BS 5 Centrifugation

8/13/2019 BS 5 Centrifugation

1/69


2/69

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 pasteor a more

concentrated

suspension

More

I ntroduction (2/8)


3/69

Separation costfor recovering whole cells or cell debris:I ntroduction (3/8)

Ultrafiltration

more

economical

Centrifugation

more

economical

Ultrafiltration

Centrifugation


4/69

Schematic presentation ofa laboratory centrifuge:I ntroduction (4/8)


5/69

Care of centrifuges:(1) Avoid imbalancein the rotor, which may be caused by:

a. Tube crackingduring the run

* Conventional glass (Pyrex) centrifuge tubes

withstand only 34000 g.Use centrifuge tubes made from

polypropylene or polycarbonate.

b. Misbalanceof the tubesin the first place

Small tubesbalanced by volume by eye; large

tubes (> 200 mL)should be weighed.

(2) Any spillage should be immediatelyrinsed away.

Avoid corrosion of centrifuge rotors.

(3) Do notuse the machine at top speed constantly.

I ntroduction (5/8)


6/69

________________________________________________________________________

I ntroduction (6/8)


7/69

* Relative Centrifugal Force, RCF=g

r2

1s1047.0

s60

min

min

2rpm1

-

g= 980 cm/s2

r: in cm

)((rpm)10119.1

cm/s980

cm)(rpm

s1047.0rpm)(

RCF 252

21

2

r

r-

-

Often an average RCF is determined using a value for rmidway between the top and bottom of the sample

container.

I ntroduction (7/8)


8/69

ravg= 7 cm

20,000 rpm RCF = 31,000(centrifugal force = 31,000 g)

I ntroduction (8/8)


9/69

FORCES DEVELOPED IN CENTRIFUGAL

SEPARATION

The acceleration from a centrifugal force: a= 2rwhere = angular velocity, rad/s

r= radial distance from center of rotation

Settling by gravity force: gd

v sg )(18

2

-

Settling in centrifuges: r

d

v s2

2

)(18 -


10/69

Gravitational sedimentation istoo slow to be practicalfor bacteria, and conventional centrifugation is too slow

for protein macromolecules.

FORCES DEVELOPED IN CENTRIFUGAL SEPARATION (2/3)

__________


11/69

[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 mand a density of 1.05 g/cm3. The fluid hasphysical 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:

rd

dt

drv s

22

)(18

- td

r

rs

22

1

2 )(18

ln

-or

(To be conti nued)


12/69

Example: laboratory bottle centr ifuge

Solution (contd):

td

r

rs

22

1

2 )(18

ln

-

t= 0, r= 3 cm; t= ?, r= 10 cm

Data: d= 8.0 m = 8.0

10-4

cm; = 1 cP = 0.01 g/cm-s; s= 1.05 g/cm3; = 1.0 g/cm3;rad/s3.52

60

2500rpm500

t-

-2

24

)3.52()105.1(01.018

)100.8(

3

10ln

t= 2467 s = 41.3 min#


13/69

* Sedimentation Coefficient, s

The velocity of a particle through a viscous medium

is usuallyproportional to the accelerating field.

rd

v s2

2

)(18

- )(18

2

- sd

s

Unit of s:svedberg(S; 1 S = 10

13second)

Svedberg: the inventorof ultracentrifuge

rsv 2

FORCES DEVELOPED IN CENTRI FUGAL SEPARATION (3/3)


14/69

[Example] Estimate the time it would take to completely

clarify a suspension of 70 Sribosomes 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:

5

4

2

0

1

r

dr

sdt

t

h8.1s29080

s60

min1

rev

2

min

rev10000s1070

223.045ln1 2

13

2

- st

#

rsdt

drv 2


15/69


16/69

TUBULAR BOWL CENTRIFUGE (3/6)


17/69

The movement of the particle in the z

direction(due to the convection of the

feed flow):

)( 212

0 RR

Q

dt

dz

-

where Q= the volumetric flow rateR1= the distance of liquid interface

from the axis of rotation

The movement of the particle in the rdirection:

rd

dt

drs

22

)(18

-

gd

v sg )(

18

2

-

g

rv

dt

drg

2




18/69

)( 212

0 RR

Q

dt

dz

-

g

rvdt

drg

2

;

The trajectory of a particle in the

centrifuge:

Q

RR

g

rv

dtdz

dtdr

dz

drg

)(

/

/2

1

2

02 -

Consider a particle enters the centrifuge at R1(that is,

at z= 0, r= R1)anddo not reach R0until at z =

Q

RR

g

v

R

R g )(ln

2

1

2

0

2

1

0 -

)/ln(

)(

10

22

1

2

0

RRg

vRRQ

g -

or




19/69

For R0and R1being approximately equal,

)/ln(

)(

10

22

1

2

0

RRg

vRRQ

g -

2101

110

1010

110

1010

10

2

1

2

0 2)(/)(

))((

]/)(1ln[

))((

)/ln(RRRR

RRR

RRRR

RRR

RRRR

RR

RR

-

--

-

-

-- 4324

1

3

1

2

1)1ln( xxxxxNote:

)(222

gg v

gRvQ

Note: vgis a function only of the particles themselves,and is a function only of the particular centrifuge.




20/69

* Continuous tubular bowl

centrifugefor separation of

two liquids:

An internal baffleprovides a

separate passage adjacent to

the bowl wall to conduct the

heavier-phase liquid to a

different discharge elevation.



21/69

[Example] A bowl centrifuge is used to concentrate a

suspension of Escher ichia coli prior to cell disruption. The

bowl of this unit has an inside radius of 12.7 cmand alength of 73.0 cm. The speed of the bowl is 16,000 rpmand

the volumetric capacity is 200 L/h. Under these conditions,

this centrifuge works well. (a) Calculate the settling

velocity vgfor 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:

22

22

2or

2

R

Qgv

g

RvQ gg

(To be conti nued)


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[Example] Analysis of bowl centrifuge

222

R

Qgvg

Solution:

Data: R =12.7 cm; = 73 cm; = 16,000 rpm = 1674.7 rad/s;Q= 200 L/h = 55.56 cm3/s; g= 980 cm/s2

vg= 2.63 10-7cm/s

Using the same centrifuge,1

2

1

2

1

2

g

g

g

g

vv

vv

QQ

gd

v sg )(18

2

-16

1

4

)2/1(

/

/

/

/ 2

12

2

1

2

2

1

2

1

2

2

2

1

2

dd

d

d

Q

Q

(a) Calculate the settling velocity vgfor the cells.

(b) Estimate the volumetric capacity of this same centrifuge for celldebris.

#


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[Example] Beer with a specific gravity of 1.042and a

viscosity of 1.4 10-3N-s/m2contains 1.5% solids, whichhave a density of 1160 kg/m3. It is clarified at a rate of 240

L/hin a bowl centrifuge, which has an operating volume of0.09 m3and a speed of 10,000 rev/min. The bowl has a

radius of 5.5 cmand is fitted with a 4-cm outlet. Calculate

the effect on feed rate of an increase in bowl speed to 15,000

rev/min andthe minimum particle size that can be removed

at the higher speed.

Solution:

All conditions except the bowl speedremain the same.

2

1

2

2

1

2

Q

Q

)]([)]/[ln(18

)(

)/ln(

)(2

1

2

010

22

10

22

1

2

0RR

RR

d

RRg

vRRQ s

g --

-

(To be conti nued)


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Calculate: when = 15,000 rev/min, Q= ? d= ?Solution (contd):

)]([)]/[ln(18

)( 21

2

0

10

22

RRRR

dQ s -

-

2

1

2

2

1

2

Q

Q 2

22

)10000(

)15000(

240

Q

/sm105.1s3600

h

L1000

mL/h540 34

3

2

-

Q

[Example] Beer with a specific gravity of 1.042and a viscosity of 1.4 10-3N-s/m2contains 1.5% solids, which have a density of 1160 kg/m3. It

is clarified at a rate of 240 L/hin a bowl centrifuge, which has an

operating volume of 0.09 m3and a speed of 10,000 rev/min. The bowlhas a radius of 5.5 cmand is fitted with a 4-cm outlet.

(To be conti nued)


25/69

)]([

)]/[ln(18

)( 21

2

0

10

22

RR

RR

dQ s -

-

1s157060

215000 -

Operating volume32

1

2

0 m09.0)]([ - RR

]09.0[)4/5.5ln()104.1(18

)10421160()1570(105.1

3

224

-

-

-

d

d= 2.14 107m

Calculate: when = 15,000 rev/min, Q= ? d= ?Solution (contd):

[Example] Beer with a specific gravity of 1.042and a viscosity of 1.4 10-3N-s/m2contains 1.5% solids, which have a density of 1160 kg/m3. It

is clarified at a rate of 240 L/hin a bowl centrifuge, which has an

operating volume of 0.09 m3and a speed of 10,000 rev/min. The bowl

has a radius of 5.5 cmand is fitted with a 4-cm outlet.

#


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SEPARATION OF L IQUIDS BY CENTRI FUGATION (2/3)


27/69

The differential force across a

thickness dris:dF= r2dm

r

dFdPrdrdm

2and])2[(

rdrr

rdrrdP

22

2

])2[(

-

Integration between r1and r2:

21222

212

rrPP --




28/69

21222

212

rrPP --

At the liquid-liquid interface,

Pressure exerted by the light

phase of thickness (r2 r1)

= Pressure exerted by the heavyphase of thickness (r2 r4)

21222

2

4

2

2

2

22rrrr LH --

LH

LH rrr

-

-

21

242

2

* The interface at r2must be located at a radius smaller

than r3.



29/69

[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 919.5 kg/m3and that of the aqueous

phase is 980.3 kg/m3. The radius for overflow of the light

liquid has been set at 10.160 mmand the outlet for the

heavy liquid at 10.414 mm. Calculate the location of the

interface in the centrifuge.

Solution:

LH

LH rrr

-

-

2

1

2

42

2

5.9193.980

)160.10(5.919)414.10(3.980 2222

-

-

r

r2= 13.75 mm#


30/69

DISK CENTRIFUGE

DI SK CENTRIFUGE (2/14)


31/69

A short, wide bowl8 to 20 in.in diameter turns on a verticalaxis. 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 liquidenters the bowl at the bottom,

flows into the channels, and

upward past the disks.




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The operation can be made continuous.DI SK CENTRIFUGE (3/14)


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___

____

___


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Collection of solid:



35/69

A properly operated disc centrifuge should separate99% of the solids from the liquid streamand produce

an 8090% 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 thediameter of the particle.

gd

vvQ sgg )(18

;2

-

* Cell debris (particle size 0.5 m)can beseparated with flow rates of 300500 L/h.

( )


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Consider a particle located

at position (x, y), where xis

the distance from the edge

of the outer disks along the

gapbetween the disk, and

yis the distance normal to

the lower disk. Liquid isfed into the centrifuge so

that it flows upward

through the gap between

the disks, entering at R0and leaving at R1.

( )



38/69

The velocity of the particle in the xdirection is:

sin0 vvdtdx -

where v0is the convective liquid velocity, and vis theparticles velocity under centrifugation.

( )

DISK CENTRIFUGE (10/14)


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There are three important characteristics of v0:

(1) Under most conditions, v0>> vsin.(2) v0is a function of radius.

(3) v0is a function of y.

)()2(

0 yfrn

Qv

dt

dx

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



40/69

)()2(

0 yfrn

Qv

dt

dx

Note: Q= (total cross sectional area)(average velocity)

dy

rn

yQfrndyvrnQ

00

0

)2(

)(1)2(

1)2(

1)(1

0

dyyf



41/69

The velocity of the particle in the ydirection is:

coscos2

g

rvv

dt

dyg

The trajectory of a particlebetween the disks of this

centrifuge is:

cos)(

2

/

/ 22

ryQgf

vn

dtdx

dtdy

dx

dy g

)()2(

0 yfrn

Qvdtdx



42/69

cos)(

2

/

/ 22

ryQgf

vn

dtdx

dtdy

dx

dy g

sin0 xRr -

cos)sin()(

2 20

2

xRyQgf

vndxdy g -

sin0 xRr -



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sin0 xRr -

cos)sin()(

220

2

xRyQgf

vn

dx

dy g-

Integration for those particlesthat are most difficult to

capture,that is,

At x= 0, y= 0 (The most unfavorable entering position.)

At x= (R0 R1)/sin, y= (They are captured at the wall.)

)(cot)(3

2 31

3

0

2

- gg vRR

g

nvQ

1)(1

0

dyyf


44/69

[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 vgfor these cells has been measured as1.07 10-4cm/s. The centrifuge has 80 discswith an angle of40, 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 capacityQ

for this centrifuge.

Solution:

-

cot)(

3

2 31

3

0

2

RRg

nvQ g

Data: vg= 1.07 10-4cm/s; n= 80; R0= 15.7 cm; R1= 6 cm; = 40; g=980 cm/s2

rad/s62860

26000

Q= 3.14 104cm3/s = 31.4 L/s

#


45/69

SCALEUP OF CENTRIFUGATION

Use laboratory data to predict performance of

commercially available centrifuges.

Commercially available centrifuges are designed on amechanical basisand 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

SCALEUP OF CENTRIFUGATION (2/5)


46/69

Scaleup of centrifugation based on the equivalent time GtGt: a measurement of the difficulty of a given separation

tg

RGt

2

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 Gtis determined, a large-scale

centrifuge that has a similar Gtshould be considered.

* This approach must be regarded as only a crude

approximation.



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Values of Gtfor various solids:


48/69

[Example] It has been shown that bacterial cell debris

has Gt= 54 106s. For a centrifuge bowl of 10 cmindiameter, find the centrifuge speedif a fullsedimentation in 2 his required.

Solution:

tg

RGt

2

)36002(980

)5(

1054

26

rpm580,11min

s60

rad2

rev1rad/s1212

#



49/69

Scaleup of centrifugation using the factor (Q= vg)Scaleup involves choosing a centrifuge that hasthe required valueto meet the processrequirements of vgand Q.

* The value of is really the area of a gravitationalsettlerthat will have the same sedimentation

characteristics as the centrifuge for the same feed

rate.



50/69

Scaleup of centrifugation using the factor (Q= vg)

* Scaleup from a laboratory test of Q1and 1to Q2using similar type and geometry centrifuges:

2

2

1

1

QQ

* Scaleup if different centrifuges are used:

22

2

11

1

E

Q

E

Q

Eis the efficiency of a centrifuge, which is determined

experimentally.


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[Example] Recovery of starch particles.

= 10-3kg/m-s; s= 100 kg/m3(a) Calculate the effective diameter of the starch particles.

Solution:

m/s1066.5s60

min

ft3.28

m

gal7.48

ft

ft1202

gal/min2 63

2

-

gv

A starch table with the dimensions of 2 ft wide and120 ft longcan

handle a slurry feed rate of 2 gal/min.

gdv sg )(18

2

- )8.9)(100()10(18

1066.53

26

--

d

d= 1.02 10-5m(To be continued)


53/69

[Example] Recovery of starch particles. The centrifuge has a value of31,500 m2. (b) Estimate the centrifuge throughput, assuming that you

can operate at 50% of the theoretical maximum.

Solution (contd):

Qat 50% of the theoretical maximum

= vg(0.5) = (5.66 10-6) (0.5 31500)

gal/min1410min

s60

L28.32

gal7.48

m

L1000

s

m089.0

3

3

#

m/s1066.5 6-gv

[Example] A new recombinant protein is produced in


54/69

[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 minat

2000 rpm. In the lab centrifuge, the inner radius of the

solution is 5 cmand the bottle tip radius is 15 cm. The cell

suspension contains only 7% by volume of cells. We areasked to recommend the size and type of centrifuge for

separating 10 m3 of this suspension per day.

Solution:

g

rv

dt

drg

2 t

gR

R

dtg

v

r

dr

0

20

1

t

RRgv

g

tv

R

Rg

g

2

10

2

1

0 )/ln(orln

(To be continued)

Q= vg


55/69

[Example] Recommend the size and type of centrifuge for separating

10 m3 of a yeast suspension per day.

t

RRgvg 2

10 )/ln(

Solution (contd):

Data: R1= 5 cm; R0= 15 cm; t= 30 min; = 2000 rpmvg= 1.36 105cm/s

2

5

3

m851

cm/s101.36

day/m10

-

gv

Q

* In general, a safety factor of 2is introduced for disc

centrifuges, while no safety factor is neededfor tubular

bowl centrifuges.

#

[Example] We want to centrifuge chlorella cells using an


56/69

[Example] We want to centrifuge chlorella cells using an

available disc bowl centrifuge operated at 6000 rpm. The

centrifuge has 80 discswith an angle of 40, an outer radiusof 15.7 cm, and an inner radius of 6 cm. The cell suspensionhas a viscosity of 1 cpand a density difference of 0.1 g/cm3.

The effective diameter of chlorella cells is 4.3 104cm.Assume the efficiency of the disc centrifuge is 0.5; estimate

the throughput.

Solution:

cm/s1001.1)980)(1.0()01.0(18

)103.4()(

18

4242

--

- gd

v sg

1s628s60

min

rev

2rev/min6000 -

- ERR

g

nvQ g

cot)(

3

2 31

3

0

2

= 14,820 cm3/s

#

s-cm

g:poise


57/69

SCROLL TYPE OF DECANTING CENTRIFUGE

Horizontal Type

* An internal scroll conveyoris used to move the decanted

solid out of the machine.

* Centrifugal force: 5006,000 g


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* Scroll Decanting

Centrifuge: Vertical

Type (2/2)


59/69

ULTRACENTRIFUGE

The term ultracentrifuge was originally applied by T.Svedbergto 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-forcecentrifuge(up to 75,000 rpm, with RCF values up to

500,000 g).

ULTRACENTRIFUGE (2/3)


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ULTRACENTRIFUGE (3/3)


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SELECTION OF EQUIPMENT FOR LIQUID-

SOLID SEPARATIONS

Major function:

(1) Recover solids

(2) Clarify liquid

Operation mode:

(1) Continuous

(2) Batch, automatic(3) Batch

Major function Operation Classification


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Classification Equipment Subclassification


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Major function Operation Classification


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Classification Equipment Subclassification


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CENTRIFUGAL EXTRACTOR


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CENTRIFUGAL EXTRACTOR

CENTRIFUGAL EXTRACTOR (2/2)


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BS 5 Centrifugation

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Transcript of BS 5 Centrifugation