Biochemical Techniques and Instrumentation

4.1.2. Basic Principles of Sedimentation

Particles or cells in a liquid suspension sediment at the bottom of a container due to gravity. The time required for such separation is usually very long. The sedimentation effect is mainly influenced by the Earth’s gravitational field (g=98.1cms^-2). Therefore, small particles will not separate under normal gravitational field and require centrifugal force. This force  increases the  rate of sedimentation of particles in a centrifugal field.

If a particle (m) in a centrifuge tube filled with a liquid is in centrifugal field, the particle (m) is acted by three forces:

• F_C: the centrifugal force
• F_B: the buoyant force
• F_f: the frictional force between particle and liquid

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As the particles moves towards the bottom of the centrifuge tube, its velocity (v) will increase due to the increase in the radial distance (r). At the same time, the particles also encounter a frictional drag  proportional to their velocity. The frictional force (F_f) of a particle is the product of its velocity and its frictional coefficient (f). The frictional force always acts in the opposite direction to sedimentation.

The rate of sedimentation is dependent upon the applied centrifugal field (cms^-2), G. The centrifugal field is determined by the radial distance (r) of the particle from the axis of rotation (in cm) and the square of angular velocity (ω) of the rotor (in radians per second).

G = ω²r

The average angular velocity (ω) is defined as the ratio of the angular displacement in the given time interval. One radian (1 rad) represents the angle subtended at the centre of a circle by an arc with a length equal to the radius of the circle. One revolution of the rotor can be expressed as 2π radians since 360^o equals 2π radians. The angular velocity in rads per seconds of the rotor can be expressed in terms of rotor speed, s:

ω = 2πs/60

and therefore the centrifugal field can be expressed as:

G = 4π² (rev.min^-1)² r/ 3600 or 4π²s²r/3600

The centrifugal field is generally expressed in multiples of the gravitational field, g (98.1cms^-1). The relative centrifugal field, g (RCF) is the ratio of the centrifugal acceleration at a specified radius and the speed to the standard acceleration of gravity. It can be calculated as follows:

RCF = 4π² (rev.min^-1)² r/ 3600 x 98.1 = G/g

RCF units are dimensionless and revolutions per minute are expressed as r.p.m:

RCF = 1.12 x 10^-5 x r.p.m² x r

The sedimentation rate or velocity of the biological particle is expressed as its sedimentation coefficient (s):

s = ν/ω²r

The sedimentation coefficients of biological macromolecules are relatively small and are usually expressed as Svedberg units, S. One Svedberg units equals 10^-13s.