Zeta potential equation defining

Finally, it is noted that, according to Equation 10.34, the electrophoretic mobility is insensitive to the exact position of the hydrodynamic slip plane in the permeable layer. It implies that for such soft structures the notion zeta potential, as defined in Section 10.1, loses its meaning. 

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... 

Here and t] are, respectively, the relative permittivity and the viscosity of the electrolyte solution. This formula, however, is the correct limiting mobility equation for very large particles and is valid irrespective of the shape of the particle provided that the dimension of the particle is much larger than the Debye length 1/k (where k is the Debye-Htickel parameter, defined by Eq. (1.8)) and thus the particle surface can be considered to be locally planar. For a sphere with radius a, this condition is expressed by Ka l. In the opposite limiting case of very small spheres (Ka 3> 1), the mobility-zeta potential relationship is given by Hiickel s equation [2],... 

The surface potential is not accessible by direct experimental measurement it can be calculated from the experimentally determined surface charge (equations 32-34) by equations 40a and 40b. The zeta potential, calculated from electrophoretic measurements, is typically lower than the surface potential, J/q, calculated from diffuse double-layer theory. The zeta potential reflects the potential difference between the plane of shear and the bulk phase. The distance between the surface and the shear plane cannot be defined rigorously. 

Looking back at Equation 5.3, in an open tubular (OT) capillary with thin double layer and in the absence of significant polarization, C is the zeta potential of the wall Cw, and is defined as potential on a hypothetical surface of shear close to the tube wall. For porous/nonporous packing particles that are nonconducting, C is zeta potential at the particle surface Cp. 

FIGURE 2.1 The reduced electrophoretic mobility of a positively charged spherical colloidal particle of radius a in a KCl solution at 25°C as a function of reduced zeta-potential el/kTfor various values of ku. is defined by Equation (2.17). Calculated via Equation (2.16). 

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 ... 

The potential at the distance r = L from the particle surface is defined as the zeta potential, and is equivalent to the electrokinetic potential. More specifically, it is the electrical potential at the location of the hydrodynamic shear (shpping) plane against a point in the bulk fluid far removed from the particle s surface (Figure 2.18). Hence, the zeta potential is the potential difference between the dispersion medium and the stationary layer of fluid attached to the dispersed particle (Figure 2.19). Quantitatively, this can be calculated from the equation ... 

Electrokinetic phenomena, namely electrophoresis, electro-osmosis and streaming potential are discussed in Vol. 1 at a fundamental level. These effects arise because of charge separation at the interface that is induced for example by application of an electric field. The plane at which the liquid starts to move is defined as the shear plane and the potential at this plane is defined as the electrokinetic or zeta potential. A schematic picture is given that describes the shear plane and zeta potential. The latter is mostly assumed to be equal to the Stern potential and in the absence of specific adsorption it can be equated to the surface potential, which is the parameter... 

In Equation 19.12, Cq = 8.854 x j-i qi -1 jg jjjg dielectric constant in vacuum, e is the relative dielectric permittivity of the solvent (e = 78.5 for water at room temperature 298 K), and are the electrokinetic zeta potential defined at the shear plane (see Figure 19.3), r is the dynamic viscosity of the solvent (q = 8.91 x 10 kgm" s for water at room temperature 298 K), and E is the externally applied electric field. The first equation in Equation 19.12 represents the fluid motion in a stationary channel under the action of an externally appUed electric field. The motion is called electro-osmosis and the velocity is v. The second equation in Equation 19.12 gives the velocity v, of charged suspended colloidal particle (or a dissolved molecule) driven by the same electric field. This phenomenon is called electrophoresis. The EDL thickness 1/k depends on the concentration of background electrolyte [18,19,25,26]. 

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