Zeldovich mechanism

${\displaystyle {\text{N}}_2^{}+\text{O}\stackrel{k_1}{\leftrightarrow }\text{NO}+\text{N}}$

${\displaystyle \text{N}+{\text{O}}_2^{}\stackrel{k_2}{\leftrightarrow }\text{NO}+\text{O}}$

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

${\displaystyle {\text{N}}_2^{}+{\text{O}}_2^{}\stackrel{k}{\leftrightarrow }2\text{NO}}$

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),

${\displaystyle \text{N}+\text{OH}\stackrel{k_3}{\leftrightarrow }\text{NO}+\text{H}}$

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

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

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

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