Theory of centrifugation

Theory of centrifugation


1.

Centrifugal Force

The centrifugal force can be expressed by the equation:



m = mass of particle (g)

r = rotation radius (cm)

ω = angular velocity (rad/s)


The relative centrifugal force (rcf , the ratio of centrifugal force and
terrestrial gravity,
in g = m / s
2
):






r = rotation radius (in cm)

rpm = revolution per minute


The force (f
1
) to sediment a spherical particle in a less dense solution is;


F
1

= (volume of particle) . (relative density) . (centrifugal force)





d =
diameter of particle (cm)

σ = density of particle ( g / cm
3
)

ρ = density of solution (g / cm
3
)


The frictional force (f
2
) slows the sedimentation of the (here: spherical) particle, as:




d = diameter of particle (cm)

η = viscosity of solution (poise = g . cm
-
1

. s

–
1

v = velocit
y of particle movement (cm/s)


When f
1

= f
2

(particle sediments at fixed velocity)






If the solution is homogenous

[d
2

/ 18 [ (σ
–

ρ) / η ] is a proportional constant (s, called sedimentation coefficient)
expressed in seconds. For convenience s is u
sually multiplied by 10
13

and expressed
as Svedberg unit (S), thus

s = S . 10
-
13

F = mrω
2


Rcf = r (2 π {rpm}
2

/ 60) . (1 / 980 665)
or

Rcf = 11.18 . r . (rpm / 1000)
2


F
1

= 1 / 6 . π d
3

. (σ
–
=
ρ) . rω
2


f
2
= 3 π d η v



F
1

=
f
2




1 / 6 π
d
3

(σ
–
=
ρ
⤠⸠
r
=
ω
2

= 3 π
d
=
η
v
†



瘠v⁤
2

/ 18 [ (σ
–
=
ρ) / η ] . rω
2