# Centrifuge

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Centrifuge - A device which separates particles or droplets suspended in a liquid based on their relative densities,using centrifugal force generated by spinning the sample rapidly around a fixed axis. The device decreases the sedimentation time of these particles through the use of centripetal acceleration.

## Types of centrifuges

Centrifuges fall into three different categories based on size: laboratory, process-scale, and human-sized. Laboratory centrifuges are the smallest of the three and are primarily used for cell sedimentation and purification. Industrial sized centrifuges are significantly larger than laboratory centrifuges and are utilized for large separation processes. The largest centrifuges are human-sized and are scientifically utilized by space agencies and biomedical research to simulate high gravity conditions.

### Laboratory centrifuges

Laboratory Centrifuges are frequently used in various scientific protocols such as DNA and protein purification. The most common laboratory centrifuge is the bench top centrifuge because they are multipurpose and have removable rotors. Laboratory centrifuges can spin up to about 20,000 rpm.

### Process scale centrifuges

Biological and chemical processing plants use large-scale centrifuges for separation and sedimentation. The two most common separation centrifuges are tubular bowl centrifuges and disk stack centrifuges. Large gas chromatography centrifuges are also used in Uranium purification.

#### Tubular bowl centrifuge

In the tubular bowl centrifuge fluid enters the bottom of the centrifuge and exits out the top. Particles separated from the centrifuge are collected on the side of the bowl and need to be cleaned after processing. Fortunately, the bowl is usually easy to remove and wash. Another application for the tubular bowl centrifuge is the separation of a light liquid from a heavy liquid because of the density difference.

#### Disk stack centrifuge

The disk stack centrifuge is fed from the top into a basin and after passing through a series of disks the clarified liquid is removed from the top. Similar to the tubular bowl centrifuge, the dense particles are captured on the side of the centrifuge. Some disk stack centrifuges have solid discharge valves that can clean the sides and prevent buildup.

### Human-sized centrifuge

Moving to a larger scale, human-sized centrifuges are used for high gravity training by NASA and entertainment value in carnival rides such as the Gravitron. Human sized centrifuges spin much slower than their smaller counterparts as sedimentation is undesired.[1][2]

(PD) Photo: National Aeronautics and Space Administration (NASA)
NASA's 20 g centrifuge.

## Equations governing centrifuges

### Sedimentation velocity

• The speed at which a particle falls out of solution in Earth’s gravitational field.

${\displaystyle V_{g}={\frac {\pi d_{p}\Delta \rho g}{18\mu }}}$

Where: dp - diameter of the particle (cm), ∆ρ – the difference in densities between the particle and the solvent (g/cm3), g – gravitational constant (980 cm/s2), μ - viscosity of the solvent (g/cm*s)

### RCF: “Relative Centrifugal Force” or g’s

• The strength of the centrifugal acceleration in multiples of gravitational acceleration

${\displaystyle \ RCF={\frac {r\omega ^{2}}{g}}\,}$

Where: r – radius of the centrifuge (cm), ω – angular velocity (rad/s), g – gravitational constant (980 cm/s2)

Note: To convert an RPM value to ${\displaystyle \omega }$, multiply the RPM value by 0.105. For example, 1000 RPM becomes 1000 x 0.105 rad/s, which is 105 rad/s. In terms of RPMs, the above formula is equivalently written as

${\displaystyle \ RCF={\frac {r{\mbox{ }}({\mbox{RPM }}\times 0.105)^{2}}{g}}\,}$

### Particle velocity

• The speed at which the particle falls out of solution in the centrifuge

${\displaystyle V_{r}=V_{g}*RCF}$

### Retention flow rate

• In an process scale centrifuge, the flow rate at which all the particles will sediment out of solution.

${\displaystyle Q_{r}et=V_{g}*\Sigma }$

Where: V_g - sedimentation velocity (cm/s), ∑ - sigma factor (cm2)

### Sigma Factor

• ${\displaystyle \Sigma }$ is the operation constant representing the geometry and speed of the centrifuge.

#### For tubular bowl centrifuge:

${\displaystyle \Sigma ={\frac {(\pi L(r_{o}^{2}-r_{i}^{2})\omega ^{2})}{gln(r_{o}/r_{i})}}}$

Where: L – length of the column (m), ro - outer radius of centrifuge (cm), ri - inner radius of centrifuge (cm), ω – angular velocity (rad/s), g – gravitational constant (980 cm/s2)

#### For a disk stack centrifuge:

$\displaystyle \Sigma = \frac{2\pi n(r_o^3-r_i^3) ω^2}{(3g \tan(\theta)}$

Where: ω – angular velocity (rad/s), n – number of discs, ro - outer radius of disks (cm), ri - inner radius of disks (cm), θ - angle between disc and vertical (rad), g – gravitational constant (980 cm/s2)