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.^[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

1. Y.B. Zel'dovich (1946). "The Oxidation of Nitrogen in Combustion Explosions". Acta Physicochimica U.S.S.R. 21: 577–628
2. Zeldovich, Y. A., D. Frank-Kamenetskii, and P. Sadovnikov. Oxidation of nitrogen in combustion. Publishing House of the Acad of Sciences of USSR, 1947.
3. Williams, Forman A. "Combustion theory". (1985).
4. Zeldovich, I. A., Barenblatt, G. I., Librovich, V. B., Makhviladze, G. M. (1985). Mathematical theory of combustion and explosions.
5. 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.
6. 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.
7. "San Diego Mechanism".