Dukhin number - Citizendia

Dukhin number is dimensionless quantity that characterizes contribution of the surface conductivity to various electrokinetic and electroacoustic effects, as well as to conductivity and permittivity of fluid heterogeneous systems. Surface conductivity is an additional Electric conductivity of Fluid in the vicinity of the charged surface Electrokinetic phenomena is a family of several different effects that occur in Heterogeneous Fluids or in porous bodies filled with fluid Permittivity is a Physical quantity that describes how an Electric field affects and is affected by a Dielectric medium and is determined by the ability Heterogeneous is an adjective used to describe an object or system consisting of multiple items having a large number of structural variations

It was introduced by Lyklema in “Fundamentals of Interface and Colloid Science” ^[1].

IUPAC Technical Report ^[2] prepared by a group of most known world experts on this subject uses this term explicitly.

Dukhin number is a ratio of the surface conductivity: $κ σ$ to the fluid bulk electric conductivity K_m multiplied by particle size a ::

$\ Du = \frac{\kappa^{\sigma}}{{\Kappa_m}a}$

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. Surface conductivity is an additional Electric conductivity of Fluid in the vicinity of the charged surface Surface conductivity is an additional Electric conductivity of Fluid in the vicinity of the charged surface Double Layer (interfacial (DL also called electrical double layer EDL is a structure that appears on the surface of an object when it is placed into a Liquid 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:

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

where parameter m characterizes contribution of electro-osmosis into motion of ions within DL:

$m = \frac{2\varepsilon_0\varepsilon_m R^2T^2}{3\eta F^2 D}$

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

There are several ways to measure ‘’’Dukhin number’’’. Surface conductivity is an additional Electric conductivity of Fluid in the vicinity of the charged surface Fick's laws of diffusion describe Diffusion and can be used to solve for the diffusion coefficient D. In Electrochemistry, Physics and Vascular plant biology, electro-osmosis, also called electroendosmosis, is the motion of polar In Physics and Chemistry, the Faraday constant (named after Michael Faraday) is the magnitude of Electric charge per mole of Thermodynamic temperature is the absolute measure of Temperature and is one of the principal parameters of Thermodynamics. Relationship with the Boltzmann constant The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working An ion is an Atom or Molecule which has lost or gained one or more Valence electrons giving it a positive or negative electrical charge In Chemistry, valence, also known as valency or valency number, is a measure of the number of Chemical bonds formed by the Atoms Double Layer (interfacial (DL also called electrical double layer EDL is a structure that appears on the surface of an object when it is placed into a Liquid This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner. A dielectric is a nonconducting substance ie an insulator. The term was coined by William Whewell in response to a request from Michael Faraday. Permittivity is a Physical quantity that describes how an Electric field affects and is affected by a Dielectric medium and is determined by the ability Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress. Fick's laws of diffusion describe Diffusion and can be used to solve for the diffusion coefficient D. Some of them are described in the Ref. 2, section 4. 4.

References

^ Lyklema, J. “Fundamentals of Interface and Colloid Science”, vol. 2, page. 3. 208, 1995
^ ”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

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[http://www.dispersion.com/ Dispersion Technology

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