Dukhin number

The Dukhin number (Du) is a dimensionless quantity that characterizes the contribution of the

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]

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

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

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