Thermodynamic Formalism for Non-uniform Systems with Controlled Specification and Entropy Expansiveness

This report addresses the issue of formulating thermodynamic equations of state for multi-component chemical systems that can be consistently applied locally (on a volumetric, molar or specific basis) and so can form the thermodynamic basis of a theory for non-equilibrium transport in non-uniform multicomponent reacting fluids.The development of local equations of state, for application in non-uniform multi-component fluid systems, requires the introduction of localised composition variables, such as mole or mass fractions, which are not independent.Robust, unambiguous methods for the mathematical handling of such dependencies are developed, while maintaining close contact with equivalent global thermodynamic relations encountered in uniform systems.While four candidate thermodynamic functions can be the basis of a local equation of state, associated respectively with internal energy, Helmholtz energy, Gibbs energy and enthalpy, the most practically useful is based on the molar Gibbs energy for which the function depends only on intensive state variables (temperature, pressure and composition).

The thermodynamic treatment of nonuniform systems of Cahn and Hilliard is shown to be equivalent to the self-consistent thermodynamic formalism of Hart. All parameters of the two treatments have been rigorously related and key equations have been shown to be equivalent.