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Relaxation invariants of chemical reactions

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Abstract

The dynamics of complex chemical reactions is described by nonlinear differential equations that cannot be solved analytically. Transients near a stationary state are characterized by a linear relaxation time. The duration of the transition process as a whole is determined by the nonlinear relaxation time, which includes the time to reach the neighborhood of a stable stationary state and the time to further approach it. Quantitative estimation of relaxation times is associated with the determination of the coordinates of the stationary state and the spectrum of eigenvalues. Each eigenvalue characterizes the linear relaxation time of one of the reagents. The general estimation of the linear relaxation time is made by the “slowest” reagent. To calculate the nonlinear relaxation time, integration of a dynamic reaction model is required, which is not possible in the general case. The paper describes a method for estimating relaxation times without integrating a dynamic reaction model. The idea of the method is to transform the source nonlinear system of differential equations into a linear one, the integration of which is possible in an exact form. Concentration and concentration-temperature stoichiometric autonomous conservation laws are used for the transformation. The exact solutions found with their help express the concentration and temperature relaxation invariants of chemical reactions that depend on the reaction mechanism, but do not depend on the type of kinetic law. These invariants allow us to calculate the time to reach any given values of reagent concentrations and temperature and can be used to solve the inverse problem of identifying the mechanisms of chemical reactions occurring by any mechanisms with arbitrary kinetics in an open non-isothermal gradientless reactor.

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    N. I. Kol’tsov

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Kol’tsov, N.I. Relaxation invariants of chemical reactions. Reac Kinet Mech Cat 135, 2307–2321 (2022). https://doi.org/10.1007/s11144-022-02253-3

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