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.^[1][2][3][4] The reaction mechanisms read as

${\displaystyle {\ce {{N2}+ O <->[k_1] {NO}+ {N}}}}$

${\displaystyle {\ce {{N}+ O2 <->[k_2] {NO}+ {O}}}}$

where ${\displaystyle k_{1}}$ and ${\displaystyle k_{2}}$ are the reaction rate constants in Arrhenius law. The overall global reaction is given by

${\displaystyle {\ce {{N2}+ {O2}<->[k] 2NO}}}$

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),^[5][6]

${\displaystyle {\ce {{N}+ {OH}<->[k_3] {NO}+ {H}}}}$

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^[7]

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

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

${\displaystyle {\frac {d[\mathrm {NO} ]}{dt}}=k_{1f}[\mathrm {N} _{2}][\mathrm {O} ]+k_{2f}[\mathrm {N} ][\mathrm {O} _{2}]+k_{3f}[\mathrm {N} ][\mathrm {OH} ]-k_{1b}[\mathrm {NO} ][\mathrm {N} ]-k_{2b}[\mathrm {NO} ][\mathrm {O} ]-k_{3b}[\mathrm {NO} ][\mathrm {H} ]}$

N formation

Similarly, the rate of N concentration increase is

${\displaystyle {\frac {d[\mathrm {N} ]}{dt}}=k_{1f}[\mathrm {N} _{2}][\mathrm {O} ]-k_{2f}[\mathrm {N} ][\mathrm {O} _{2}]-k_{3f}[\mathrm {N} ][\mathrm {OH} ]-k_{1b}[\mathrm {NO} ][\mathrm {N} ]+k_{2b}[\mathrm {NO} ][\mathrm {O} ]+k_{3b}[\mathrm {NO} ][\mathrm {H} ]}$

References