9780521516358book.pdf

and therefore the centrifugal field can be expressed as:

G¼^4 

(^2) ðrev min (^1) Þ^2 r
3600

¼^4 

(^2) s (^2) r
3600
ð 3 : 3 Þ
The centrifugal field is generally expressed in multiples of the gravitational field,
g(981cms–2). Therelative centrifugal field(g), RCF, which is the ratio of the centrifugal
acceleration at a specified radius and the speed to the standard acceleration of gravity,
can be calculated from the following equation:

RCF¼^4 

(^2) ðrev min (^1) Þ^2 r
3600  981

¼G

g

ð 3 : 4 Þ

RCF units are therefore dimensionless (denoting multiples ofg) and revolutions per

minute are usually abbreviated as r.p.m.: RCF¼1.12 10 ^5 r.p.m.^2 r.

Although the relative centrifugal force can easily be calculated, centrifugation

manuals usually contain anomographfor the convenient conversion between rela-

tive centrifugal force and speed of the centrifuge at different radii of the centrifuga-

tion spindle to a point along the centrifuge tube. A nomograph consists of three

columns representing the radial distance (in mm), the relative centrifugal field and

the rotor speed (in r.p.m.). For the conversion between relative centrifugal force and

speed of the centrifuge spindle in r.p.m. at different radii, a straight-edge is aligned

through known values in two columns, then the desired figure is read where the

straight-edge intersects the third column. See Figure 3.1 for an illustration of the

usage of a nomograph.

In a suspension of biological particles, the rate of sedimentation is dependent not

only upon the applied centrifugal field, but also on the nature of the particle, i.e. its

density and radius, and also the viscosity of the surrounding medium.Stokes’ Law

describes these relationships for the sedimentation of a rigid spherical particle:

¼

2

9

r^2 ðpmÞ

 g ð^3 :^5 Þ

Example 2CALCULATION OF ANGULAR VELOCITY

Question For the pelleting of the microsomal fraction from a liver homogenate, an
ultracentrifuge is operated at a speed of 40 000 r.p.m. Calculate the angular velocity,
v, in radians per second.

Answer The angular velocity,v, may be calculated using the equation:

!¼^2 rev min

 1

60

!¼ 2 3.141640,000/60 rad s^1 ¼4188.8 rad s^1

76 Centrifugation