New thermodynamic-transport theory for systems with continuous component density distributions

Abstract Transport theories, equilibrium, and non-equilibrium thermodynamics become useless when applied to materials, such as multicomponent mixtures of dissociating or reacting gases, industrial fuels or polymers, which must be characterized by very large numbers of equations and composition parameters (e.g., component diffusivities, specific heats, chemical affinities, chemical potentials, heats of reactions). This work deals with a new theory in which the numerous equations and parameters required in current thermodynamic and transport theories for such materials are replaced by a smaller number of proper moments of the distribution function. Introducing new conservation laws (expressed in terms of moments) together with new definitions for chemical potentials, specific heats, heat and mass fluxes, diffusivities, affinities and entropy-production rates, a new theory is presented for continuous systems. A few thermodynamic functions and rules are also re-examined. The advantage of the proposed theory lies mainly in the practical possibility to approximate the behavior of many multicomponent gaseous mixtures as well as many industrial fuels and polymers by a much smaller number of moments than the number of distinct chemical components present.