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Clearing factor

In centrifugation the clearing factor or k factor represents the relative pelleting efficiency of a given centrifuge rotor at maximum rotation speed. It can be used to estimate the time <math>t</math> (in hours) required for sedimentation of a fraction with a known sedimentation coefficient <math>s</math> (in svedbergs):

<math>t = \frac{k}{s} </math>

The value of the clearing factor depends on the maximum angular velocity <math>\omega</math> of a centrifuge (in rad/s) and the minimum and maximum radius <math>r</math> of the rotor:

<math>k = \frac{\ln(r_{\rm{max}} / r_{\rm{min}})}{\omega^2} \times \frac{10^{-13}}{3600}</math>

As the rotational speed of a centrifuge is usually specified in RPM, the following formula is often used for convenience:[1]

<math>k = \frac{2.53 \cdot 10^5 \times \ln(r_{\rm{max}} / r_{\rm{min}})}{(\rm{RPM}/1000)^2}</math>

Centrifuge manufacturers usually specify the minimum, maximum and average radius of a rotor, as well as the <math>k</math> factor of a centrifuge-rotor combination.

For runs with a rotational speed lower than the maximum rotor-speed, the <math>k</math> factor has to be adjusted:

<math>k_{\rm{adj}} = k \left( \frac{\mbox{maximum rotor-speed}}{\mbox{actual rotor-speed}} \right)</math>2

The K-factor is related to the sedimentation coefficient <math>S</math> by the formula:

<math>T = \frac{K}{S}</math>

Where <math>T</math> is the time to pellet a certain particle in hours. Since <math>S</math> is a constant for a certain particle, this relationship can be used to interconvert between different rotors.

<math> \frac{T_1}{K_1} = \frac{T_2}{K_2}</math>

Where <math>T_1</math> is the time to pellet in one rotor, and <math>K_1</math> is the K-factor of that rotor. <math>K_2</math> is the K-factor of the other rotor, and <math>T_2</math>, the time to pellet in the other rotor, can be calculated. In this manner, one does not need access to the exact rotor cited in a protocol, as long as the K-factor can be calculated. Many online calculators are available to perform the calculations for common rotors.

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