Review - Stability of Transport and Rate Processes

Abstract

About fifty years ago, the Turing instability demonstrated that even simple reaction-diffusion systems might lead to spatial order and differentiation, while the Rayleigh-Bénard instability showed that the maintenance of nonequilibrium might be the source of order in fluids subjected to a thermodynamic force above a critical value. Therefore, distance from global equilibrium in the form of magnitude of a thermodynamic force emerges as another constraint of stability; some systems may enhance perturbations, and evolve to highly organized states called the dissipative structures after a critical distance on the thermodynamic branch. Although the kinetics and transport coefficients represent short-range interactions, chemical instabilities may lead to long-range order and coherent time behavior, such as a chemical clock, known as Hopf bifurcation. Stability analyses of linear and nonlinear modes for stationary homogeneous systems are useful in understanding the formation of organized structures. This review presents the stability of equilibrium and nonequilibrium systems of transport and rate processes with some case studies. It underlines the relationships between complex behavior and stability of systems using the classical and nonequilibrium thermodynamics approaches.

Keywords

• transport and rate processes, Gibbs stability theory, fluctuation theory, entropy production, dissipative structures, Lyapunov functions