Centrifugation is a mechanical process which involves the use of the centrifugal force to separate particles from a solution according to their size, shape, density, medium viscosity and rotor speed. The denser components of the mixture migrate away from the axis of the centrifuge, while the less dense components of the mixture migrate towards the axis. Chemists and biologists may increase the effective gravitational force of the test tube so that the precipitate (pellet) will travel quickly and fully to the bottom of the tube. The remaining liquid that lies above the precipitate is called a supernatant or supernate.
There is a correlation between the size and density of a particle and the rate that the particle separates from a heterogeneous mixture, when the only force applied is that of gravity. The larger the size and the larger the density of the particles, the faster they separate from the mixture. By applying a larger effective gravitational force to the mixture, like a centrifuge does, the separation of the particles is accelerated. This is ideal in industrial and lab settings because particles that would naturally separate over a long period of time can be separated in much less time.
The rate of centrifugation is specified by the angular velocity usually expressed as revolutions per minute (RPM), or acceleration expressed as g. The conversion factor between RPM and g depends on the radius of the centrifuge rotor. The particles' settling velocity in centrifugation is a function of their size and shape, centrifugal acceleration, the volume fraction of solids present, the density difference between the particle and the liquid, and the viscosity. The most common application is the separation of solid from highly concentrated suspensions, which is used in the treatment of sewage sludges for dewatering where less consistent sediment is produced.
The centrifugation method has a wide variety of industrial and laboratorial applications; not only is this process used to separate two miscible substances, but also to analyze the hydrodynamic properties of macromolecules. It is one of the most important and commonly used research methods in biochemistry, cell and molecular biology. In the chemical and food industries, special centrifuges can process a continuous stream of particle turning into separated liquid like plasma. Centrifugation is also the most common method used for uranium enrichment, relying on the slight mass difference between atoms of U-238 and U-235 in uranium hexafluoride gas.
Mathematical formula
In a liquid suspension, many particles or cells will gradually fall to the bottom of the container due to gravity; however, the amount of time taken for such separations is not feasible. Other particles, which are very small, can not be isolated at all in solution until they are exposed to a high centrifugal force. As the suspension is rotated at a certain speed or revolutions per minute (RPM), the centrifugal force allows the particles to travel radially away from the rotation axis. The general formula for calculating the revolutions per minute (RPM) of a centrifuge is:
,
where g represents the respective force of the centrifuge and r the radius from the center of the rotor to a point in the sample.
However, depending on the centrifuge model used, the respective angle of the rotor and the radius may vary, thus the formula gets modified. For example, the Sorvall #SS-34 rotor has a maximum radius of 10.8 cm, so the formula becomes , which can further simplify to .
When compared to gravity, the particle force is called the 'Relative Centrifugal Force' (RCF). It is the perpendicular force exerted on the contents of the rotor as a result of the rotation, always relative to the gravity of the earth, which measures the strength of rotors of different types and sizes. For instance, the RCF of 1000 x g means that the centrifugal force is 1000 times stronger than the earthly gravitational force. RCF is dependent on the speed of rotation in rpm and the distance of the particles from the center of rotation. The most common formula used for calculating RCF is:
,
where is a constant; r is the radius, expressed in centimetres, between the axis of rotation and the center; and rpm is the speed in revolutions per minute.