The Generalized Maxwell-Stefan Formulation of Irreversible Thermodynamics

3 THE GENERALIZED MAXWELL-STEFAN FORMULATION OF IRREVERSIBLE THERMODYNAMICS 

Until now, we have considered that the ditfusion process took place under essentially isobaric conditions, in nonelectrolyte systems and in the absence of external force fields, such as centrifugal or electric fields. In this section we shall generalize our analysis to include the influence of external force fields. The best starting point for a generalized treatment is the theory of irreversible thermodynamics. The treatment below is similar to that given by Lightfoot (1974) but readers will also find the books by de Groot and Mazur (1962) and Haase (1969) very useful. 

The purpose of the study of irreversible thermodynamics is to extend classical thermodynamics to include systems in which irreversible processes (e.g., diffusion and heat transfer) are taking place. Such an extension is made possible by assuming that for systems not too far from equilibrium the postulate of local equilibrium applies Departures from local equilibrium are sufficiently small that all thermodynamic state quantities may be defined locally by the same relations as for systems at equilibrium.  

With the help of this postulate, it is possible to obtain an explicit expression for a, the rate of entropy production per unit volume due to various irreversible processes taking place within the system (see, e.g., Slattery, 1981). The rate of entropy production due to diffusion is 

The requirement that 0 follows from the second law of thermodynamics. 

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