Tangential electric fields

A tangential electric field VE acting on these charges produces a relative motion between the interface and the solution just outside the diffuse layer. In view of the thinness of the diffuse layer, a balance of the tangential viscous and electrical forces can be written... 

For many particles, the diffuse-charge layer can be characterized adequately by the value of the zeta potential. For a spherical particle of radius / o which is large compared with the thickness of the diffuse-charge layer, an electric field uniform at a distance from the particle will produce a tangential electric field which varies with position on the particle. Laplace s equation [Eq. (22-22)] governs the distribution... 

All four processes have the same origin, since they are all based on the phenomenon of slip of the hquid along the surface of the other phase when a tangential electric field is present, or conversely, on the phenomenon that an electric field will arise during slip of the liquid. 

Electroosmotic flow (EOF) is the term used to describe the movement of a liquid in contact with a solid surface when a tangential electric field is applied.5 This movement is also known as electroosmosis or electrooen-doosmosis. Electroosmotic flow can be eliminated if necessary. However, EOF is often used, when flowing in the same direction as the analytes, to increase the speed with which the analytes reach the detector or, when flowing in the opposite direction from the analytes, to improve resolution. 

As shown, (17.3) implies that the Raman scattered intensity is proportional to the incident radiation intensity, and in turn on the square of the incident electric field amplitude. However, since Raman scattering depends on the dielectric polarization within the crystal, it is the internal field which must actually be considered, and the internal field is altered from the incident field by boundary conditions at the surface that require continuity of the tangential electric field and normal electric... 

We consider the cylindrical nanowire geometry shown in Fig. 17.1, with an incident plane wave normal to the cylinder axis and with an amplitude Eg. This is the simplest case to solve analytically and the one most often treated in experimental spectroscopic investigations of single nanowires. Possible orientations of linearly polarized incident light with respect to the wire axis are bounded by two cases. The first is the transverse magnetic (TM) polarization where the electric field is polarized parallel to the wire axis, and the second is the transverse electric (TE) polarization where the electric field is polarized perpendicularly to the wire axis. In TM polarization, the condition of continuity of the tangential electric field is expected to maximize the internal field, while in TE polarization, the dielectric mismatch should suppress the internal field. The incident plane wave may be expanded in cylindrical functions as ... 

For a perfect magnetic wall, the tangential magnetic and normal electric fields are obtained by antisymmetric extensions, while the normal magnetic and the tangential electric fields by symmetric ones. 

AC Electroosmosis is due to the interactions of the tangential electric field with the induced charges on each electrode, which results in electroosmotic force and fluid velocity in the horizontal direction. The AC-EO flow was previously explained in Refs. [2-4]. The tangential AC electric field produces electroosmotic fluid velocity due to the potential drop across double layer on the electrodes, which can be represented as [4]... 

The factor (1 in Eq. (2) measures the tangential electric field at the particle siuface. It is this component which generates the electrophoretic or electroacoustic motion. For a fixed frequency, it can be seen from Eq. (4) that (1 +J) depends on the permittivity of the particles and on die function X - Kg/K a, where Ks is the surface conductance of the double layer X measures the enhanced conductivity due to the charge at the particle surface. It is usually small unless the zeta potential is very high, so for most emulsions with large ka, X has a negligible effect. The ratio fp/f is also small for oil-in-water emulsions. Equation (4) can then be reduced to/= 0.5 and hence the dynamic mobility becomes ... 

The second mode of electroconvection in electrolytes is electroosmosis, either of the equilibrium, quasi-equilibrium, or nonequilibrium type. Equilibrium (or quasi-equilibrium) electroosmosis pertains to the electrolyte slip resulting from the action of tangential electric field upon the space charge of quasi-equilibrium... 

EDL. NEO pertains to the similar action of tangential electric field upon ESC of the nonequilibrium EDL. 

Li et al. [9] and Stone et al. [10] later extended Taylor s perfectly conducting limit to allow for the effect of finite liquid conductivities, showing in these cases that the tangential electric field within the slender conical liquid meniscus dominates. However, the tangential liquid phase electric field Ei also scales as MR and thus an exact balance between the Maxwell stress... 

The absence of tangential ion conduction also results in a weaker liquid phase tangential electric field. As such, the AC electrospray behavior was found to be insensitive to liquid conductivity [12]. This passivity of the liquid phase is compounded by the formation of a thin, highly conducting, permanent negatively charged... 

A fundamental electrokinetic phenomenon is the electroosmotic flow of a liquid electrolyte (solution of positive and negative ions) past a charged surface in response to a tangential electric field. Electrophoresis is the related phenomenon of motion of a colloidal particle or molecule in a background electric field, propelled by electroosmotic flow in the opposite direction. The basic physics is as follows ... 

The angular dependences of the MSEFs in a film at the air-Al and water-Al interfaces shown in Fig. 1.17a are remarkable in three respects. First, independently of the immersion medium, the z-component of the electric field within the film is dominant, while the x- and y-components are almost zero at aU angles of incidence (p. In other words, the tangential electric fields are quenched. This is observed for all metals. The second feature, which is common to all substrates in air (e.g., compare with Fig. 1.15a), is the attenuation of the perpendicular MSEF component, whose maximum value for Al is 0.73. It can be shown [161] that such an attenuation of the (El)-component in the case of a metal substrate is observed for films with 2 > 1-4, which includes the majority of films. Finally, it should be noted that if the radiation is incident fi om water onto a metal substrate, the perpendicular MSEFs within the film are enhanced by a factor of about 2, as for Si substrates (Fig. 1.15a). 

The distribution of the electric fields along z-axis in the air-model film-Al system is shown in Fig. 1.16b. The standing-wave patterns produced by the tangential electric field components exhibit nodes at a metal surface, while the normal component has an antinode. As seen from the insert in Fig. 1.16i>, the tangential electric fields, which are continuous at interfaces (1.8.8°), decay dramatically after crossing the metal surface, typically at a distance similar to the depth of the skin layer (1.3.14°). 

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