Zeldovich–Liñán model

In combustion, Zel'dovich–Liñán model is a two-step reaction model for the combustion processes, named after Yakov Borisovich Zel'dovich and Amable Liñán. The model includes a chain-branching and a chain-breaking (or radical recombination) reaction. The model was first introduced by Zel'dovich in 1948^[1] and later analysed by Liñán using activation energy asymptotics in 1971.^[2] The mechanism reads as

{\begin{aligned}{\rm {{F}+{\rm {X}}}}&\rightarrow 2{\rm {X}}\\{\rm {{X}+{\rm {{X}+{\rm {M}}}}}}&\rightarrow 2{\rm {{P}+{\rm {M}}}}\end{aligned}}

where ${\rm {F}}$ is the fuel, ${\rm {X}}$ is an intermediate radical, ${\rm {M}}$ is the third body and ${\rm {P}}$ is the product. The first reaction is the chain-branching reaction, which is considered to be auto-catalytic (consumes no heat or releases no heat), with very large activation energy and the second reaction is the chain-breaking (or radical-recombination) reaction, where all of the heat in the combustion is released, with almost negligible activation energy.^[3]^[4]^[5]

References

^ Zeldovich, Y. B. (1948). K teorii rasprostraneniya plameni. Zhurnal Fizicheskoi Khimii, 22(1), 27-48.
^ Liñán, A. (1971). A theoretical analysis of premixed flame propagation with an isothermal chain reaction. AFOSR Contract No. E00AR68-0031, 1.
^ Gubernov, V. V., Kolobov, A. V., Polezhaev, A. A., & Sidhu, H. S. (2011). Pulsating instabilities in the Zeldovich–Liñán model. Journal of mathematical chemistry, 49(5), 1054-1070.
^ Tam, R. Y. (1988). Damköhler-number ratio asymptotics of the Zeldovich-Liñán model. Combustion science and technology, 62(4-6), 297-309.
^ Dold, J., Daou, J., & Weber, R. (2004). Reactive-diffusive stability of premixed flames with modified Zeldovich-Linán kinetics. Simplicity, Rigor and Relevance in Fluid Mechanics, 47-60.

[1] Zeldovich, Y. B. (1948). K teorii rasprostraneniya plameni. Zhurnal Fizicheskoi Khimii, 22(1), 27-48.

[2] Liñán, A. (1971). A theoretical analysis of premixed flame propagation with an isothermal chain reaction. AFOSR Contract No. E00AR68-0031, 1.

[3] Gubernov, V. V., Kolobov, A. V., Polezhaev, A. A., & Sidhu, H. S. (2011). Pulsating instabilities in the Zeldovich–Liñán model. Journal of mathematical chemistry, 49(5), 1054-1070.

[4] Tam, R. Y. (1988). Damköhler-number ratio asymptotics of the Zeldovich-Liñán model. Combustion science and technology, 62(4-6), 297-309.

[5] Dold, J., Daou, J., & Weber, R. (2004). Reactive-diffusive stability of premixed flames with modified Zeldovich-Linán kinetics. Simplicity, Rigor and Relevance in Fluid Mechanics, 47-60.

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See also

References