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# Surface conductivity

Surface conductivity is an additional electric conductivity of fluid in the vicinity of the charged surface. Fluid conductivity is associated with ions motion in electric field. Concentration of ions is higher close to the charged surfaces. They are attracted there by electrostatic forces induced by the surface charge. This layer with higher ions concentration is a part of the interfacial Double Layer. Higher concentration of ions in this layer leads to higher conductivity.

Smoluchowski was the first one who recognized importance of the surface conductivity at the beginning of the 20th century .

There is detail description of the surface conductivity by Lyklema in "Fundamentals of Interface and Colloid Science" 

Double Layer has two regions, according to well established Gouy-Chapmann-Stern model, Ref.2. The upper level, which is in contact with fluid bulk is diffuse layer. Interior part, that is in contact with interface is Stern layer.

It is possible that lateral ions motion in both part of the DL contributes to the surface conductivity.

Contribution of the Stern layer is less known. It is often called "additional surface conductivity" .

Theory of the surface conductivity over diffuse part of the DL has been developed by Bikerman . He derived a simple equation that links surface conductivity κσ with properties of ions and interface. For symmetrical electrolyte and assuming indentical ions diffusion coefficients D+=D-=D it is given in the Ref.2: ${\kappa}^{\sigma} = \frac{4F^2Cz^2D(1+3m/z^2)}{RT\kappa}(cosh\frac{zF\zeta}{2RT}-1)$

where

T is absolute temperature
R is gas constant
C is ions concentration in bulk
z is ion valency
ζ is electrokinetic potential

Parameter m characyterizes contribution of electro-osmosis into motion of ions within DL: $m = \frac{2\varepsilon_0\varepsilon_m R^2T^2}{3\eta F^2 D}$

There is dimensionless parameter Dukhin number that characterizes contribution of the surface conductivity to variety of electrokinetic phenomena, such as electrophoresis, and electroacoustic phenomena.

## References

1. ^ M. von Smoluchowski, Physik, Z., 6, 529 (1905)
2. ^ Lyklema, J. "Fundamentals of Interface and Colloid Science", vol. 2, Academic Press, 1995
3. ^ Dukhin, S.S. and Derjaguin, B.V. "Electrokinetic Phenomena", John Wiley and Sons, NY (1974)
4. ^ Bikerman, J.J. Z.Physik.Chem. A163, 378, 1933