Boundary equation electrophoresis

In order to illustrate the effects of media structure on diffusive transport, several simple cases will be given here. These cases are also of interest for comparison to the more complex theories developed more recently and will help in illustrating the effects of media on electrophoresis. Consider the media shown in Figure 18, where a two-phase system contains uniform pores imbedded in a matrix of nonporous material. Solution of the one-dimensional point species continuity equation for transport in the pore, i.e., a phase, for the case where the external boundaries are at fixed concentration, Ci and Cn, gives an expression for total average flux... 

These equations (and others that follow) are based on the solutions of equations of motion for the particles, as well as the electrolyte, that we use in Chapter 12 in the context of electrophoresis. It turns out that the analysis of Krasny-Ergen fails to satisfy one of the boundary conditions and does not take into account energy dissipations caused by the electric currents arising from the motion of the electrolyte. It is more appropriate for kRs -> oo. 

It is apparent from the above sections that the understanding of electrophoretic mobility involves both the phenomena of fluid flow as discussed in Chapter 4 and the double-layer potential as discussed in Chapter 11. In both places we see that theoretical results are dependent on the geometry chosen to describe the boundary conditions of the system under consideration. This continues to be true in discussing electrophoresis, for which these two topics are combined. As was the case in Chapters 4 and 11, solutions to the various differential equations that arise are possible only for rather simple geometries, of which the sphere is preeminent. 

During the past two decades, much attention has been drawn in this area and advances have been made in theoretical analysis concerning the applicability of Eq. (1) in a variety of systems. This chapter presents the state of understanding of the electrophoretic motion of colloidal particles under various conditions. We first introduce the basic concept and fundamental electrokinetic equations for electrophoretic motion. Then, we review some recent studies on the mobility of a single particle, the boundary effects and the particle interactions in electrophoresis. In addition, a few theoretical methods, which have been used to investigate the boundary effects and particle interactions, will be highlighted and demonstrated in the context. 

Using the derived equations It Is possible to calculate all dynamic parameters of analytical importance [3]. Moreover, the model considerations can be extended to moving boundary electrophoresis as well as zone electrophoresis. Due to the fact that dlffuslonal effects play no role In the steady-state of isotachophoresls and It does e.g. In zone electrophoresis, the zone-characteristics will be different. 

A careful account of the problem can be found in Ref. [95]. Ohshima et al. [96] first found a numerical solution of the problem, valid for arbitrary values of the zeta potential or the product Ka. In the same paper, they dealt with the problem of finding the sedimentation potential and the DC conductivity of a suspension of mercury drops. The problems are solved following the lines of the electrophoresis theory of rigid particles previously derived by O Brien and White [18]. The liquid drop is assumed to behave as an ideal conductor, so that electric fields and currents inside the drop are zero, and its surface is equipotential. The main difference between the treatment of the electrophoresis of rigid particles and that of drops is that there is a velocity distribution of the fluid inside the drop, Vj, governed by the Navier-Stokes equation with zero body force (in the case of electrophoresis), and related to the velocity outside the drop, v, by the boundary conditions ... 

The moving boundary spreading in the electrophoresis of protein is usually measured in terms of the refractive index gradient dn/dr, where n is the refractive index. The results are often recorded as shown in Figure 13.12. The formation of the boundary, its spreading, and its separation (if any) are functions of diffusion. The equation of the moving boundary is given in the form... 

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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