Quasi-kinetic model

Quasi-kinetic models deal with processes that are controlled by mass transfer rates rather than by chemical reaction rates. These models assume nearly instantaneous attainment of equilibrium within the region of interest, so changes in the species distribution are controlled by the rate of transfer of substances into or out of that region. These models are constrained by continuity equations making them similar to the chemical reactors models in Chapter 4. 

As for the quasi (pseudo)-steady-state case, the basic assumption in deriving kinetic equations is the well-known Bodenshtein hypothesis according to which the rates of formation and consumption of intermediates are equal. In fact. Chapman was first who proposed this hypothesis (see in more detail in the book by Yablonskii et al., 1991). The approach based on this idea, the Quasi-Steady-State Approximation (QSSA), is a common method for eliminating intermediates from the kinetic models of complex catalytic reactions and corresponding transformation of these models. As well known, in the literature on chemical problems, another name of this approach, the Pseudo-Steady-State Approximation (PSSA) is used. However, the term "Quasi-Steady-State Approximation" is more popular. According to the Internet, the number of references on the QSSA is more than 70,000 in comparison with about 22,000, number of references on PSSA. 

The thermal and kinetic models discussed above are the basis for determining the processing conditions for reactive processing by ionic polymerization,29 addition polymerization, vulcanization of rubbers and radical polymerization, although in the latter case additional assumptions of a constant initiation rate and a quasi-stationary concentration of radicals are made.89 These models can also be used to solve optimization problems to improve the performance and properties of end-products. 

To applying Eq. (2.47) to non-isothermal problems, it is necessary to generalize it by introducing temperature-dependent constants. The basic approach was proposed by Ziabicki94,95 who developed a quasi-static model of non-isothermal crystallization in the form of a kinetic rate equation ... 

To answer the question whether quasi-stationarity can be observed in our kinetic model at e - 0 it is first necessary to examine a subsystem of fast motions ("a fast subsystem ) so as to establish if it has a unique and stable steady-state solution. 

For this analysis it is of importance to classify mechanisms (their associated kinetic models here are the sets of quasi-steady-state equations) to answer the question of what class of mechanisms possesses a unique and stable solution for the quasi-steady-state equations, and which one can have several solutions, i.e. several steady states. 

Thus in each concrete case quasi-homogeneous models (in particular, models of the polychronous kinetics) need to be confirmed by special experiments eliminating the effects of autowave processes on the reaction dynamics. 

Edelman, R. B. Fortune, 0. F. "A Quasi-Global Chemical Kinetic Model for the Finite-Rate Combustion of Hydrocarbon Fuels With Application to Turbulent Burning and Mixing in Hypersonic Engines and Nozzles" AIAA Paper 69-86, AIAA,... 

Various rate expressions may be derived from a kinetic model, depending on the assumptions of quasi-equilibrium and rate determining step. Experimental data should provide information which expression describes best the rate dependency. 

A traditional kinetic model of steady-state catalytic reaction assumes quasi-steady-state concentrations of intermediate species on the catalyst surface. This assumption is often invalid for unsteady-state conditions characterized by continuous changes in a fluid phase composition and temperature above the catalyst surface. Additionally, the catalyst itself can interact with the reaction mixture and can undergo significant changes, influenced by changing conditions in the gas phase. Such a modification of the catalyst can be con-... 

A simple kinetics model of the three-state mechanism that takes into account bottlenecks to intramolecular energy transfer can be developed by splitting the phase space region A into the quasi-periodic motion region A and the highly chaotic region A2, with A = A + A2. Such a kinetics model is presented in Fig. 22. Let be the rate constant for flow of phase space points from Ai into... 

Thus, the proposed method for analyzing the kinetics of defect formation, based on the quasi-epitaxy model, clearly demonstrates the role of the surface in the ADC equilibrium and allows one to assess the effects of temperature and Jb of the equilibration of defect concentrations. Computer simulations of defect formation kinetics in II-VI crystal non-equilibrium chalcogen vapor systems indicate that steady state defect concentrations in the surface layer are reached very rapidly and, accordingly, are not... 

The kinetic model of styrene auto-initiation proposed by Hui and Hameilec [27] was used as a starting point for this work. The Mayo initiation mechanism was assumed (Figure 7.2) but the acid reaction was of course omitted. After invoking the quasi-steady-state assumption (QSSA) to approximate the reactive dimer concentration, Hui and Hameilec used different simplifying assumptions to derive initiation rate equations that are second and third order in monomer concentration. 

These controversial results on the kinetics of Me UPD processes, obtained on the basis of the simplest approach assuming quasi-homogeneous substrate surfaces, led to the development of a different kinetic model including surface inhomogeneities, gradients of Meads> and surface diffusion as discussed in the following. 

From a kinetic point of view, the fine subdivision and absence of in-1i aparticle mass transfer allows oxide microcrystals to be considered as quasi-<-ontinuous with the liquid phase. Homogeneous kinetic models are reasonable lor these materials and provide an adequate description in most cases (Yasunaga and Ikeda, 1986). Rale control by mass transfer has been invoked in certain cases for synthesized and compacted oxides and attributed to the oxides ... 

There are many ways one can try to reduce the computational burden. Ideally, one would find numerical methods which are guaranteed to retain accuracy while speeding the calculations, and it would be best if the procedure were completely automatic i.e. it did not rely on the user to provide any special information to the numerical routine. Unfortunately, often one is driven to make physical approximations in order to make it feasible to reach a solution. Common approximations of this type are the quasi-steady-state approximation (QSSA), the use of reduced chemical kinetic models, and interpolation between tabulated solutions of the differential equations (Chen, 1988 Peters and Rogg, 1993 Pope, 1997 Tonse et al., 1999). All of these methods were used effectively in the 20th century for particular cases, but all of these approximated-chemistry methods share a serious problem it is hard to know how much error is... 

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