Film theory binary systems

The film theory, once developed for equimolar binary mass transfer in non-reactive systems (Lewis and Whitman, 1924), was free from contradictions. Nowadays, it is widely applied for much more complicated processes, and therefore, additional assumptions have to be made. These assumptions are in some conflict with physical backgrounds, and thus, application of this theory becomes problematic (Kenig, 2000). 

In Chapter 7 we define mass transfer coefficients for binary and multicomponent systems. In subsequent chapters we develop mass transfer models to determine these coefficients. Many different models have been proposed over the years. The oldest and simplest model is the film model this is the most useful model for describing multicomponent mass transfer (Chapter 8). Empirical methods are also considered. Following our discussions of film theory, we describe the so-called surface renewal or penetration models of mass transfer (Chapter 9) and go on to develop turbulent eddy diffusivity based models (Chapter 10). Simultaneous mass and energy transport is considered in Chapter 11. 

In the remainder of this chapter we present solutions to this set of equations. As in Chapter 8 on film theory we begin with the binary case and then go on to consider multicomponent systems. 

Combined solution-diffusion-film-theory models have been presented already in several publications on aqueous systems, however, either 100% rejection of the solute is assumed [38], or detailed experimental flux and rejection results are required in order to find parameters by nonlinear parameter estimation [43, 44]. Consequently, it is difficult to apply these models for predictive purposes. In OSN, it is also important to account for the effect of different activities of the species on both sides of the membrane. We have proposed a set of equations [32], Eqs. (7) to (13), taking these factors into account We assume a binary system, although the equations could be generalized for a system of n components. In this analysis component 1 is the solute and component 2 is the solvent. The only parameters to be estimated, other than physical properties, are... 

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