Electro-osmosis diffuse double layer

Clays are generally considered to be effective barriers for flow of water and solutes due to their low permeability and high ion adsorption capacity. However, as environmental criteria for the emission of contaminants and water from clay barriers become increasingly stringent, it is crucial to be aware of all relevant driving forces and fluxes and to take them into account in model assessments. In this respect the processes of chemical and electro-osmosis may not be neglected in clayey materials of hydraulic conductivity < 10-9 m/s [7], At these low conductivities the surface charge of the clay particles and the counter-ion accumulation in diffuse double layers enable explanation and quantification of osmotic processes and semi-permeability in clays [1],... 

In the article on electro-osmosis (q.v.) a similar formula, but with 4 in place of the factor 6, is derived. Since electrophoresis is the reverse of electro-osmosis, the same expression should apply in both cases to the potential at the surface of shear between the two phases. The explanation of the apparent discrepancy is that instead of applying Stokes s law to a small sphere, the derivation of the electro-osmotic effect is based on the model of a parallel plate capacitor, i.e. on a large solid surface whose radius of curvature is negligible (compared with the thickness of the diffuse double layer). Closer analysis of the problem by Henry and Booth has shown that 4 is the correct factor for large particles, independent of their size and shape, but that for most systems, e.g. stable colloidal solutions, the factor varies between 4 and 6, depending on the size of the particle and the thickness of its atmosphere. 

Electro-osmosis is an important process in capillary electrophoresis. When the separation capillary is filled with a working electrolyte, an electric double layer is always formed on the inner wall surface due to ionizable groups of the capillary wall material and/or ions absorbed on to the capillary wall. For example, in quartz capillaries, the silanol groups present at the surface form the fixed negative part of the electric double layer. The positive part is then formed by ions present in the solution. A fraction of the ions forming the electrolyte part of the electric double layer is always fixed by electrostatic forces near the capillary wall and forms the so-called Stern layer the rest of these ions form, however, the mobile diffuse layer. The potential this creates between the Stern layer and the bulk solution is termed the zeta potential (in V), and is given by... 

Electro-osmosis produces an effective slip of the liquid outside the double layer past to the solid surface. In the classical continuum model of the diffuse layer, the... 

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