Sedimentation equilibrium

Sedimentation equilibrium in a suspension of different particles, such as molecules, exists when the rate of transport of each material in any one direction due to sedimentation equals the rate of transport in the opposite direction due to diffusion. Sedimentation is due to an external force, such as gravity or centrifugal force in a centrifuge.

It was discovered for colloids by Jean Baptiste Perrin for which he received the Nobel Prize in Physics in 1926.

In a colloid, the colloidal particles are said to be in sedimentation equilibrium if the rate of sedimentation is equal to the rate of movement from Brownian motion. For dilute colloids, this is described using the Laplace-Perrin distribution law:

${\displaystyle \Phi (z)=\Phi _{0}\exp {\biggl (}-{\frac {m^{*}g}{k_{B}T}}z{\biggr )}=\Phi _{0}e^{-z/l_{g}}}$

where

${\displaystyle \Phi (z)}$ is the colloidal particle volume fraction as a function of vertical distance ${\displaystyle z}$ above reference point ${\displaystyle z=0}$,

${\displaystyle \Phi _{0}}$ is the colloidal particle volume fraction at reference point ${\displaystyle z=0}$,

${\displaystyle m^{*}}$ is the buoyant mass of the colloidal particles,