Physics:Zel'dovich mechanism

Zel'dovich mechanism is a chemical mechanism that describes the oxidation of nitrogen and NO_x formation, first proposed by the Russian scientists Yakov Borisovich Zel'dovich, David A. Frank-Kamenetskii and P. Ya. Sadovnikov in 1947. The reaction mechanisms read as

Failed to parse (syntax error): {\displaystyle \ce{{N2} + O <->[k_1] {NO} + {N},}}

Failed to parse (syntax error): {\displaystyle \ce{{N} + O2 <->[k_2] {NO} + {O},}}

where $k_1$ and $k_2$ are the reaction rate constants in Arrhenius law. The overall global reaction is given by

Failed to parse (syntax error): {\displaystyle \ce{ {N2} + {O2} <->[k] 2NO.}}

The overall reaction rate is mostly governed by the first reaction (i.e., rate-determining reaction), since the second reaction is much faster than the first reaction and occurs immediately following the first reaction. At fuel-rich conditions, due to lack of oxygen, reaction 2 becomes weak, hence, a third reaction is included in the mechanism, also known as extended Zel'dovich mechanism (with all three reactions),

Failed to parse (syntax error): {\displaystyle \ce{{N} + {OH} <->[k_3] {NO} + {H}.}}

The forward rate constants of the reactions are given by

$\begin{array}{rl}{k}_{1f}& =1.47\times 10^{13}{T}^{0.3}{e}^{-75286.81/RT},\\ k_{2f}& =6.40\times 10^{9}T{e}^{-6285.5/RT},\\ k_{3f}& =3.80\times 10^{13},\end{array}$

where the pre-exponential factor is measured in units of cm, mol, s and K, temperature in kelvins, and the activation energy in cal/mol; R is the universal gas constant.

NO formation

The rate of NO concentration is given by

$\frac{d[\mathrm{N}\mathrm{O}]}{dt}=k_{1f}[{\mathrm{N}}_2][\mathrm{O}]+k_{2f}[\mathrm{N}][{\mathrm{O}}_2]+k_{3f}[\mathrm{N}][\mathrm{O}\mathrm{H}]-k_{1b}[\mathrm{N}\mathrm{O}][\mathrm{N}]-k_{2b}[\mathrm{N}\mathrm{O}][\mathrm{O}]-k_{3b}[\mathrm{N}\mathrm{O}][\mathrm{H}].$