A new approach to the use of Lyapunov's functions. I. Stability and qualitative properties of paths in gas-solid systems

This paper contributes to the simulation of transients and stability properties of singular states in engineering and environmental gas-solid systems. Qualitative properties of paths around equilibrium, quasi-equilibrium and disequilibrium states in closed and open systems are investigated by Lyapunov functions or functionals, V, determined by an original method. The method requires first to assume a constant-sign time derivative of V with respect to perturbed dynamical equations, V˙, and next to determine V itself from a matrix formula. Such functions V, which may be of an indefinite sign, describe qualitative properties of system paths, and may be derived from the derivatives V˙ attributed to the constant-sign rates of entropy production or related exergy sink. Examples confirming the effectiveness of the approach for testing stability and qualitative properties of paths in non-reacting and reacting gas-solid systems are presented. A nontrivial example of the research benefit is presented in the paper in the form of the original classification of drying-moistening paths, based on the nontrivial saddle form of V in countercurrent systems and the focus form of V in co-current systems.