Mass balance laws and the decomposition, evolution and stability of chemical systems

Abstract

The laws of mass balance (conservation of atomic species) for reacting, diffusing and conducting material bodies are shown to provide a direct and simple decomposition of the reaction and diffusion processes. They also provide significant simplifications in implementing the condition of charge neutrality of the reaction processes and yield a reduction in the number of independent variables (thermodynamic forces) that occur in the dissipation inequality. General solutions of dissipation inequality are obtained which include the Onsager forms as special cases. These solutions yield a complete system of nonlinear constitutive relations for the viscous stresses, heat flux, diffusion fluxes, and the mass supplies associated with the chemical reactions. It is shown that chemically closed systems in fixed containers evolve toward static states whenever (1) the entropy production function vanishes only when all of the thermodynamic forces vanish, (2) the total free energy at constant temperature, constant total mass, and constant total masses of the atomic constituents possesses an absolute lower bound in an equilibrium state (thermodynamic stability), (3) the body is in thermal contact with an external environment at constant temperature, and (4) the body forces which act on each chemical constituent possess a potential function. Asymptotic stability of the thermodynamic equilibrium point is shown under the additional assumption that the total free energy has one and only one minimum at constant temperature, constant total mass, and constant total masses of the atomic constituents.