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 $t$ (in hours) required for sedimentation of a fraction with a known sedimentation coefficient $s$ (in svedbergs):

: $t\; =\; \backslash frac\{k\}\{s\}$

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

: $k\; =\; \backslash frac\{\backslash ln(r\_\{\backslash rm\{max\}\}\; /\; r\_\{\backslash rm\{min\}\})\}\{\backslash omega^2\}\; \backslash times\; \backslash frac\{10^\{13\}\}\{3600\}$

As the rotational speed of a centrifuge is usually specified in RPM, the following formula is often used for convenience:[http://www.coleparmer.com/techinfo/techinfo.asp?htmlfile=basic-centrifugation.htm&ID=30 "Basics of Centrifugation"]

: $k\; =\; \backslash frac\{2.53\; \backslash cdot\; 10^5\; \backslash times\; \backslash ln(r\_\{\backslash rm\{max\}\}\; /\; r\_\{\backslash rm\{min\}\})\}\{(\backslash rm\{RPM\}/1000)^2\}$

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

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

: $k\_\{\backslash rm\{adj\}\}\; =\; k\; \backslash left(\; \backslash frac\{\backslash mbox\{maximum\; rotor-speed\}\}\{\backslash mbox\{actual\; rotor-speed\}\}\; \backslash right)$²

The K-factor is related to the sedimentation coefficient $S$ by the formula:

$T\; =\; \backslash frac\{K\}\{S\}$

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

$\backslash frac\{T\_1\}\{K\_1\}\; =\; \backslash frac\{T\_2\}\{K\_2\}$

Where $T\_1$ is the time to pellet in one rotor, and $K\_1$ is the K-factor of that rotor. $K\_2$ is the K-factor of the other rotor, and $T\_2$, 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. [http://www.google.com/search?q=centrifuge%20calculator Many online calculators] are available to perform the calculations for common rotors.