Electric, double layer field coupling

The first basic ingredient in our description of the electric double layer is the coulombic interaction. It seems quite natural to assume that the fields are coupled according to a coulombic Hamiltonian of the same... 

Alterations in Electrical Double Layer Structure by an External Field Coupling to the Membrane... 

Another important consideration in attempts to understand the coupling of electromagnetic fields to biomembranes is the subsequent or concomitant effect on the structure of the electrical double layer adjacent to the membrane surface upon exposure. Alterations in double layer structure could, for example, occur if the net effect of the membrane-field interaction results in a redistribution of membrane surface change. There exist other possible means of effecting changes in the structure of the double layer, some of which will also be discussed below. 

Induced-charge and second-kind electrokinetic phenomena arise due to electrohydrodynamic effects in the electric double layer, but the term nonlinear electrokinetic phenomena is also sometimes used more broadly to include any fluid or particle motion, which depends nonlinearly on an applied electric field, fit the classical effect of dielectrophoresis mentioned above, electrostatic stresses on a polarized dielectric particle in a dielectric liquid cause dielectro-phoretic motion of particles and cells along the gradient of the field intensity (oc VE ). In electrothermal effects, an electric field induces bulk temperature gradients by Joule heating, which in turn cause gradients in the permittivity and conductivity that couple to the field to drive nonlinear flows, e.g., via Maxwell stresses oc E Ve. In cases of flexible solids and emulsions, there can also be nonlinear electromechanical effects coupling the... 

Henry [ 157] solved the steady-flow continuity and Navier-Stokes equations in spherical geometry, neglecting inertial terms but including pressure and electrical force terms, coupled with Poisson s equation. The electrical force term in Henry s analysis consisted of the sum of the externally applied electric field and the field due to the double layers. His major assumptions are low surface potential (i.e., potentials less than approximately 25 mV) and undistorted double layers. The additional parameter ku appearing in the Henry... 

Another determination of the surface equilibrium entails the use of the coupling of the DC electric field present at charged interfaces with the electromagnetic field, as described in the theoretical section. Integration of the nonlinear polarization over the whole double layer leads to the following expression of the effective susceptibility tensor ... 

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... 

Section 4.6 may be considered the prototype of modem electrokinetics, because all relevant features were covered the coupling of hydrodynamic and electric fluxes and double layer polarization. However, the elaboration remained restricted to electrophoresis, which is the most familiar electrokinetlc phenomenon. Other types of electrokinetics, summarized in table 4.1. basically require the same theory, although there may be considerable differences in the elaboration (what is stationary what is moving boundiuy condition , etc.). With sec. 4.6 we consider the fundamentals sufficiently explained and illustrated and we shall therefore not repeat and apply this theory to other electrokinetlc phenomena. Instead, two important extensions will now be briefly reviewed inclusion of double layer overlap, as occurs in plugs, in the present section and measurement in alternating fields in the following. 

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