Electrostatic retardation coefficient

The aim of this section is to consider the dynamic adsorption layer structure of ionic surfactant on the surface of rising bubbles. Results obtained in the previous section cannot be transferred directly to this case. The theory describing dynamic adsorption layers of ionic surfactant in general should take into accoimt the effect of electrostatic retardation of the adsorption kinetics of surfactant ions (Chapter 7). The structure of the dynamic adsorption layer of nonionic surfactants was analysed in the precedings section in the case when the adsorption process is kinetic controlled. In this case, it was assumed that the kinetic coefficients of adsorption and desorption do not depend on the surface coverage. On the other hand, the electrostatic barrier strongly depends on F , and therefore, the results of Section 9.1. cannot be used for the present case.. 

The coefficients a(p, c) and tj(p, c) describe chemical and physical effects on the kinetics of deposition. The transport of particles from the bulk of the flowing fluid to the surface of a collector or media grain by physical processes such as Brownian diffusion, fluid flow (direct interception), and gravity are incorporated into theoretical formulations for fj(p, c), together with corrections to account for hydrodynamic retardation or the lubrication effect as the two solids come into close proximity. Chemical effects are usually considered in evaluating a(p, c). These include interparticle forces arising from electrostatic interactions and steric effects originating from interactions between adsorbed layers of polymers and polyelectrolytes on the solid surfaces. 

The three most important forces for the long range interaction between macroscopic particles and a surface are steric-polymer forces, electrostatic interactions and Van der Waals forces. If we assume than the Van der Waals interactions between two atoms in a vaccuum are non-retarded and additive, we saw in the previous chapter that the form of the Van der Waals pair potential is w = —CJD where C is the coefficient in the atom-atom pair potential and D is the distance between the two... 

This diffusion coefficient describes only the self-diffusion of an ion in a homogeneous phase (obtainable by tracer experiments). If a concentration gradient exists, as is often the case in electrolyte solutions, the diffusion of all ions is balanced by their electrostatic interaction. Potential gradients are generated between faster- and slower-moving ions (diffusion potentials) which retard the first and accelerate the latter ions and lead to equal rates of diffusion. The common diffusion coefficient of a binary salt at low concentration may be used here as an example. This coefficient is coimected to the individual mobilities by... 

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