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| The '''Dukhin number''' (''Du'') is a dimensionless quantity that characterizes the contribution of the [[surface conductivity]] to various [[electrokinetic]] and [[Electroacoustic music|electroacoustic]] effects, as well as to [[electrical conductivity]] and [[permittivity]] of fluid [[heterogeneous]] systems.
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| It was introduced by Lyklema in “Fundamentals of Interface and Colloid Science”.<ref>Lyklema, J. “Fundamentals of Interface and Colloid Science”, vol.2, page.3.208, 1995</ref>
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| IUPAC Technical Report prepared by a group of most known world experts on this subject uses this term explicitly.<ref name='PAC'>{{cite journal|title=Measurement and Interpretation of Electrokinetic Phenomena (IUPAC Technical Report)|journal=[[Pure and Applied Chemistry]] (10) , (2005)|year=2005|first=|last=|authors=A. V. DELGADO, F. GONZÁLEZ-CABALLERO, R. J. HUNTER, L. K. KOOPAL, AND J. LYKLEMA|volume=77|issue=10|pages=1753–1805|id= |url=http://www.iupac.org/objID/Article/pac7710x1753|format=|accessdate=2009-11-28 }}</ref>
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| Dukhin number is a ratio of the [[surface conductivity]] <big><math>\kappa^{\sigma}</math></big> to the fluid bulk electrical conductivity K<sub>m</sub> multiplied by particle size a :
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| :<math> \ Du = \frac{\kappa^{\sigma}}{{\Kappa_m}a}</math>
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| There is another expression of this number that is valid when surface conductivity is associated only with ions motion above [[slipping plane]] in the [[double layer]]. In this case, value of the surface conductivity depends on ζ-potential, which leads to the following expression for the Dukhin number for symmetrical electrolyte with equal ions [[diffusion coefficient]]:
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| :<math> \ Du = \frac{2(1+3m/z^2)}{{\kappa}a}\left(\mathrm{cosh}\frac{zF\zeta}{2RT}-1\right)</math>
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| where parameter ''m'' characterizes contribution of [[electro-osmosis]] into motion of ions within DL:
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| :<math> m = \frac{2\varepsilon_0\varepsilon_m R^2T^2}{3\eta F^2 D}</math>
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| * F is [[Faraday constant]]
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| * T is [[absolute temperature]]
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| * R is [[gas constant]]
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| * C is ions concentration in bulk
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| * z is [[ion]] [[valence (chemistry)|valency]]
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| * ζ is [[electrokinetic potential]]
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| * ε<sub>0</sub> is [[vacuum]] [[dielectric]] [[permittivity]]
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| * ε<sub>m</sub> is fluid dielectric permittivity
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| * η is [[dynamic viscosity]]
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| * D is [[diffusion coefficient]]
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| There are several ways to measure Dukhin number.<ref name='PAC' />
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| ==References==
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| {{Reflist}}
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| {{DEFAULTSORT:Dukhin Number}}
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| [[Category:Chemical mixtures]]
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| [[Category:Colloidal chemistry]]
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| [[Category:Condensed matter physics]]
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| [[Category:Matter]]
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| [[Category:Soft matter]]
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