International Journal of Heat and Mass Transfer, Vol.40, No.14, 3467-3485, 1997
Variational Thermomechanical Processes and Chemical-Reactions in Distributed Systems
In this synthesizing work several interrelated variational principles are constructed for various field representations of dynamics of simultaneous transfer of heat, mass and electric charge, in chemically reacting systems at mechanical equilibrium or not. The underlying physical principle is invariance of the entropy production or energy dissipation. The variational framework, which stems from functionals of various thermodynamic potentials, is quite vast and diverse. It includes : nonstationary extension of Onsager’s variational formulation, gradient representations, vectors of thermal, chemical and mechanical displacements, potentials of thermal field, functional Hamiltonian formalism, Poissonian brackets, and a thermomechanical dissipative action : Each of these methods is supplemented by a physical assumption, which is in general not incorporated into the original variational formulation : this is the assumption of a local thermal equilibrium. The most original and valuable result is inclusion of chemical reactions in variational dynamics, with chemical nonlinearities governed by kinetics of mass action. A method was also successfully discovered, based on equivalent variational problems, which makes it possible to show the equivalence of thermodynamic potentials at nonequilibrium, and, in particular, the practical usefulness of free energy functionals. Finally, an extended action approach for thermomechanical chemical kinetics in distributed systems was worked out. This should be important for biophysical systems such as, for example, contracting muscles, whose dynamics are described by dissipative Lagrange equations containing the mechanical equation of motion and equations of chemical kinetics (the Guldberg-Waage mass action law and its nonlocal generalizations).
Keywords:THERMODYNAMIC-EQUILIBRIUM;CONSTITUTIVE-EQUATIONS;DISSIPATIVE PROCESSES;LAGRANGE-FORMALISM;HEAT-TRANSFER;PRINCIPLE;FLUIDS;FLOW;FORMULATION;POTENTIALS