Zeldovich–Liñán model
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In combustion, Zeldovich–Liñán model is a two-step reaction model for the combustion processes, named after Yakov Borisovich Zeldovich and Amable Liñán. The model includes a chain-branching and a chain-breaking (or radical recombination) reaction. The model was first introduced by Zeldovich in 1948[1] and later analysed by Liñán using activation energy asymptotics in 1971.[2] The mechanism with a quadratic or second-order recombination that were originally studied reads as
where is the fuel, is an intermediate radical, is the third body and is the product. The mechanism with a linear or first-order recombination is known as Zeldovich–Liñán–Dold model which was introduced by John W. Dold.[3][4] This mechanism reads as
In both models, the first reaction is the chain-branching reaction, which is considered to be auto-catalytic (consumes no heat and 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.[5][6][7] Therefore, the rate constants are written as[8]
where and are the pre-exponential factors, is the activation energy for chain-branching reaction which is much larger than the thermal energy and is the temperature.
In his analysis, Liñán showed that there exists three types of regimes, namely, slow recombination regime, intermediate recombination regime and fast recombination regime.[9] These regimes exist in both aforementioned models.