# Zeldovich mechanism

(Redirected from Zel'dovich mechanism)

Zel'dovich mechanism is a chemical mechanism that describes the oxidation of nitrogen and NOx formation, first proposed by the Russian scientists Yakov Borisovich Zel'dovich, David A. Frank-Kamenetskii and P. Ya. Sadovnikov in 1947.[1][2][3] 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),[4][5]

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

The forward rate constants of the reactions are given by[6]

{\displaystyle {\begin{aligned}k_{1f}&=1.47\times 10^{13}\,T^{0.3}e^{-75286.81/RT},\\k_{2f}&=6.40\times 10^{9}\,Te^{-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, 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

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

## References

1. ^ Zeldovich, Y. A., D. Frank-Kamenetskii, and P. Sadovnikov. Oxidation of nitrogen in combustion. Publishing House of the Acad of Sciences of USSR, 1947.
2. ^ Williams, Forman A. "Combustion theory". (1985).
3. ^ Zeldovich, I. A., Barenblatt, G. I., Librovich, V. B., Makhviladze, G. M. (1985). Mathematical theory of combustion and explosions.
4. ^ Lavoie, G. A., Heywood, J. B., Keck, J. C. (1970). Experimental and theoretical study of nitric oxide formation in internal combustion engines. Combustion science and technology, 1(4), 313–326.
5. ^ Hanson, R. K., Salimian, S. (1984). Survey of rate constants in the N/H/O system. In Combustion chemistry (pp. 361–421). Springer, New York, NY.
6. ^ "San Diego Mechanism".