The Dukhin number () is a dimensionless quantity that characterizes the contribution of the surface conductivity to various electrokinetic and electroacoustic effects, as well as to

electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...

and

permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...

of fluid

heterogeneous Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...

systems. The number was named after Stanislav and Andrei Dukhin.

Overview

It was introduced by Lyklema in “Fundamentals of Interface and Colloid Science”.Lyklema, J.J. "Fundamentals of Interface and Colloid Science", vol.2, page.3.208, 1995 . A recent IUPAC Technical Report used this term explicitly and detailed several means of measurement in physical systems. The Dukhin number is a ratio of the surface conductivity

\kappa^

to the fluid bulk electrical conductivity K_m multiplied by particle size ''a'': :

= \frac.

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 Diffusivity, mass diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion). Diffusivity is enc ...

: :

= \frac\left(\mathrm\frac-1\right),

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

m = \frac.

* ''F'' is

Faraday constant In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of ...

* ''T'' is

absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic ...

* ''R'' is

gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...

* ''C'' is ions concentration in bulk * ''z'' is ion valency * ζ is

electrokinetic potential Zeta potential is the electrical potential at the slipping plane. This plane is the interface which separates mobile fluid from fluid that remains attached to the surface. Zeta potential is a scientific term for electrokinetic potential in coll ...

* ε₀ is

vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or " void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often ...

dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the ma ...

* ε_m is fluid dielectric permittivity * η is

dynamic viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ...

* ''D'' is

References

{{DEFAULTSORT:Dukhin Number Chemical mixtures Colloidal chemistry Condensed matter physics Soft matter