Double-layer thickness, equation defining

The surface charge density is given as a = eKif/, where e is the permittivity and K is not conductivity but a special variable defined in equation 19 thus, ij/ depends on surface charge density and the solution ionic composition (through k). The variable 1/k is called the double-layer thickness, and for water at 25 °C it is given by... 

The potential at the boundary between the Stern layer and the diffuse part of the double layer is called the zeta potential ( ) and has values ranging from 0-100 mV. Because the charge density drops off with distance from the surface, so does the zeta potential the distance from the immobile Stern layer to a point in the bulk liquid at which the potential is 0.37 times the potential at the interface between the Stern layer and the diffuse layer, is defined as the double layer thickness and is denoted 8 (Figure 3.26). The equation describing 8 (Knox 1987) is ... 

Next, let us consider the application of Equation (21) to a particle migrating in an electric field. We recall from Chapter 4 that the layer of liquid immediately adjacent to a particle moves with the same velocity as the surface that is, whatever the relative velocity between the particle and the fluid may be some distance from the surface, it is zero at the surface. What is not clear is the actual distance from the surface at which the relative motion sets in between the immobilized layer and the mobile fluid. This boundary is known as the surface of shear. Although the precise location of the surface of shear is not known, it is presumably within a couple of molecular diameters of the actual particle surface for smooth particles. Ideas about adsorption from solution (e.g., Section 7.7) in general and about the Stern layer (Section 11.8) in particular give a molecular interpretation to the stationary layer and lend plausibility to the statement about its thickness. What is most important here is the realization that the surface of shear occurs well within the double layer, probably at a location roughly equivalent to the Stern surface. Rather than identify the Stern surface as the surface of shear, we define the potential at the surface of shear to be the zeta potential f. It is probably fairly close to the... 

Electrostatic interactions in solutions containing charged particles and ions can be described using the Poisson-Boltzmann equation. A charged surface attracts counterions into a double layer of thickness defined by the Debye length, which depends on counterion concentration and solvent dielectric constant. From simplified theories, expressions can be derived for the attractive interaction potential between charged spheres. 

Equation 3.90 defines the thickness of the diffuse double layer Lqq... 

The hydrodynamics of fluid flow in micro-particle electrophoresis chambers are described by solutions to the Navier-Stokes equation for steady laminar fluid flow (equation (19.1)) with boundary values defined by the chamber geometry. When considering the dimensions of an experimental chamber compared to the thickness of the double-layer (mm to nm), fluid flow at the surface would appear to move at a constant velocity. In other... 

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