Dukhin number

The Dukhin number (Du) is a dimensionless quantity that characterizes the contribution of the surface conductivity to various electrokinetic and electroacoustic effects, as well as to electrical conductivity and permittivity of fluid heterogeneous systems. The number was named after Stanislav Dukhin. ^[1]

Overview

It was introduced by Lyklema in “Fundamentals of Interface and Colloid Science”. ^[2] A recent IUPAC Technical Report used this term explicitly and detailed several means of measurement in physical systems. ^[3] . There is detail description of this parameter given in the book published by Elsevier in 2025 ^[4]

The Dukhin number is a ratio of the surface conductivity ${\displaystyle \kappa ^{\sigma }}$ to the fluid bulk electrical conductivity K_m multiplied by particle size a:

${\displaystyle {\rm {Du}}={\frac {\kappa ^{\sigma }}{{\mathrm {K} _{m}}a}}.}$

There is another expression of this number that is valid when the surface conductivity is associated only with ions motion above the slipping plane in the double layer. In this case, the 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:

${\displaystyle {\rm {Du}}={\frac {2(1+3m/z^{2})}{{\kappa }a}}\left(\mathrm {cosh} {\frac {zF\zeta }{2RT}}-1\right),}$

where the parameter m characterizes the contribution of electro-osmosis into motion of ions within the double layer

${\displaystyle m={\frac {2\varepsilon _{0}\varepsilon _{m}R^{2}T^{2}}{3\eta F^{2}D}}.}$

• F is Faraday constant
• T is absolute temperature
• R is gas constant
• C is ions concentration in bulk
• z is ion valency
• ζ is electrokinetic potential
• ε₀ is vacuum dielectric permittivity
• ε_m is fluid dielectric permittivity
• η is dynamic viscosity
• D is diffusion coefficient

References

1. Mukhopadhyay, Rajendrani (June 2009). "Electrokinetics: it's in their genes". Analytical Chemistry. 81 (11): 4166–4168. doi: 10.1021/ac9006683 . ISSN   0003-2700. PMID   19408938.
2. Lyklema, J.J. "Fundamentals of Interface and Colloid Science", vol.2, page.3.208, 1995 ISBN   978-0-12-460524-4.
3. Delgado, A. V.; González-Caballero, F.; Hunter, R. J.; Koopal, L. K.; Lyklema, J. (2005). "Measurement and Interpretation of Electrokinetic Phenomena (IUPAC Technical Report)" (PDF). Pure and Applied Chemistry . 77 (10): 1753–1805. doi:10.1351/pac200577101753. hdl: 10481/29099 . S2CID   16513957.
4. Dukhin, Andrei S.; Xu, Renliang (2025). Zeta potential: fundamentals, methods, and applications. London Cambridge, MA: Academic Press. ISBN   978-0443334436.