake. and  is the specific resistance to filtration (m/kg).

23. Modification of Darcy's law – p.36 Considering Rc & alpha some more: w is dry mass/unit area solids: Rc alpha = Rc/w so: w

24. Modification of Darcy's law – equation (4.11) General filtration equation:

25. Constant pressure filtration Constant P filtration - integrate general equation: Time over filtrate volume to give: a b i.e: Filtrate volume

26. Constant pressure filtration summary: Need to know: viscosity, pressure, and filter area & slurry mass fraction, liquid density (and cake moisture - if poss.) Time over filtrate volume a b Need to calculate: c then  and Rm Filtrate volume

28. Constant pressure:y = m x + c

30. different cloths or media,

31. slurry agitation,

32. filter aids and flocculants

34. medium resistance

36. filtration pressure

37. filter area

38. Slurry mass fraction

39. liquid density

41. Constant pressure filtration

44. Variable pressure and rate equation:numerical integration of: plot

46. cake formation in slurry tank (F)

47. drying and/or washing (D and W)

48. discharge - then back to formation (D & Di)W D D & Di F

52. Mass wet cake deposited = mcV (kg)

53. mass slurry filtered = mcV + V (kg)All above is per cycle, hence 3600/tfor output per hour.

54. Industrial equipment Vacuum belt filter (continuous) Image appears courtesy of Polyfilters UK Limited www.polyfilters.com

55. Industrial equipment Vacuum belt filter (continuous) Image supplied courteousy of BHS-Sonthofen GmbH, Germany www.bhs-sonthofen.de

56. Industrial equipment Vacuum disc filter (continuous) Image courtesy of FLSmidth, Inc.

57. Industrial equipment Tube pressure filter (batch) Image courtesy of Mesto Minerals (Sala) AB

59. Cake filtration mechanism

60. Modification of Darcy's law

61. Constant pressure filtration

62. Constant rate filtration

63. Variable rate & pressure filtration