Microstructural models, combustion wave

While providing a simple method for analyzing the redistribution of energy in the combustion wave, the models discussed in the previous section do not account for the local structural features of the reaction medium. Microstructural models account for details such as reactant particle size and distribution, product layer thickness, etc., and correlate them with the characteristics of combustion (e.g., U,T,). 

The equations used to describe the combustion wave propagation for microstructural models are similar to those in Section IV,A [see Eq. (6)]. However, the kinetics of heat release, 4>h may be controlled by phenomena other than reaction kinetics, such as diffusion through a product layer or melting and spreading of reactants. Since these phenomena often have Arrhenius-type dependences [e.g., for diffusion, 2)=9)o exp(— d// T)], microstructural models have similar temperature dependences as those obtained in Section IV,A. Let us consider, for example, the dependence of velocity, U, on the reactant particle size, d, a parameter of medium heterogeneity ... 

The microstructural models described here represent theoretical milestones in gasless combustion. Using similar approaches, other models have also been developed. For example, Makino and Law (1994) used the solid-liquid model (Fig. 20c) to determine the combustion velocity as a function of stoichiometry, degree of dilution, and initial particle size. Calculations for a variety of systems compared favorably with experimental data. In addition, an analytical solution was developed for diffusion-controlled reactions, which accounted for changes in X, p, and Cp within the combustion wave, and led to the conclusion that U< Ud(Lak-shmikantha and Sekhar, 1993). 

With this model, the microstructure of the combustion wave was studied, and compared with experimental results (Hwang et al, 1997 Mukasyan et al, 1996). For example, sequences of combustion front propagation at the microscopic level, obtained experimentally and by calculation, are shown in Fig. 24. In addition, it was demonstrated that fluctuations in combustion wave shape and propagation correlate with the heterogeneity of the reactant mixture (e.g., porosity and particle size). 

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