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{{For|specific types of electrophoresis (for example, the process of administering medicine, [[iontophoresis]])}}
[[File:Motion by electrophoresis of a charged particle.svg|thumb|300px|Illustration of electrophoresis]]
[[File:Retardation Force.svg|thumb|300px|Illustration of electrophoresis retardation]]

'''Electrophoresis''' is the motion of [[Interface and colloid science|dispersed particles]] relative to a fluid under the influence of a spatially uniform [[electric field]].<ref>{{cite book |first=J. |last=Lyklema |title= Fundamentals of Interface and Colloid Science |volume=vol. 2 |page=3.208 |year=1995}}</ref><ref>{{cite book |first=R.J. |last=Hunter |title=Foundations of Colloid Science |publisher=Oxford University Press |year=1989}}</ref><ref>{{cite book |first=S.S. |last=Dukhin |coauthors=B.V. Derjaguin |title=Electrokinetic Phenomena |publisher=J. Willey and Sons |year=1974}}</ref><ref>{{cite book |first=W.B. |last=Russel |coauthors=D.A. Saville and W.R. Schowalter |title=Colloidal Dispersions |publisher=Cambridge University Press |year=1989}}</ref><ref>{{cite book |first=H.R. |last=Kruyt |title=Colloid Science |publisher=Elsevier |volume=Volume 1, Irreversible systems |year=1952}}</ref><ref>{{cite book |first=A.S. |last=Dukhin |coauthors=P.J. Goetz |title=Ultrasound for characterizing colloids |publisher=Elsevier |year=2002}}</ref> This [[electrokinetic phenomena|electrokinetic phenomenon]] was observed for the first time in 1807 by Ferdinand Frederic Reuss ([[Moscow State University]]),<ref>{{cite journal |first=F.F. |last=Reuss |journal=Mem. Soc. Imperiale Naturalistes de Moscow |volume=2 |page=327 |year=1809}}</ref> who noticed that the application of a constant [[electric field]] caused [[clay]] particles dispersed in [[water]] to migrate. It is ultimately caused by the presence of a charged interface between the particle surface and the surrounding fluid.  It is the basis for a number of analytical techniques used in biochemistry for separating molecules by size, charge, or binding affinity. 

Electrophoresis of positively charged particles (cations) is called '''cataphoresis''', while electrophoresis of negatively charged particles (anions) is called '''anaphoresis'''.

== History ==
{{See also|History of electrophoresis}}

== Theory ==

Suspended particles have an [[electric surface charge]], strongly affected by surface adsorbed species,<ref>
{{cite journal
| last1=Hanaor
| first1=D.A.H.
| last2=Michelazzi
| first2=M.
| last3=Leonelli
| first3=C.
| last4=Sorrell
| first4=C.C.
| title= The effects of carboxylic acids on the aqueous dispersion and electrophoretic deposition of ZrO<sub>2</sub>
| journal= Journal of the European Ceramic Society
| year=2012
| volume=32
| issue=1
| pages=235–244
| url=http://www.sciencedirect.com/science/article/pii/S0955221911004171
| doi=10.1016/j.jeurceramsoc.2011.08.015}}</ref> on which an external electric field exerts an [[electrostatic]] [[Coulomb force]]. According to the [[Double layer (interfacial)|double layer]] theory, all surface charges in fluids are screened by a [[diffuse layer]] of ions, which has the same absolute charge but opposite sign with respect to that of the surface charge. The electric field also exerts a force on the ions in the [[diffuse layer]] which has direction opposite to that acting on the [[surface charge]]. This latter force is not actually applied to the particle, but to the [[ions]] in the diffuse layer located at some distance from the particle surface, and part of it is transferred all the way to the particle surface through [[Viscosity|viscous]] [[Stress (physics)|stress]]. This part of the force is also called electrophoretic retardation force.
When the electric field is applied and the charged particle to be analyzed is at steady movement through the diffuse layer, the total resulting force is zero :
:<math> F_{tot}  =  0  =  F_{el}  +  F_{f} +  F_{ret}</math>

Considering the [[Drag (physics)|drag]] on the moving particles due to the [[viscosity]] of the dispersant, in the case of low [[Reynolds number]] and moderate [[electric field]] strength ''E'', the velocity of a dispersed particle ''v'' is simply proportional to the applied field, which leaves the electrophoretic [[Electrical mobility|mobility]] μ<sub>e</sub> defined as:

:<math>\mu_e = {v \over E}.</math>

The most known and widely used theory of electrophoresis was developed in 1903 by [[Marian Smoluchowski|Smoluchowski]]<ref>{{cite journal |first=M. |last=von Smoluchowski |journal=Bull. Int. Acad. Sci. Cracovie |volume=184 |year=1903}}</ref>

:<math>\mu_e = \frac{\varepsilon_r\varepsilon_0\zeta}{\eta}</math>,

where ε<sub>r</sub> is the [[dielectric constant]] of the [[dispersion medium]], ε<sub>0</sub>  is the [[Vacuum permittivity|permittivity of free space]] (C²&nbsp;N<sup>−1</sup>&nbsp;m<sup>−2</sup>), η is [[dynamic viscosity]] of the dispersion medium (Pa&nbsp;s), and ζ is [[zeta potential]] (i.e., the [[electrokinetic potential]] of the [[slipping plane]] in the [[double layer (interfacial)|double layer]]). 

The Smoluchowski theory is very powerful because it works for [[dispersed particles]] of any [[shape]] at any [[concentration]]. Unfortunately, it has limitations on its validity. It follows, for instance, from the fact that it does not include [[Debye length]] κ<sup>−1</sup>. However, Debye length must be important for electrophoresis, as follows immediately from the Figure on the right. Increasing thickness of the double layer (DL) leads to removing point of retardation force further from the particle surface. The thicker DL, the smaller retardation force must be. 

Detailed theoretical analysis proved that the Smoluchowski theory is valid only for sufficiently thin DL, when particle radius ''a'' is much greater than the [[Debye length]] :
  
:<math> a \kappa \gg 1</math>.

This model of "thin Double Layer" offers tremendous simplifications not only for electrophoresis theory but for many other electrokinetic theories. This model is valid for most [[aqueous]] systems because the Debye length is only a few [[nanometers]] there. It breaks only for nano-colloids in solution with [[ionic strength]] close to water.

The Smoluchowski theory also neglects contribution of [[surface conductivity]]. This is expressed in modern theory as condition of small [[Dukhin number]]:

:<math>     Du \ll 1    </math>

In the effort of expanding the range of validity of electrophoretic theories, the opposite asymptotic case was considered, when [[Debye length]] is larger than particle radius:

:<math>     a \kappa < \!\, 1</math>.

Under this condition of a "thick Double Layer", [[Erich Hückel|Hückel]]<ref>{{cite journal |first=E. |last=Hückel |journal=Physik. Z. |volume=25 |page=204 |year=1924}}</ref> predicted the following relation for electrophoretic mobility: 

:<math>\mu_e = \frac{2\varepsilon_r\varepsilon_0\zeta}{3\eta}</math>.

This model can be useful for some nanoparticles and non-polar fluids, where Debye length is much larger than in the usual cases. 

There are several analytical theories that incorporate [[surface conductivity]] and eliminate the restriction of a small [[Dukhin number]], pioneered by Overbeek<ref>{{cite journal |first=J.Th.G |last=Overbeek |journal=Koll.Bith |page=287 |year=1943}}</ref> and Booth.<ref>{{cite journal |first=F. |last=Booth |journal=Nature |volume=161 |page=83 |year=1948|bibcode = 1948Natur.161...83B |doi = 10.1038/161083a0 |pmid=18898334}}</ref> Modern, rigorous theories valid for any [[Zeta potential]] and often any ''aκ'' stem mostly from Dukhin-Semenikhin theory.<ref>{{cite journal |first=S.S. |last=Dukhin |coauthors=N.M. Semenikhin |journal=Koll.Zhur |volume=32 |page=366 |year=1970}}</ref> In the '''thin Double Layer''' limit, these theories confirm the numerical solution to the problem provided by O'Brien and White.<ref>{{cite journal |first=R.W. |last=O'Brien |coauthors=L.R. White |journal=J. Chem. Soc. Faraday Trans. |volume=2 |issue=74 |page=1607 |year=1978}}</ref>

==See also==
*[[Affinity electrophoresis]]
*[[Capillary electrophoresis]]
*[[Dielectrophoresis]]
*[[DNA electrophoresis]]
*[[Electroblotting]]
*[[Electrofocusing]]
*[[Gel electrophoresis]]
*[[Immunoelectrophoresis]]
*[[Isotachophoresis]]
*[[Pulsed field gel electrophoresis]]

==References==
{{Commons|Electrophoresis}}
{{Reflist}}

==Further reading==
* {{cite book |author=Voet and Voet |year=1990 |title=Biochemistry |publisher=John Wiley & Sons}}
* {{cite journal |first=G.C. |last=Jahn |coauthors=D.W. Hall and S.G. Zam |year=1986 |title=A comparison of the life cycles of two ''Amblyospora'' (Microspora: ''Amblyosporidae'') in the mosquitoes ''Culex salinarius'' and ''Culex tarsalis'' Coquillett |journal=J. Florida Anti-Mosquito Assoc. |volume=57 |pages=24–27}}
* {{cite journal |first=M.N. |last=Khattak |coauthors=R.C. Matthews |year=1993 |title=Genetic relatedness of ''Bordetella'' species as determined by macrorestriction digests resolved by pulsed-field gel electrophoresis |journal=Int. J. Syst. Bacteriol. |volume=43 |issue=4 |pages=659–64}}
* {{cite journal |first=D.P.J. |last=Barz |coauthors=P. Ehrhard |year=2005 |title=Model and verification of electrokinetic flow and transport in a micro-electrophoresis device |journal=Lab Chip |volume=5 |pages=949–958}}
* {{cite journal |first=J. |last=Shim |coauthors=P. Dutta and C.F. Ivory |year=2007 |title=Modeling and simulation of IEF in 2-D microgeometries |journal=[[Electrophoresis (journal)|Electrophoresis]] |volume=28 |pages=527–586}}

==External links==
* [http://web.med.unsw.edu.au/phbsoft/mobility_listings.htm List of relative mobilities]

[[Category:Electromagnetism]]
[[Category:Electrophoresis| ]]
[[Category:Colloidal chemistry]]
[[Category:Analytical chemistry]]