9780521516358book.pdf

whereis the sedimentation rate of the sphere, 2/9 is the shape factor constant for

a sphere,ris the radius of particle,rpis the density of particle,rmis the density of

medium,gis the gravitational acceleration andZis the viscosity of the medium.

Accordingly a mixture of biological particles exhibiting an approximately spherical

shape can be separated in a centrifugal field based on their density and/or their size.

The time of sedimentation (in seconds) for a spherical particle is:

t¼^9

2



!^2 r^2 pðpmÞ

lnrb

rt

ð 3 : 6 Þ

wheretis the sedimentation time,is the viscosity of medium,rpis the radius of

particle,rbis the radial distance from the centre of rotation to bottom of tube,rtis the

radial distance from the centre of rotation to liquid meniscus,rpis the density of the

particle,rmis the density of the medium and!is the angular velocity of rotor.

Thesedimentation rateor velocity of a biological particle can also be expressed as

itssedimentation coefficient(s), whereby:

s¼ 

!^2 r

ð 3 : 7 Þ

Since the sedimentation rate per unit centrifugal field can be determined at different

temperatures and with various media, experimental values of the sedimentation

coefficient are corrected to a sedimentation constant theoretically obtainable in water

at 20C, yielding the S20,W value. The sedimentation coefficients of biological

Example 3CALCULATION OF RELATIVE CENTRIFUGAL FIELD

Question A fixed-angle rotor exhibits a minimum radius,rmin, at the top of the centrifuge
tube of 3.5 cm, and a maximum radius,rmax, at the bottom of the tube of 7.0 cm.
See Fig. 3.2a for a cross-sectional diagram of a fixed-angle rotor illustrating
the position of the minimum and maximum radius. If the rotor is operated at a
speed of 20 000 r.p.m., what is the relative centrifugal field, RCF, at the top
and bottom of the centrifuge tube?

Answer The relative centrifugal field may be calculated using the equation:

RCF¼1,12 10 ^5 r.p.m.^2 r

Top of centrifuge tube:

RCF¼1,12 10 ^5 (20 000)^2 3.5¼15 680

Bottom of centrifuge tube:

RCF¼1,12 10 ^5 (20 000)^2 7.0¼31 360

This calculation illustrates that with fixed-angle rotors the centrifugal field at the

top and bottom of the centrifuge tube might differ considerably, in this case exactly

two-fold.

78 Centrifugation