Minimum of entropy generation as a general evolution criterion for nonlinear structured
systems with fixed boundaries.
Author: Stanislaw Sieniutycz
The purpose of our presentation is a general thermodynamic framework for balance and
kinetic equations of structured heterogeneous systems and chemical networks which is
consistent with the second law of thermodynamics. Methods effective in classical
irreversible thermodynamics of single-phase systems are here extended to include boundary
discontinuities, surface reactions and interface transports in multiphase systems. Complex
multiphase and multireaction systems are analyzed by methods of the network (system)
theory in which topological and graphical methods of electrical networks are extended to
quite general energo-chemical systems. Chemical Ohms law links chemical force (affinity)
and chemical flux (reaction rate), and chemical conversions follow simple rules of the
algebra for chemical resistances. There are two main methods coming from thermodynamics of
single-phase systems, which can effectively be applied to complex structured systems. The
first method starts with the derivation of balance equations for mass, energy and momentum
and terminates at the entropy balance; from the knowledge of the entropy source ss kinetic
laws are postulated. Yet, our main objective is the second (newer) method which is based
on the variational formulation of second law and concept of nonlinear chemical resistance.
It is an optimization method in which an entropy functional is minimized to predict
kinetic laws and secure appropriate balance equations. The method does not postulate
linearity; rather it rests on state-dependent dissipation functions. It follows that the
variational method assures classical nonlinear kinetics of mass action and nonlinear set
of diffusion-reaction equations under the condition of local thermal equilibrium. Still
local disequibria can be predicted which are shown to be responsible for onset of
interfacial and bulk instabilities. Hamiltonian form of transport equations and laws of
chemical kinetics is valid, which is efficient to accommodate nonlinear effects.
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