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
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