Poisson equation electrophoretic mobility

Here the first term is the usual diffusive current, with Dc being the usual cooperative diffusion constant of the polymer molecule. The second term is a convective current due to the presence of induced electric field arising from all charged species in the system, p is the electrophoretic mobility of the polymer molecule derived in the preceding section. From the Poisson equation, we obtain... 

The electrophoretic mobility, e, is calculated by solving the Poisson equation with the appropriate boundary conditions. The final relation is of the type... 

The sign reversal takes place also in the electrophoretic mobility of a non-uniformly charged soft particles, as shown in this section. We treat a large soft particle. The x-axis is taken to be perpendicular to the soft surface with its origin at the front edge of the surface layer (Fig. 21.8). The soft surface consists of the outer layer —d < x < 0) and the inner layer (x < —d), where the inner layer is sufficiently thick so that the inner layer can be considered practically to be infinitely thick. The liquid flow m(x) and equilibrium electric potential i//(x) satisfy the following planar Navier-Stokes equations and the Poisson-Boltzmann equations [39] ... 

Scharp, K.A. and Brooks, D.E., Calculation of the electrophoretic mobility of a particle bearing bound polyelectrolyte using the nonlinear Poisson-Boltzmann equation, Biophys. J., 47, 563, 1985. 

Here, Dc is the cooperative diffusion coefficient of the chain if the couphng to the counterion cloud were to be absent. In dilute solutions, Dc is inversely proportional to the radius of gyration, is the velocity of the polyelectrolyte chains and ii is the electrophoretic mobility of the polyelectrolyte chain (discussed in Section 7.4). From the Poisson equation (Equation 3.9), we get... 

In the case of a thin and dense double layer, the electric field is distorted by the particles in the fluid because of the (usually) larger particle size and the compactness of the double layer (von Smoludiowski, 1917, 1921). The principal result of this is that the electrophoretic friction, F3, is considerably reduced because the oppK>sitely charged ions in the path of the moving particle do not interfere with the particle s motion, and those ions slightly tangential to the partide contribute little to the friction. This increases the mobility of these partides. Here the electrophoretic mobility is derived using Poisson s equation ... 

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