Equilibrium and nonequilibrium steady states in the reversible Oregonator model
15 May 1992-Vol. 162, Iss: 43499, pp 265-270
TL;DR: In this article, a relationship between nonequilibrium steady states and the equilibrium state has been established using the thermodynamic formulation of chemical affinity, which is also a measure of the distance from equilibrium of the system.
Abstract: For the reversible Oregonator model a relationship between nonequilibrium steady states and the equilibrium state has been established using the thermodynamic formulation of chemical affinity, which is also a measure of the distance from equilibrium of the system. In this model the distance from equilibrium is found to be a function of the constant concentrations of reactant and product and a stoichiometric factor between them for an overall open system reaction in which there is no accumulation of the intermediates for each instant of time or over a complete cycle of the oscillations. Assuming that the system is initially in a far from equilibrium situation for certain values of the stoichiometric factor and the concentrations of reactant and product, the equilibrium state can be attained in many cases merely by changing the bifurcation parameters (the concentrations of reactant and product and the stoichiometric factor between them) suitably.
Citations
More filters
TL;DR: In this paper, the authors investigated the features of thermodynamic equilibrium state of the reversible Oregonator (RO) model with close system approximation for a plausible stoichiometry, in which there is no overall change in the concentrations of the intermediates.
Abstract: We have investigated the features of thermodynamic equilibrium state of the reversible Oregonator (RO) model with close system approximation for a plausible stoichiometry, in which there is no overall change in the concentrations of the intermediates. For Field-Forsterling (ff) parameters, this model with close system approximation attains the state of thermodynamic equilibrium at equilibrium concentration of its final product in the order of 104 mol l-1, which is obviously unrealistic in a laboratory experiment. From numerical experiment, we report that if the equilibrium constant of the fifth step (K5) is assigned a value less than 1.0 (which is opposite to that proposed by Field), the RO model under open system approximation could execute oscillations, as well as under close system approximation could evolve to a thermodynamic equilibrium state with reasonably low and realistic equilibrium concentration of its final product for the overall reaction considered here. To accommodate the findings of this numerical work for the RO kinetic steps with K5 <1, we have found it necessary to revise the 2-variable diffusion-reaction model of Tyson.
3 citations
References
More filters
1,321 citations
TL;DR: In this paper, it was shown that the paradox of Fourier's heat conduction theory (propagation of temperature disturbances with infinite velocity) is a consequence of an insufficient description of the thermodynamical state in nonequilibrium.
Abstract: It is shown that the paradox ofFourier's heat conduction theory (propagation of temperature disturbances with infinite velocity) is a consequence of an insufficient description of the thermodynamical state in nonequilibrium. Taking heat flow and flow of momentum as additional state variables and thoroughly investigating the equation of entropy balance, we derive an extended theory of thermodynamics of irreversible processes, which can be shown to remove the paradox of heat conduction theory for materials with appropriate equations of state. The velocity of temperature propagation is calculated explicitly for a one atomic ideal gas using an approximate solution of the Boltzmann equation.
611 citations
TL;DR: In this paper, the authors extended the five-step Oregonator model by taking into account the reversibility of the various steps and found that there is a critical distance from equilibrium which must be exceeded before the steady state becomes unstable.
Abstract: The five‐step Oregonator model of the oscillatory Belousov–Zhabotinskii reaction has been expanded by taking into account the reversibility of the various steps. Forward and reverse rate constants have been assigned to four of the five steps by direct analogy to the detailed Field, Koros, and Noyes model of the Belousov–Zhabotinskii reaction. The rate constants and stoichiometry of the fifth step were parametrized and the stability of the steady state was investigated as a function of both of these parameters and the over‐all distance of the system from equilibrium. It was found that there is a critical distance from equilibrium which must be exceeded before the steady state becomes unstable. Numerical integration of the differential equations resulting from the model indicated that the system executes apparent limit cycle oscillations when the steady state is unstable. Introduction of reversibility into the Oregonator leads to a striking change in the range of values of the fifth step stoichiometric parameter over which oscillations will occur. This change is discussed in terms of the chemistry of the Belousov–Zhabotinskii reaction. Under some conditions the reversible Oregonator shows excitability such that a small finite perturbation of an infinitesimally stable steady state may be greatly amplified before the system returns to rest. An apparently analogous phenomenon appears in the Belousov–Zhabotinskii reaction itself.
80 citations
23 citations