Centrifugation: Theory and Practice

Helmut Wieczorek

11.7.2012

Relative centrifugal field, rotor radius and rpm

Stokes‘ Law: Friction, buoyancy and the centrifugal force

Differential centrifugation

Density gradient centrifugation

The k‐factor (clearing factor): relative pelleting efficiency of a rotor

Centrifugation: Theory and Practice

A

Bv1

v2

r

r

vr

2

2 )2

∆∆

2 2

∆∆ 2 60 )2

∆∆ 0.01 2

∆∆ 1 0.01 2 1

relative centrifugal field (RCF)

centrifugal field = gravitational acceleration

∆∆

2

Relative centrifugal field, rotor radius and rpm

∆ r ∆

∆∆

2

v

v

v1 v2=

Beckman Coulter (2006) Rotors and Tubes. User‘s Manual

Nomogram

Hands‐on examples

RCF = ∆∆ 1 0.01 2 1

42.2 Ti: at same rpm double RCF compared to 90 Ti

rav =  55.4 mm rav =  106 mm

90 Ti 42.2 Ti

rotor

axis

rav

RCF  x  t = const.   RCF ~∆

100,000 g  x  60 min  =  200,000 g  x  30 min  =  50,000 g   x  120 min  = 20,000 g  x  300 min

2 x rpm 4 x RCFRCF   ~ rpm2

4 x r  2 x rpmr       ~ rpm2

RCF   ~ r 2 x RCF  2 x rotor radius

Stokes‘ Law: Friction, buoyancy and the centrifugal force

~

rs2 2

Time to pellet a particle

Völkl, A. (2010) Ultracentrifugation. In: Encyclopedia of Life Sciences (ELS)

=  

Sedimentation velocity of a sphere (particle)

rs3 2 = 6

Equilibrium between net and drag force

6 Drag (frictional) force rs radius of the sphere

viscositysedimentation rate of the sphere

rs3 2

Net force (difference of the weight of a sphere and its buoyancy, both caused by gravity)

buoyant density of spherebuoyant density of buffer

Völkl, A. (2010) Ultracentrifugation.  In: Encyclopedia of Life Sciences (ELS)

Differential centrifugation

pellet supernatant

pellet supernatant

supernatantpellet

supernatantpellet

~

2

Völkl, A. (2010) Ultracentrifugation.  In: Encyclopedia of Life Sciences (ELS)

Density gradient centrifugation

~

2 2

~

2

Beckman Coulter (2006) Rotors and Tubes. User‘s Manual

Rotors

ln max⁄ min

2 1013 3600−1

ln max⁄ min

2 60−1 2 10−13 3600−1

ln max⁄ min

2 60−1 2 10−13 3600−1

2.533 1011 ln max⁄ min

2

The k‐factor (clearing factor): relative pelleting efficiency of a rotor

2

ln max⁄ min

2

Sedimentation coefficient in Svedberg units (S)

s =  x  1/ 2r

1 S = 10‐13 seconds

a

b

a

ba

a

bb

Run times for any two rotors

90 Ti

42.2 Ti

rmin 34.2 mm         r max 76.5 mmln rmax / rmin =  0.81

rmin 98 mm         r max 113 mmln rmax / rmin =  0.14

Hands‐on examples: comparison of rotors

k‐factor of 90 Ti at 223,000 g (64,000 rpm):      50 (kb) 

k‐factor of 42.2 Ti at maximum RCF: 12 (ka) (223,000 g, 42,000 rpm)

a1250 60min ca. 14min

Hands‐on examples: comparison of rotors

k‐factor of VTi 65.1 at 288,000 g (61,000 rpm):      15 (kb) 

k‐factor of SW 41 Ti at maximum RCF :   124 (ka)(288,000 g, 41,000 rpm)SW 41 Ti

VTi 65.1

rmin 67.4 mm         r max 153.1 mmln rmax / rmin =  0.82

rmin 68.5 mm         r max 84.9 mmln rmax / rmin =  0.22

(roughly)a15124 12 h ca. 1.5h

a

b

a

b

Run times for any two rotors

aa

bb