Definitions

# 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):

$t = frac\left\{k\right\}\left\{s\right\}$

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

$k = frac\left\{ln\left(r_\left\{rm\left\{max\right\}\right\} / r_\left\{rm\left\{min\right\}\right\}\right)\right\}\left\{omega^2\right\} times frac\left\{10^\left\{-13\right\}\right\}\left\{3600\right\}$

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

$k = frac\left\{2.53 cdot 10^5 times ln\left(r_\left\{rm\left\{max\right\}\right\} / r_\left\{rm\left\{min\right\}\right\}\right)\right\}\left\{\left(rm\left\{RPM\right\}/1000\right)^2\right\}$

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:

$k_\left\{rm\left\{adj\right\}\right\} = k left\left(frac\left\{mbox\left\{maximum rotor-speed\right\}\right\}\left\{mbox\left\{actual rotor-speed\right\}\right\} right\right)$

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