Editing Differential centrifugation (section)

== Theory ==
In a viscous fluid, the ''rate'' of [[sedimentation]] of a given suspended particle (as long as the particle is denser than the fluid) is largely a function of the following factors:
* Gravitational force
* Difference in density
* Fluid viscosity
* Particle size and shape

Larger particles sediment more quickly and at lower centrifugal forces. If a particle is less dense than the fluid (e.g., fats in water), the particle will not sediment, but rather will float, regardless of strength of the g-force experienced by the particle. [[Centrifugal force]] separates components not only on the basis of density, but also of particle size and shape. In contrast, a more specialized [[equilibrium density-gradient centrifugation]] produces a separation profile dependent on particle-density alone, and therefore is suitable for more fine-grained separations.

High g-force makes sedimentation of small particles much faster than [[Brownian motion|Brownian]] [[diffusion]], even for very small (nanoscale) particles. When a centrifuge is used, [[Stokes' law]] must be modified to account for the variation in g-force with distance from the center of rotation.<ref>{{cite book|last1=Harding |first1=Stephen E. |last2=Scott |first2=David |last3=Rowe |first3=Arther |title=Analytical Ultracentrifugation: Techniques and Methods |date=16 December 2007 |publisher=Royal Society of Chemistry |isbn=978-1-84755-261-7 |url=https://books.google.com/books?id=vm0oDwAAQBAJ&pg=PA271|language=en}}</ref>

:<math> D = \sqrt{ \frac{18 \eta \, \ln(R_f/R_i)}{( \rho_p - \rho_f) \omega^2 t} } </math>

where
* D is the minimum diameter of the particles expected to sediment (m)
* η (or μ) is the fluid [[dynamic viscosity]] (Pa.s)
* R<sub>f</sub> is the final [[radius of rotation]] (m)
* R<sub>i</sub> is the initial radius of rotation (m)
* ρ<sub>p</sub> is particle volumetric mass density (kg/m<sup>3</sup>)
* ρ<sub>f</sub> is the fluid volumetric mass density (kg/m<sup>3</sup>)
* ω is the [[angular velocity]] (radian/s)
* t is the time required to sediment from R<sub>i</sub> to R<sub>f</sub> (s)