Electrophoresis

# Overview
Electrophoresis is the movement of an electrically charged substance under the influence of an electric field. This movement is due to the Coulomb force, which may be related to fundamental electrical properties of the body under study and the ambient electrical conditions by the equation given below. F is the Coulomb force, q is the charge carried by the body, E is the electric field:
The resulting electrophoretic migration is countered by forces of friction such that the rate of migration is constant in a constant and homogeneous electric field:
Where v is the velocity and f is the frictional coefficient.
The electrophoretic mobility \mu is defined as followed.
The expression above applied only to ions at a concentration approaching 0 and in a non-conductive solvent. Polyionic molecules are surrounded by a cloud of counterions which alter the effective electric field applied on the ions to be separated. This renders the previous expression a poor approximation of what really happens in an electrophoretic apparatus.
The mobility depends on both the particle properties (e.g., surface charge density and size) and solution properties (e.g., ionic strength, electric permittivity, and pH).  For high ionic strengths, an approximate expression for the electrophoretic mobility (m2.V/s) is given by the Smoluchowski equation,
where \epsilon is the dielectric constant of the liquid (), \epsilon_0 is the permittivity of free space (C2.N.m-2), \eta is the viscosity of the liquid (Pa.s), and \zeta is the zeta potential (i.e., the electrokinetic potential, taken as equal to the surface potential) of the particle (V).

# Applications
Gel electrophoresis is an application of electrophoresis in molecular biology. Biological macromolecules  usually proteins, DNA, or RNA  are loaded on a gel and separated on the basis of their electrophoretic mobility.  (The gel greatly retards the mobility of all molecules present.)
Electrophoretic displays (EPD's) are a class of information display that form images by electrophoretic motion of charged, colored pigment particles.  Products incorporating electrophoretic displays include the Sony Librie electronic book reader, and the iRex iLiad e-newspaper tablet, both of which use electrophoretic films manufactured by E Ink Corporation.
Electrophoresis is also used in the process of DNA fingerprinting.  Certain DNA segments that vary vastly among humans are cut at recognition sites by restriction enzymes (restriction endonuclease). After the resulting DNA fragments are run through electrophoresis, the distance between bands are measured and recorded as the DNA "fingerprint."
Coatings, such as paint or ceramics, can be applied by electrophoretic deposition.  The technique can even be used for 3-D printing.

# Electrophoretic mobility
The electrophoretic mobility, often called Electrical mobility or just 'mobility', describes the motion of charged species in a fluid due to an external electric field. The velocity of the ion is proportional to its charge and to the electric field. The mobility is the proportionality coefficient.
The definition of the electrophoretic mobility (represented by the Greek letter nu) is:
where u is the ion velocity due to the electric field E, z is the ion charge and F the Faraday constant.
Another simpler definition commonly used is:
where u is the ion velocity due to the electric field E.

## Nernst Einstein equation
The value of the mobility can be found from the diffusion coefficient thanks to the Nernst Einstein equation:
where D is the ion diffusion coefficient, R is the universal gas constant and T is the absolute temperature.