Lably
Skip to content

Centrifugation

Mechanical process

  • 13 min read
  • 4 chapters
  • 1 lab on Lably

Learn it on Lably

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, this may take an unacceptably long time. Other particles, which are very small, cannot be isolated at all in solution unless they are exposed to a high centrifugal force. As the suspension is rotated at a certain speed (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:

RPM=gr,

where g represents the relative centrifugal acceleration (RCF) and r the radius from the center of the rotor to a point in the sample (and the result is multiplied by 60 to convert from seconds to minutes).

However, depending on the centrifuge model used, the angle of the rotor and the radius may both 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 RPM=299gr, which can further simplify to RPM=91g.

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 Earth's 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:

RCF=1.118×10−5×r×(rpm)2,

where 1.118×10−5 is a constant empirical factor; r is the radius, expressed in centimetres, between the axis of rotation and a point in the sample; and rpm is the speed in revolutions per minute.

Historically, many separations have been carried out at the speed of 3000 rpm; a rough guide to the ‘g’ force exerted at this speed is to multiply the centrifugation radius by a factor of 10, so a radius of 160 mm gives approximately 1600 x g. This is a rather arbitrary approach, since the RCF applied is linearly dependent on the radius, so a 10% larger radius means that a 10% higher RCF is applied at the same speed. Roughly, the above formula can be simplified to RCF=10×r, with an error of only 0.62%.

Sign in to keep reading

3 more chapters are free with a Lably account.

More in Chemistry