rate of sedimentation depends on applied centrifugal field (g) being directed radially outwards. g depends on Angular velocity and radial distance.

1. Calculation of g value
from RPM
Presented By:
Ankit Tiwari
Ph.D. Scholar
GGV Bilaspur

2. Introduction
 Centrifuge : is equipment that puts an object in rotation
around a fixed axis applying a potentially strong force
perpendicular to the axis of spin (outward).
 It is a device by which centrifugation is effected.
Fig: A table top Centrifuge

3. Calculation
 Rate of sedimentation depends on applied centrifugal field (g)
being directed outwards.
 G depends on – Angular velocity ώ (radian sec-1)
– Radial distance r ( cm)
 We see the relation between RCF and RPM :
where,
v = linear velocity
ώ = Angular velocity and r = radius
G = ώ2r
v = ώr

4. Ca= v2/r
Centrifugal acceleration
Centrifugal force (CF) = m. Ca
CF = m.v2/r = m. ώ2r2/r
we can manipulate ώ and r.
Now,
ώ = 2π.rpm = 2π.rpm/60
CF = ώ2r/g

5. Put the value of ώ in the equation of CF :
CF = 4π2rpm2.r /g
CF = RCF= 4π2rpm2.r /g
Putting the value of g = 980 m/s2
π = 3.1514
We get,
3600
3600
RCF = 1.12.10-5.rpm2.r

6. Example : Relationships between RCF (g) and RPM for
centrifuge with radius = 18.6 cm
RPM = 1500
RCF = 1.12.10-5.rpm2.r
= 1.12.10-5.(1500)2.18.6
RCF (g) = 478 m/s2
RPM = 8000
RCF = 1.12.10-5.rpm2.r
= 1.12.10-5. (8000)2.18.6
= 13330 m/s2

7. Sedimentation coefficient
 The sedimentation coefficient (s) of a particle characterizes
its sedimentation during centrifugation.
Where , s = sedimentation coefficient
m = mass of the particle
v = particle specific volume
ρ = density of the medium
f = frictional coefficient of particle
s= m.(1-vρ)
f

8.  Derivation of the sedimentation coefficient equation :
Fb Fc
Ff
As we know,
∑ F = m.a
Suppose the velocity of the particle is constant then a = 0, so
∑ F = 0
∑ F = Fc-( Fb + Ff)
Fc-( Fb + Ff) = 0

9. Because,
Fc = m. ώ2r
Fb = mdis .ώ2r
Ff = f.v
So,
m. ώ2r – (mdis .ώ2r + f.v) = 0
By fluid dynamics we know,
mdis = m. ρ fluid & v = 1/ρ
ρ particle
So,
mdis = m. ρ. V
Now,
m. ώ2r – mdis .ώ2r –f .v = 0

10. m. ώ2r-m.ρv.ώ2r = f.v
m. ώ2r(1- v.ρ) = f.v
m.(1- v.ρ) = v/ώ2r
f
s = v/ώ2r = m (1- v.ρ)
f
Since m ( mass in gram of a single particle) = M/N
M = molar mass in g/mol
N = Avogadro no. (6.023 x 1023)
m .(1- v.ρ)
s =
f

11.  Important conclusions:
1. The higher the mass, the greater the sedimentation speed.
>
2. Shape of the particle affects its sedimentation speed.
S= M(1-vρ)
N.f

12. 3. A more dense particle move rapidly than the less one.
4. Density of the field also affects sedimentation speed.
vρ = ρmedium / ρ particle
= density of medium / density of particle
If, vρ = 1 then particle will not move (densities are equal)
vρ > 1 then particle will float ( particle less dense)
vρ <1 then particle will sink ( particle more dense)

13. Material density (g/cm3)
Microbial cells 1.05-1.15
Mammalian cells 1.04-1.10
Organelles 1.10-1.60
Proteins 1.30
DNA 1.70
RNA 2.00
Densities of biological material