Physics:Zeldovich mechanism

Zel'dovich mechanism is a chemical mechanism that describes the oxidation of nitrogen and NO_x formation, first proposed by the Russian physicist Yakov Borisovich Zel'dovich in 1946. 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}}}

Assuming the initial concentration of NO is low and the reverse reactions can therefore be ignored, the forward rate constants of the reactions are given by

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

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

NO formation

The rate of NO concentration increase is given by

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

N formation

Similarly, the rate of N concentration increase is

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