Sedimentation equilibrium in a suspension of different particles, such as
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
s, exists when the rate of transport of each material in any one direction due to
sedimentation
Sedimentation is the deposition of sediments. It takes place when particles in suspension settle out of the fluid in which they are entrained and come to rest against a barrier. This is due to their motion through the fluid in response to the ...
equals the rate of transport in the opposite direction due to
diffusion
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
. Sedimentation is due to an external force, such as
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
or
centrifugal force
In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is paralle ...
in a centrifuge.
It was discovered for colloids by
Jean Baptiste Perrin
Jean Baptiste Perrin (30 September 1870 – 17 April 1942) was a French physicist who, in his studies of the Brownian motion of minute particles suspended in liquids ( sedimentation equilibrium), verified Albert Einstein’s explanation of this ...
for which he received the
Nobel Prize in Physics
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
in 1926.
Colloid
In a
colloid
A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend ...
, the colloidal
particle
In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object which can be described by several physical property, physical or chemical property, chemical ...
s are said to be in sedimentation equilibrium if the rate of sedimentation is equal to the rate of movement from
Brownian motion
Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas).
This pattern of motion typically consists of random fluctuations in a particle's position insi ...
. For dilute colloids, this is described using the Laplace-Perrin distribution law:
where
is the colloidal particle volume fraction as a function of vertical distance
above reference point
,
is the colloidal particle volume fraction at reference point
,
is the
buoyant mass
Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pr ...
of the colloidal particles,
is the
standard acceleration due to gravity,
is the
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
,
is the absolute
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
,
and
is the sedimentation length.
The buoyant mass is calculated using
where
is the difference in mass density between the colloidal particles and the suspension medium, and
is the colloidal particle volume found using the volume of a sphere (
is the radius of the colloidal particle).
Sedimentation length
The Laplace-Perrin distribution law can be rearranged to give the sedimentation length
. The sedimentation length describes the
probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...
of finding a colloidal particle at a height
above the point of reference
. At the length
above the reference point, the concentration of colloidal particles decreases by a factor of
.
If the sedimentation length is much greater than the diameter
of the colloidal particles (
), the particles can diffuse a distance greater than this diameter, and the substance remains a suspension. However, if the sedimentation length is less than the diameter (