Understanding Batch and Continuous Settling of Particle Suspensions

1. Tutorial #3 MR #3.1, 3.5, 3.9, 3.12. To be discussed on Feb 5, 2014. By either volunteer or class list. Week # 3MR Chapter 3 MARTIN RHODES (2008) Introduction to Particle Technology , 2nd Edition. Publisher John Wiley & Son, Chichester, West Sussex, England.

2. Settling of a suspension of particles Equation (3.5)

3. Equation (3.6) Ufs

4. Re < 0.3: Re > 500: Batch settling Equation (3.20)

5. Khan & Richardson Archimedes number, Ar: (*) Equation (*): A maximum is observed at e = (n/(n+1); Inflection point at e = (n-1)/(n+1)

6. Sharp interfaces in sedimentation Variation of dimensionless setting flux with suspension concentration ReP<0.3, n=4.65

7. Concentration interface in sedimentation UPS1, UPS2 are particle volumetric flux Ups = Up * C =Up * (1-e) • The gradient of the curve at concentration C is the velocity of a layer of suspension of this concentration. (b) The slope of a chord joining two points at concentration C1 and C2 is the velocity of discontinuity or interface between suspensions of these concentrations.

8. The batch settling test C2 C2 C3 Determination of interface and layer velocities from a batch flux plot

9. Type 1 batch settling. Zones A, B and S are zones of constant concentration. Zone A is a clear liquid; zone B is a suspension of concentration equal to the initial suspension concentration; zone S is a suspension of settled bed or sediment concentration

10. Change in positions of interface AB, BS and AS with time in Type 1 batch settling

11. S Type 2 batch settling. Zones A, B and S are zones of constant concentration. Zone A is clear liquid; zone B is a suspension of concentration equal to the initial suspension concentration; zone S is a suspension of settled bed concentration. Zone E is a zone of variable concentration.

12. Change in positions of interface AB, BEmin, EmaxS and AS with time in Type 2 batch settling

13. Determining if settling will be Type 1 or Type 2. A line through CS tangent to the flux curve gives CB1 and CB2. Type 2 settling occurs when initial suspension concentration is between CB1 and CB2.

14. Relationship between the Height-Time curve and the flux plot Analysis of batch settling test

15. Analysis of batch settling; relative velocities of a plane of concentration C and the particles in the plane

16. Volume of particles which have passed through this plane in time t

17. Continuous settling • Settling of a suspension in a flowing fluid Continuous settling; downflow only

18. Equation (3.41) ** Upward flow of a particle suspension in a vessel gives total downward particle flux. (1-e) **

19. Total flux plot for settling in downward flow

20. Total flux plot for settling in upward flow

21. A real thickener (with upflow and downflow sections) A real thickener, combining upflow and downflow (F, L and V are volumes; CF, CL and CV are concentrations)

22. Total flux plot for a thickener at critical loading

23. Total flux plot for an underloaded thickener

24. Total flux plot for an overloaded thickener

25. Alternative total flux plot shape; thickener at critical loading

26. Alternative total flux plot shape; Overloaded thickener

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