Zeldovich mechanism

Zel'dovich mechanism is a chemical mechanism that describes the oxidation of nitrogen and NOx formation, first proposed by the Russian physicist Yakov Borisovich Zel'dovich in 1946.[1][2][3][4] The reaction mechanisms read as

N 2 + O ↔ k 1 NO + N {\displaystyle {\ce {{N2}+ O <->[k_1] {NO}+ {N}}}}
N + O 2 ↔ k 2 NO + O {\displaystyle {\ce {{N}+ O2 <->[k_2] {NO}+ {O}}}}

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

N 2 + O 2 ↔ k 2 NO {\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]

N + OH ↔ k 3 NO + H {\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]

k 1 f = 1.47 × 10 13 T 0.3 e − 75286.81 / R T k 2 f = 6.40 × 10 9 T e − 6285.5 / R T k 3 f = 3.80 × 10 13 {\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

d [ N O ] d t = k 1 f [ N 2 ] [ O ] + k 2 f [ N ] [ O 2 ] + k 3 f [ N ] [ O H ] − k 1 b [ N O ] [ N ] − k 2 b [ N O ] [ O ] − k 3 b [ N O ] [ H ] {\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

d [ N ] d t = k 1 f [ N 2 ] [ O ] − k 2 f [ N ] [ O 2 ] − k 3 f [ N ] [ O H ] − k 1 b [ N O ] [ N ] + k 2 b [ N O ] [ O ] + k 3 b [ N O ] [ H ] {\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} ]}

See also

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".