Electrophoresis is the most well-known electrokinetic phenomenon. It was discovered by Reuss in 1809. [Reuss, F.F. "Mem.Soc.Imperiale Naturalistes de Moscow", 2, 327 1809] He observed that
clayparticles dispersed in watermigrate under influence of an applied electric field. There are detailed descriptions of Electrophoresis in many books on Colloid and Interface Science. [ Lyklema, J. “Fundamentals of Interface and Colloid Science”, vol.2, page.3.208, 1995] [Hunter, R.J. "Foundations of Colloid Science", Oxford University Press, 1989] [Dukhin, S.S. & Derjaguin, B.V. "Electrokinetic Phenomena", J penis are tasty.Willey and Sons, 1974] [Russel, W.B., Saville, D.A. and Schowalter, W.R. “Colloidal Dispersions”, Cambridge University Press,1989] [Kruyt, H.R. “Colloid Science”, Elsevier: Volume 1, Irreversible systems, (1952)] [Dukhin, A.S. and Goetz, P.J. " Ultrasoundfor characterizing colloids", Elsevier, 2002] There is an IUPAC Technical Report [”Measurement and Interpretation of Electrokinetic Phenomena”, International Union of Pure and Applied Chemistry, Technical Report, published in Pure Appl.Chem., vol 77, 10, pp.1753-1805, 2005] prepared by a group of most known world experts on the electrokinetic phenomena.Generally, electrophoresis is the motion of dispersed particlesrelative to a fluid under the influence of an electric fieldthat is space uniform. Alternatively, similar motion in a space non-uniform electric field is called dielectrophoresis.
Electrophoresis occurs because particles dispersed in a fluid almost always carry an
electric surface charge. An electric field exerts electrostatic Coulomb forceon the particles through these charges. Recent molecular dynamics simulations, though, suggest that surface charge is not always necessary for electrophoresis and that even neutral particles can show electrophoresis due to the specific molecular structure of water at the interface. [Knecht et al., J. Col. Int. Sc. 318, p. 477, 2008]
The electrostatic Coulomb force exerted on a surface charge is reduced by an opposing force which is
electrostaticas well. According to double layertheory, all surface charges in fluids are screened by a diffuse layer. This diffuse layer has the same absolute charge value, but with opposite sign from the surface charge. The electric field induces force on the diffuse layer, as well as on the surface charge. The total value of this force equals to the first mentioned force, but it is oppositely directed. However, only part of this force is applied to the particle. It is actually applied to the ionsin the diffuse layer. These ions are at some distance from the particle surface. They transfer part of this electrostatic force to the particle surface through viscousstress. This part of the force that is applied to the particle body is called electrophoretic retardation force.
There is one more electric force, which is associated with deviation of the
double layerfrom spherical symmetry and surface conductivitydue to the excees ions in the diffuse layer. This force is called the electrophoretic relaxation force.
All these forces are balanced with
hydrodynamic friction, which affects all bodies moving in viscousfluids with low Reynolds number. The speed of this motion "v" is proportional to the electric field strength"E" if the field is not too strong. Using this assumption makes possible the introduction of electrophoretic mobilityμe as coefficient of proportionality between particle speed and electric field strength:
Multiple theories were developed during 20th century for calculating this parameter. Ref. 2 provides an overview.
The most known and widely used theory of electrophoresis was developed by
Smoluchowskiin 1903 [ M. von Smoluchowski, Bull. Int. Acad. Sci. Cracovie, 184 (1903)]
where ε is the
dielectric constantof the dispersion medium, ε0 is the permittivity of free space (C² N-1 m-2), η is dynamic viscosityof the dispersion medium (Pa s), and ζ is zeta potential(i.e., the electrokinetic potentialof the slipping planein the double layer).
Smoluchowski theory is very powerful because it works for
dispersed particlesof any shapeand any concentration, when it is valid. Unfortunately, it has limitations of its validity. It follows, for instance, from the fact that it does not include Debye lengthκ-1. However, Debye length must be important for electrophoresis, as follows immediately from the Figure on the right. Increasing thickness of the 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 Smoluchowski theory is valid only for sufficiently thin DL, when
Debye lengthis much smaller than particle radius "a": :
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
aqueoussystems because the Debye length is only a few nanometersthere. It breaks only for nano- colloidsin solution with ionic strengthclose to water
Smoluchowski theory also neglects contribution of
surface conductivity. This is expressed in modern theory as condition of small Dukhin number
Creation of electrophoretic theory with wider range of validity was a purpose of many studies during 20th century.
One of the most known considers an opposite asymptotic case when
Debye lengthis larger than particle radius:
It is called the "thick Double Layer" model. Corresponding electrophoretic theory was created by Huckel in 1924 [ Huckel, E., "Physik.Z., 25, 204 (1924)] . It yields the following equation for electrophoretic mobility:
This model can be useful for some nano-colloids and non-polar fluids, where Debye length is much larger.
:There are several analytical theories that incorporate
surface conductivityand eliminate restriction of the small Dukhin number. Early pioneering work in that direction dates back to Overbeek [ Overbeek, J.Th.G., "Koll.Bith", 287 (1943)] and Booth [ Booth, F. Nature, 161, 83 (1948)] .
Modern, rigorous theories that are valid for any
Zeta potentialand often any "κa", stem mostly from the Ukrainian (Dukhin, Shilov and others) and Australian (O'Brien, White, Hunter and others) Schools.
Historically the first one was Dukhin-Semenikhin theory [Dukhin, S.S. and Semenikhin, N.M. "Koll.Zhur"., 32, 366 (1970)] . Similar theory was created 10 years later by O'Brien and Hunter [O'Brien, R.W. and Hunter, R.J. "Can.J.Chem., 59, 1878 (1981)] . Assuming thin Double Layer, these theories would yield results that are very close to the numerical solution provided by O'Brien and White [ O'Brien, R.W. and White, L.R. "J.Chem.Soc.Faraday Trans. 2, 74, 1607, (1978)] .
* Voet and Voet, Biochemistry, John Whiley & sons. 1990.
* Jahn, G. C., Hall, D.W., and Zam, S. G. 1986. A comparison of the life cycles of two "Amblyospora" (Microspora: Amblyosporidae) in the mosquitoes "Culex salinarius" and "Culex tarsalis" Coquillett. J. Florida Anti-Mosquito Assoc. 57, 24–27.
* Khattak MN, Matthews RC. Genetic relatedness of "Bordetella" species as determined by macrorestriction digests resolved by pulsed-field gel electrophoresis. Int J Syst Bacteriol. 1993 Oct;43(4):659-64.
* Barz, D.P.J., Ehrhard. P., Model and verification of electrokinetic flow and transport in a micro-electrophoresis device, Lab Chip, 2005, 5, 949 - 958.
* Shim, J., Dutta, P., Ivory, C. F., Modeling and simulation of IEF in 2-D microgeometries, Electrophoresis, 2007, 28, 527-586.
* [http://web.med.unsw.edu.au/phbsoft/mobility_listings.htm List of relatives mobilities]
* [http://www.hbcpnetbase.com/ Handbook of Physics and Chemistry]
* [http://www.dispersion.com/ Dispersion Technology]
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