- Source: 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. 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),
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
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
Zeldovich–Liñán model
References
Kata Kunci Pencarian:
- Zeldovich mechanism
- Yakov Zeldovich
- Zeldovich–Liñán model
- Zeldovich spontaneous wave
- Reaction–diffusion system
- Diffusive–thermal instability
- Turing pattern
- Phoenix Cluster
- Superradiance
- Shock waves in astrophysics
