1. CENTRIFUGATION  Sedimentation and centrifugation Sedimentation
 When a suspension is allowed to stand, the denser solids slowly settle under the influence of gravity.
Centrifugation
 A settling process that is accelerated with a centrifugal field.

2.  Comparison between filtration and centrifugation: Feature Filtration
Introduction (2/8)
 Comparison between filtration and centrifugation:
Feature
Filtration
Centrifugation
Separation principal
Employment
Product obtained
Expense of equipment
Particle size
Removal of insolubles which are dilute, large and rigid
Dry cake
Less
Density
Used when filtration is ineffective
A paste or a more concentrated suspension
More

3.  Separation cost for recovering whole cells or cell debris:
Introduction (3/8)
 Separation cost for recovering whole cells or cell debris:
Ultrafiltration more economical
Centrifugation more economical
Ultrafiltration
Centrifugation

4.  Schematic presentation of a laboratory centrifuge:
Introduction (4/8)
 Schematic presentation of a laboratory centrifuge:

5. (1) Avoid imbalance in the rotor, which may be caused by:
Introduction (5/8)
 Care of centrifuges:
(1) Avoid imbalance in the rotor, which may be caused by:
a. Tube cracking during the run
* Conventional glass (Pyrex) centrifuge tubes withstand only g.
 Use centrifuge tubes made from
polypropylene or polycarbonate.
b. Misbalance of the tubes in the first place
 Small tubes—balanced by volume by eye; large
tubes (> 200 mL)—should be weighed.
(2) Any spillage should be immediately rinsed away.
 Avoid corrosion of centrifuge rotors.
(3) Do not use the machine at top speed constantly.

6. __________________ __________________ __________________
Introduction (6/8)
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7. * Relative Centrifugal Force, RCF =
Introduction (7/8)
* Relative Centrifugal Force, RCF =
g = 980 cm/s2
r: in cm
 Often an average RCF is determined using a value for r midway between the top and bottom of the sample container.

8. (centrifugal force = 31,000  g) 
Introduction (8/8)
ravg = 7 cm
20,000 rpm
RCF = 31,000
(centrifugal force = 31,000  g) 

9. FORCES DEVELOPED IN CENTRIFUGAL SEPARATION
The acceleration from a centrifugal force: a = w2r
where w = angular velocity, rad/s
r = radial distance from center of rotation
Settling by gravity force:
Settling in centrifuges:

10. FORCES DEVELOPED IN CENTRIFUGAL SEPARATION (2/3)
 Gravitational sedimentation is too slow to be practical for bacteria, and conventional centrifugation is too slow for protein macromolecules.
__________

11. [Example] A laboratory bottle centrifuge is used to collect yeast cells after fermentation. The centrifuge consists of a number of cylinders rotated perpendicularly to the axis of rotation. During centrifugation, the distance between the surface of liquid and the axis of rotation is 3 cm, and the distance from the bottom of the cylinder to that axis is 10 cm. The yeast cells can be assumed to be spherical, with a diameter of 8.0 mm and a density of 1.05 g/cm3. The fluid has physical properties close to those of water. The centrifuge is to be operated at 500 rpm. How long does it take to have a complete separation?
Solution: or
(To be continued)

12. Solution (cont’d): t = 0, r = 3 cm; t = ?, r = 10 cm
Example: laboratory bottle centrifuge
Solution (cont’d):
t = 0, r = 3 cm; t = ?, r = 10 cm
Data: d = 8.0 mm = 8.0  10-4 cm; m = 1 cP = 0.01 g/cm-s; rs = 1.05 g/cm3; r = 1.0 g/cm3;
 t = 2467 s = 41.3 min #

13. * Sedimentation Coefficient, s
FORCES DEVELOPED IN CENTRIFUGAL SEPARATION (3/3)
* Sedimentation Coefficient, s
“The velocity of a particle through a viscous medium is usually proportional to the accelerating field.” 
Unit of s: svedberg (S; 1 S = second)
 Svedberg: the inventor of ultracentrifuge

14. [Example] Estimate the time it would take to completely clarify a suspension of 70 S ribosomes in a high speed centrifuge operating at 10,000 rpm. During centrifugation, the distance between the surface of liquid and the axis of rotation is 4 cm, and the distance of travel of particles radially outward is 1 cm.
Solution:  #

15. TUBULAR BOWL CENTRIFUGE
 Suspension is usually fed through the bottom, and clarified liquid is removed from the top.
 Solid deposits on the bowl’s wall as a thick paste.
 The suspension can be fed until solid loss in the effluent becomes prohibitive.
 An intermittent operation.

16. TUBULAR BOWL CENTRIFUGE (2/6)
Assume that a particle is located at a distance z from the bottom of the centrifuge and at a position r from the axis of rotation. This particle is moving in both the z and r directions.

17. where Q = the volumetric flow rate
TUBULAR BOWL CENTRIFUGE (3/6)
The movement of the particle in the z direction (due to the convection of the feed flow):
where Q = the volumetric flow rate
R1 = the distance of liquid interface from the axis of rotation
The movement of the particle in the r direction: 

18. The trajectory of a particle in the centrifuge:
TUBULAR BOWL CENTRIFUGE (4/6) ;
The trajectory of a particle in the centrifuge:
Consider a particle enters the centrifuge at R1 (that is, at z = 0, r = R1) and do not reach R0 until at z = or

19. For R0 and R1 being approximately equal,
TUBULAR BOWL CENTRIFUGE (5/6)
For R0 and R1 being approximately equal,
Note:
Note: vg is a function only of the particles themselves, and S is a function only of the particular centrifuge.

20. * Continuous tubular bowl centrifuge for separation of two liquids:
An internal baffle provides a separate passage adjacent to the bowl wall to conduct the heavier-phase liquid to a different discharge elevation.

21. [Example] A bowl centrifuge is used to concentrate a suspension of Escherichia coli prior to cell disruption. The bowl of this unit has an inside radius of 12.7 cm and a length of 73.0 cm. The speed of the bowl is 16,000 rpm and the volumetric capacity is 200 L/h. Under these conditions, this centrifuge works well. (a) Calculate the settling velocity vg for the cells. (b) After disruption, the diameter of debris is about one-half of that of cell and the viscosity is increased four times. Estimate the volumetric capacity of this same centrifuge operating under these new conditions.
Solution:
(To be continued)

22. Using the same centrifuge,
[Example] Analysis of bowl centrifuge
(a) Calculate the settling velocity vg for the cells.
(b) Estimate the volumetric capacity of this same centrifuge for cell debris.
Solution:
Data: R = 12.7 cm; = 73 cm; w = 16,000 rpm = rad/s; Q = 200 L/h = cm3/s; g = 980 cm/s2
 vg = 2.63  10-7 cm/s
Using the same centrifuge,  #

23. All conditions except the bowl speed remain the same.
[Example] Beer with a specific gravity of and a viscosity of 1.4  10-3 N-s/m2 contains 1.5% solids, which have a density of 1160 kg/m3. It is clarified at a rate of 240 L/h in a bowl centrifuge, which has an operating volume of 0.09 m3 and a speed of 10,000 rev/min. The bowl has a radius of 5.5 cm and is fitted with a 4-cm outlet. Calculate the effect on feed rate of an increase in bowl speed to 15,000 rev/min and the minimum particle size that can be removed at the higher speed.
Solution:
All conditions except the bowl speed remain the same.
(To be continued)

24. [Example] Beer with a specific gravity of 1. 042 and a viscosity of 1
[Example] Beer with a specific gravity of and a viscosity of 1.4  10-3 N-s/m2 contains 1.5% solids, which have a density of 1160 kg/m3. It is clarified at a rate of 240 L/h in a bowl centrifuge, which has an operating volume of 0.09 m3 and a speed of 10,000 rev/min. The bowl has a radius of 5.5 cm and is fitted with a 4-cm outlet.
Calculate: when w = 15,000 rev/min, Q = ? d = ?
Solution (cont’d):  
(To be continued)

25. Solution (cont’d): Operating volume   d = 2.14  10-7 m #
[Example] Beer with a specific gravity of and a viscosity of 1.4  10-3 N-s/m2 contains 1.5% solids, which have a density of 1160 kg/m3. It is clarified at a rate of 240 L/h in a bowl centrifuge, which has an operating volume of 0.09 m3 and a speed of 10,000 rev/min. The bowl has a radius of 5.5 cm and is fitted with a 4-cm outlet.
Calculate: when w = 15,000 rev/min, Q = ? d = ?
Solution (cont’d):
Operating volume 
 d = 2.14  10-7 m #

26. SEPARATION OF LIQUIDS BY CENTRIFUGATION
 A common operation in the food and other industries.
* Example: the dairy industry, in which the emulsion of milk is separated into skim milk and cream.

27. The differential force across a thickness dr is: dF = rw2dm
SEPARATION OF LIQUIDS BY CENTRIFUGATION (2/3)
The differential force across a thickness dr is:
dF = rw2dm
Integration between r1 and r2:

28. At the liquid-liquid interface,
SEPARATION OF LIQUIDS BY CENTRIFUGATION (3/3)
At the liquid-liquid interface,
Pressure exerted by the light phase of thickness (r2 - r1)
= Pressure exerted by the heavy phase of thickness (r2 - r4)  
* The interface at r2 must be located at a radius smaller than r3.

29. [Example] In a vegetable-oil-refining process, an aqueous phase is being separated from the oil phase in a centrifuge. The density of the oil is kg/m3 and that of the aqueous phase is kg/m3. The radius for overflow of the light liquid has been set at mm and the outlet for the heavy liquid at mm. Calculate the location of the interface in the centrifuge.
Solution: 
 r2 = mm #

30. DISK CENTRIFUGE

31. DISK CENTRIFUGE (2/14)
 A short, wide bowl 8 to 20 in. in diameter turns on a vertical axis. Inside the bowl and rotating with it are closely spaced “disks”, which are actually cones of sheet metal set one above the other.
 In operation, feed liquid enters the bowl at the bottom, flows into the channels, and upward past the disks.

32.  The operation can be made continuous.
DISK CENTRIFUGE (3/14)
 The operation can be made continuous.

33. ___
___
____

34. Collection of solid:

35. DISK CENTRIFUGE (6/14)
 A properly operated disc centrifuge should separate 99% of the solids from the liquid stream and produce an 80-90% wet solids concentrate.
 The smaller the particle diameter, the lower the flow rate, and the longer the interval between discharges.
* Flow rate is proportional to the square of the diameter of the particle.
* Cell debris (particle size  0.5 mm) can be separated with flow rates of L/h.

36. (a) The flow rate of feed that yields a clarified supernatant liquid
DISK CENTRIFUGE (7/14)
 In actual operation, the desired separation is achieved by empirically determining:
(a) The flow rate of feed that yields a clarified supernatant liquid
(b) The time interval between solid discharges that will minimize liquid loss while still allowing the solids to flow
 Discharge periods are on the order of 0.1 s.

37. DISK CENTRIFUGE (8/14)
Consider a particle located at position (x, y), where x is the distance from the edge of the outer disks along the gap between the disk, and y is the distance normal to the lower disk. Liquid is fed into the centrifuge so that it flows upward through the gap between the disks, entering at R0 and leaving at R1.

38. The velocity of the particle in the x direction is:
DISK CENTRIFUGE (9/14)
The velocity of the particle in the x direction is:
where v0 is the convective liquid velocity, and vw is the particle’s velocity under centrifugation.

39. There are three important characteristics of v0:
DISK CENTRIFUGE (10/14)
There are three important characteristics of v0:
(1) Under most conditions, v0 >> vwsinq.
(2) v0 is a function of radius.
(3) v0 is a function of y.
where Q = the total volumetric flow rate
n = number of disks
r = the distance from the axis of rotation
= the distance between disks
f(y) = some function giving the velocity variation across the distance between disks

40. Note: Q = (total cross sectional area)  (average velocity)
DISK CENTRIFUGE (11/14)
Note: Q = (total cross sectional area)  (average velocity) 

41. The velocity of the particle in the y direction is:
DISK CENTRIFUGE (12/14)
The velocity of the particle in the y direction is:
The trajectory of a particle between the disks of this centrifuge is:

42. DISK CENTRIFUGE (13/14) 

43. At x = 0, y = 0 (The most unfavorable entering position.)
DISK CENTRIFUGE (14/14)
Integration for those particles that are most difficult to capture, that is,
At x = 0, y = 0 (The most unfavorable entering position.)
At x = (R0 - R1)/sinq, y = (They are captured at the wall.) 

44. [Example] Chlorella cells are being cultivated in an open pond
[Example] Chlorella cells are being cultivated in an open pond. We plan to harvest this biomass by passing the dilute stream of cells through an available disc bowl centrifuge. The settling velocity vg for these cells has been measured as 1.07  10-4 cm/s. The centrifuge has 80 discs with an angle of 40, an outer radius of 15.7 cm, and an inner radius of 6 cm. We plan to operate the centrifuge at 6000 rpm. Estimate the volumetric capacity Q for this centrifuge.
Solution:
Data: vg = 1.07  10-4 cm/s; n = 80; R0 = 15.7 cm; R1 = 6 cm; q = 40; g = 980 cm/s2
 Q = 3.14  104 cm3/s = 31.4 L/s #

45. SCALEUP OF CENTRIFUGATION
 Use laboratory data to predict performance of commercially available centrifuges.
 Commercially available centrifuges are designed on a mechanical basis and cannot be modified easily.
 Laboratory bottle centrifuges, being batch operation, give a clear liquid and a concentrated solid or paste.
 An idealized separation, never reached in a continuous flow centrifuge.
 There are two approaches of scaleup of centrifugation:
(1) use of the equivalent time Gt
(2) sigma analysis

46. Gt: a measurement of the difficulty of a given separation
SCALEUP OF CENTRIFUGATION (2/5)
 Scaleup of centrifugation based on the equivalent time Gt
Gt: a measurement of the difficulty of a given separation
where R = a characteristic radius, often the maximum in the centrifuge
t = the time needed for a particle to reach R
* Once the value for Gt is determined, a large-scale centrifuge that has a similar Gt should be considered.
* This approach must be regarded as only a crude approximation.

47. Values of Gt for various solids:
SCALEUP OF CENTRIFUGATION (3/5)
Values of Gt for various solids:

48. [Example] It has been shown that bacterial cell debris has Gt = 54  106 s. For a centrifuge bowl of 10 cm in diameter, find the centrifuge speed if a full sedimentation in 2 h is required.
Solution:   #

49.  Scaleup of centrifugation using the S factor (Q = vgS)
 Scaleup involves choosing a centrifuge that has the required S value to meet the process requirements of vg and Q.
* The value of S is really the area of a gravitational settler that will have the same sedimentation characteristics as the centrifuge for the same feed rate.

50. * Scaleup if different centrifuges are used:
SCALEUP OF CENTRIFUGATION (5/5)
 Scaleup of centrifugation using the S factor (Q = vgS)
* Scaleup from a laboratory test of Q1 and S1 to Q2 using similar type and geometry centrifuges:
* Scaleup if different centrifuges are used:
E is the efficiency of a centrifuge, which is determined experimentally.

51. (a) Calculate the effective diameter of the starch particles.
[Example] The old process for recovering starch particles from a slurry of starch and gluten involved a gravitational settling procedure in which the slurry was fed to one end of a table where the starch particles settled and remained in the table and starch-free liquid was discharged from the opposite end of the table. We have been asked to evaluate a process improvement involving the use of continuous centrifuges. It has been reported that a starch table with the dimensions of 2 ft wide and 120 ft long can handle a slurry feed rate of 2 gal/min. The slurry has a viscosity of 10-3 kg/m-s and a density difference of 100 kg/m3. The centrifuge has a S value of 31,500 m2.
(a) Calculate the effective diameter of the starch particles.
(b) Estimate the centrifuge throughput, assuming that you can operate at 50% of the theoretical maximum.
(To be continued)

52. [Example] Recovery of starch particles.
m = 10-3 kg/m-s; rs – r = 100 kg/m3
(a) Calculate the effective diameter of the starch particles.
Solution:
A starch table with the dimensions of 2 ft wide and 120 ft long can handle a slurry feed rate of 2 gal/min.  
 d = 1.02  10-5 m
(To be continued)

53. Q at 50% of the theoretical maximum
[Example] Recovery of starch particles. The centrifuge has a S value of 31,500 m2. (b) Estimate the centrifuge throughput, assuming that you can operate at 50% of the theoretical maximum.
Solution (cont’d):
Q at 50% of the theoretical maximum
= vg(0.5S) = (5.66  10-6)  (0.5  31500) #

54. [Example] A new recombinant protein is produced in yeast
[Example] A new recombinant protein is produced in yeast. The company scientists, also known as “the boys in the lab,” separate the cells in a laboratory bottle centrifuge to give a thick paste that will be subsequently disrupted to release the protein. This separation is accomplished by centrifuging small quantities of the broth for 30 min at 2000 rpm. In the lab centrifuge, the inner radius of the solution is 5 cm and the bottle tip radius is 15 cm. The cell suspension contains only 7% by volume of cells. We are asked to recommend the size and type of centrifuge for separating 10 m3 of this suspension per day.
Solution:
Q = vgS  
(To be continued)

55. Data: R1 = 5 cm; R0 = 15 cm; t = 30 min; w = 2000 rpm
[Example] Recommend the size and type of centrifuge for separating 10 m3 of a yeast suspension per day.
Solution (cont’d):
Data: R1 = 5 cm; R0 = 15 cm; t = 30 min; w = 2000 rpm
 vg = 1.36  10-5 cm/s #
* In general, a safety factor of 2 is introduced for disc centrifuges, while no safety factor is needed for tubular bowl centrifuges.

56. [Example] We want to centrifuge chlorella cells using an available disc bowl centrifuge operated at 6000 rpm. The centrifuge has 80 discs with an angle of 40, an outer radius of 15.7 cm, and an inner radius of 6 cm. The cell suspension has a viscosity of 1 cp and a density difference of 0.1 g/cm3. The effective diameter of chlorella cells is 4.3  10-4 cm. Assume the efficiency of the disc centrifuge is 0.5; estimate the throughput.
Solution:
= 14,820 cm3/s #

57. SCROLL TYPE OF DECANTING CENTRIFUGE
Horizontal Type
* An internal scroll conveyor is used to move the decanted solid out of the machine.
* Centrifugal force: 500-6,000 g 

58. * Scroll Decanting Centrifuge: Vertical Type (2/2)

59. ULTRACENTRIFUGE
 The term “ultracentrifuge” was originally applied by T. Svedberg to any centrifuge that permitted observation of the contents of the container during the act of centrifuging.
 It is now more commonly applied to any ultrahigh-force centrifuge (up to 75,000 rpm, with RCF values up to 500,000  g).

60. ULTRACENTRIFUGE (2/3)

61. ULTRACENTRIFUGE (3/3)

62. SELECTION OF EQUIPMENT FOR LIQUID-SOLID SEPARATIONS
Major function:
Recover solids
(2) Clarify liquid
Operation mode:
Continuous
(2) Batch, automatic
(3) Batch

63. Major function Operation Classification

64. Classification Equipment Subclassification

65. Major function Operation Classification

66. Classification Equipment Subclassification

67. CENTRIFUGAL EXTRACTOR

68. CENTRIFUGAL EXTRACTOR (2/2)

69. The End of
CENTRIFUGATION