Brownian-static approximation

Inserting Eq. (385) into Eqs. (365) and (312), it is then easy to obtain the following expression for the current in the Brownian-static approximation ... 

This problem is very difficult to solve in general however, we have to keep conditions (303) in mind, which we used in order to obtain the Fokker-Planck collision term (304). With this approximation, it is expected that the ions will exhibit random Brownian motion instead of free particle motion between two successive coulombic interactions. We shall thus refer to this model as the Brownian-static model (B.s.). 

This model, as wets discussed in Chap.6, gives one an opportunity to describe the kinetics of non-ideal gas media in static and fluctuating surface field. Therefore, when approximating the kinetic operators (6.2.4), (6.2.5) one can use the results of quasiparticle method for non-ideal media kinetics (Dubrovskiy and Bogdanov 1979b), theory of liquids (Croxton 1974), theory of Brownian motion (Akhiezer and Peletminskiy 1977), theory of phase transitions, models of equilibrium properties of such systems (Jaycock and Parfitt 1981) with further application of methods of statistical thermodynamics of irreversible processes (Kreuzer and Payne 1988b) and experimental data on pair correlation function (Flood 1967). 

This section presents a theoretical study of more concentrated deformable emulsions and microemulsions where higher order interactions become important. The purpose is to relate the microseopic droplet deformability to the structure of such systems and further to their macroscopic (thermodynamic) properties. The radial distribution function and static structure factor are calculated utilising an integral equation approach in an appropriate closure approximation. This method allows us to obtain the virial equation of state as well. A semi-empirical equation of state, based on modifying the Camahan-Starling expression, as well as comparison with Brownian dynamics simulations are also presented. 

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