New variational-Lagrangian thermodynamics of viscous fluid mixtures with thermomolecular diffusion

A principle of virtual dissipation generalizing d’Alembert’s principle to nonlinear irreversible thermodynamics is applied to viscous fluid mixtures with coupled thermomolecular diffusion. Origina,l dynamical field equations are obtained directly from the variational principle. The use of new fundamental concepts and methods in the thermodynamics of open systems avoids the difficulties inherent in the classical Gibbs approach. The dissipative forces incorporated explicitly in the field equations are expressed by means of a dissipation invariant evaluated in detail in terms of coupled viscous and diffusive properties. Partial pressures and dissipative stresses are given new, unambiguous thermodynamic definitions. Lagrangian type equations with generalized coordinates are also obtained directly from the variational principle. They provide a powerful tool of simplified analysis of complex open systems as well as the foundation of a variety of finite element methods.