Accelerated diffusion of chain carriers and kinetic features of heterogeneous processes in gas-phase chain reactions

Article abstract of DOI:10.1007/s10975-008-2003-4

In gas-phase combustion processes, the regeneration of free atoms and radicals in chain propagation reactions enhances the diffusion flux of these species from the flame zone. In flame propagation in tubular reactors and in filtration combustion, this eff

Full text of DOI:10.1007/s10975-008-2003-4

ISSN 0023-1584, Kinetics and Catalysis, 2008, Vol. 49, No. 2, pp. 178–185. © MAIK “Nauka /Interperiodica” (Russia), 2008.
Original Russian Text © V.V. Azatyan, A.A. Piloyan, G.R. Baimuratova, V.V. Masalova, 2008, published in Kinetika i Kataliz, 2008, Vol. 49, No. 2, pp. 190–197.
Accelerated Diffusion of Chain Carriers and Kinetic Features
of Heterogeneous Processes in Gas-Phase Chain Reactions
V. V. Azatyan, A. A. Piloyan, G. R. Baimuratova, and V. V. Masalova
Institute of Structural Macrokinetics and Materials Research Problems, Russian Academy of Sciences,
Chernogolovka, Moscow oblast, 142432 Russia
e-mail: azatyan@ism.ac.ru
Received June 28, 2007
Abstract—In gas-phase combustion processes, the regeneration of free atoms and radicals in chain propagation
reactions enhances the diffusion flux of these species from the flame zone. In flame propagation in tubular reac-
tors and in filtration combustion, this effect facilitates the access of chain carriers to the surface even at atmo-
spheric pressure, increases the role of heterogeneous reactions (primarily chain termination), and enhances heat
removal due to heterogeneous recombination.
DOI: 10.1134/S0023158408020031
Since the discovery of chain reactions, it has gener- temperatures up to at least 1450 K. It was also demon-
ally been believed that the branched chain mechanism strated that self-heating is not a necessary condition for
and atom and radical multiplication and loss reactions chain ignition even at atmospheric pressure. Self-heat-
in gas-phase combustion become significant only at ing is significant only in developed chain combustion
pressures tens or hundreds times lower than atmo- and enhances the chain avalanche [10, 11].
spheric pressure, when there is no significant self-heat-
At appreciable rates of the recombination of chain
ing of the reaction mixture. Gas combustion at higher
carrier atoms and radicals on the reactor walls, this pro-
pressures has been considered to result from the
cess is not only a significant energy removal channel
increasing acceleration of self-heating alone (see, e.g.,
but, what is more important, a chain termination pro-
[1–4]). Even now, this view is dominant. Both critical
cess. Along with recombination, other chain carrier
reactions governing the combustion process take place
on the surface (see below). Obviously, the character of
the heterogeneous reactions of atoms and radicals, as
well as the chain nature of the overall process, deter-
mines the concentration kinetic equations and the
energy balance equation. The role of heterogeneous
reactions in combustion at atmospheric pressure is also
considered to be insignificant in numerical simulations
of gas combustion, even when various reactions of
atoms and radicals are taken into account. This is in part
due to the fact that, at atmospheric pressure, the rate of
chain termination on the reactor walls calculated in the
conventional way is much lower than the rate of the
gas-phase steps determining the combustion process. In
such calculations, the characteristic time of heteroge-
neous chain termination is taken to be equal to the aver-
age time required for a diffusing active species to travel
the average distance separating it from the reactor wall.
ignition conditions for gas mixtures (including hydro-
gen + oxygen) at atmospheric pressure and the laws of
developing combustion are thought to be only a conse-
quence of the competition between heat generation and
heat removal (see, e.g., [1–9]). In some studies using
numerical methods in the solution of sets of kinetic
equations, various reactions of atoms and radicals are
included in the reaction network. However, in the same
or later publications of the same authors, ignition and
combustion are considered to result from self-heating
alone when the gas pressure exceeds a few hundredths
of atmospheric pressure [7]. The burning gas phase is
usually in contact with a solid surface. Since gas-phase
combustion at pressures above several kilopascals is
represented as a single-step reaction, the analytical
expressions describing the system, such as the energy
balance equation, disregard the heterogeneous reac-
tions of atoms and radicals even in filtration combus-
tion [6–9], in which the ratio of the surface area to the
gas volume is fairly large.
By contrast, our analysis has demonstrated that,
owing to the periodic regeneration of chain carriers, the
At the same time, in a series of our works, including access of free valence to the surface (for example, at
10–14], it was demonstrated that a chain avalanche is atmospheric pressure) is easier through the relay-race
[
a necessary condition for the gas-phase combustion of transfer of free valence from one species to another
hydrogen-containing and many other compounds not than through diffusion. Accordingly, the role of hetero-
only at several hundredths or thousandths of atmo- geneous reactions in combustion is more significant
spheric pressure, but also at any higher pressure, and at than was believed earlier.
1
78

ACCELERATED DIFFUSION OF CHAIN CARRIERS
Vd
179
Furthermore, the relay-race diffusion of a free
valence plays an important role in so-called nonthermal
flame propagation [1, 15]. In this kind of combustion,
the active species diffusing into the fresh mixture react
with one another, giving rise to a chain avalanche even
outside the self-ignition region. The specific features of
relay-race diffusion in polymer oxidation and polymer-
ization processes are detailed in [16, 17].
~
2
This work is devoted to free valence diffusion to the
reactor walls in chain combustion and to the role of het-
erogeneous reactions in flame propagation in hydro-
gen–air mixtures at an initial pressure of 0.1 MPa. As
distinct from the processes considered in [15], hydro-
gen combustion involves no reactions between chain
carriers capable of initiating nonthermal flame propa-
gation. The mechanism and role of the diffusion of free
1
~
x
valence in ç oxidation differs radically from those of
2
relay-race diffusion in processes involving polymers.
Fig. 1. Diffusion velocity versus the distance traveled (x):
(
1) the diffusing species are not involved in the chain pro-
cess; (2) the diffusing species are chain carriers.
Free Valence Diffusion in Chain Combustion
According to Brownian motion theory, the time td
taken by a diffusing particle to travel the distance x is
given by the formula
where k is the effective rate constant of the rate-limit-
ing step of chain carrier regeneration and [B] is the con-
centration of the initial reactant involved in this step.
r
2
The chain multiplication of reactive species raises
x
4
t = ----- -- ,
(1) the free valence flux to the surface relative to the same
d
D
flux in the nonbranched chain process. The multiplier
standing before k , which accounts for the degree of
where D is the diffusion coefficient [18].
r
branching, lies between 1 and 2.
If we define the diffusion velocity (V ) as the aver-
d
Substituting t from Eq. (3) into Eq. (1) and replac-
age distance traveled by the diffusing particles per unit
time, we will obtain the following equation from
expression (1):
r
ing x with δ, we obtain the following expression for the
distance traveled by a diffusing chain carrier before its
regeneration:
dx
dt
2D
x
V = ----- = ----- -- .
(2)
d
D
k [B]
δ = 2 ------------.
(4)
r
It is clear from Eq. (2) that V decreases hyperboli-
d
cally as the distance increases (Fig. 1).
Replacing x with the chain carrier diffusion path
length δ in Eq. (2) and taking into account Eq. (4), we
arrive at the following equation for the relay-race diffu-
sion velocity:
Once the diffusing chain carriers in a chain process
have traveled some distance δ, they react to be replaced
by the same reactive species; that is, they are regener-
ated. Due to the fact that the chain carriers are highly
reactive and, accordingly, can travel only a short dis-
tance (δ) before the regeneration event, their diffusion
velocity has time to decrease only slightly. The diffu-
sion velocity of the identical chain carrier resulting
from this reaction will decrease by an equally small
value before this chain carrier reacts (see the sawtooth
curve in Fig. 1). Thus, the free valence transferred by
the relay-race mechanism from one chain carrier to
another diffuses at the average velocity defined by the
distance δ. In turn, this distance is determined by the
characteristic time of the chain carrier regeneration
reaction, which is given by
V = Dk [B].
(5)
δ
r
The subscript δ in V indicates that this quantity is
δ
actually the velocity of diffusion through the distance δ.
It is clear from Eq. (5) that, up to the constancy of [B]
in the flame front moving toward the wall, V can be
δ
considered to be approximately constant at a fixed tem-
perature. In view of Eq. (5), the time taken by the chain
carriers diffusing by the relay-race mechanism to travel
the average distance equal to the distance between the
reactor center and the wall can be represented as
relay
r
tr
= ----------------------- -- ,
Dk [B]
(6)
2
r
1
t = ------------,
(3)
g
k [B]
r
where r is the reactor radius.
KINETICS AND CATALYSIS Vol. 49 No. 2 2008

1
80
AZATYAN et al.
Obviously, since the rate of the heterogeneous reac- the third reactant M is the species removing the recom-
tion is limited by the diffusion velocity, this reaction is bination energy.
actually first-order. Therefore, considering the rate-lim-
iting role of relay-race diffusion, we can represent the
rate of the heterogeneous reaction as the reciprocal of
the characteristic time of this process:
•
2
As the HO radicals move to the surface, part of
them participate in the reaction
•
HO + ç = ç é + ç
(III)
2
2
2
2
2
Dk [B]
r
relay
kr
= ----------------------- -- .
(7)
and are then regenerated via reaction (II). Reaction (III)
r
is rate-limiting because of its comparatively high acti-
•
2
As distinct from expression (7), the expression for vation energy (~110 kJ/mol). Therefore, when the HO
the rate constant of the heterogeneous decay of chain radical is considered as the diffusing species, the com-
carriers in diffusion-controlled chain termination in the ponent B in the above expressions should be the hydro-
absence of relay-race diffusion appears as follows for a gen molecule.
cylindrical reactor of diameter d [1]:
Under the conditions examined, the rate of hydro-
gen atom adsorption,
2
k = 23.2D/d .
(8)
r
ç
(ç)s
(IV)
It is clear from expressions (7) and (8) that, unlike
relay
is much lower than the rates of the competing chain
branching and termination reactions taken separately,
but it is comparable with the difference between the
rates of these reactions, particularly near the critical
conditions. Since the kinetics of the chain process is
mainly determined by this difference, reaction (IV) can
kr, kr
is proportional to the square root of Dk [B].
r
Since the diffusion coefficient is inversely proportional
to the gas mixture concentration and appears as the
product D[B] in expression (5), the relay-race diffusion
velocity is pressure-independent. It is clear from
relay
expression (7) that, for the same reason, kr
pressure-independent.
is also exert a significant effect on the overall combustion pro-
cess.
relay
Note that expression (5) is similar to the formula
obtained by Zel’dovich et al. [19, p. 244] by solving a
differential equation of the heat conductivity type
under certain assumptions as to the spatial distribution
of reactive species. However, as distinct from expres-
sion (5), the formula reported by Zel’dovich et al. [19]
Let us compare the k4 and k values for the com-
4
bustion of 7% ç in air at 850 K and an initial pressure
2
of 0.1 MPa in a cylindrical reactor 12.6 cm in diameter.
The experimental data obtained under these conditions
are reported below. The diffusion coefficient of H
atoms in this mixture at 293 K and 0.1 MPa is approxi-
mately equal to 1 cm /s [20, 21]. Since the diffusion
coefficient of H atoms in a constant volume is propor-
tional to T [21], D = 5.5 cm /s at 850 K. The initial é
concentration under the above conditions is 2.65 ×
0 mol/cm . The rate-limiting step of the regeneration
of hydrogen atoms is reaction (I), whose rate constant
contains a first-order rate constant in place of k [B].
r
2
Accordingly, the diffusion velocity in this formula is
inversely proportional to P , unlike the diffusion
velocity in expression (5).
1.6
2
2
relay
−6
3
1
Note that, unlike kr , k defined by formula (8) is
r
proportional to D and is, accordingly, inversely propor-
tional to pressure. As a consequence, in the narrow
relay
14
3
–1 –1
is 1.9 × 10 Âı(–8350/T) cm mol s [22] (here, the
activation energy units are kelvins). Hence, for T =
pressure range below 1–1.5 kPa, k > k
. Accord-
9
3
–1 –1
r
r
850 K, k = 9.3 × 10 cm mol s . Substituting the
1
ingly, for reactors 4–7 cm in diameter, the k values cal-
r
above values of D, r, k , and é concentration into
r
2
culated using formula (8) are in agreement with the
observed values of the first ignition limit, for example,
for ç + é mixtures in the diffusion-controlled region
relay
–
1
expression (7), we obtain k4 = 120 s . At the same
time, the k value calculated using expression (8) is
4
2
2
relay
4
of chain termination.
–1
0
.8 s , which is smaller than k
by a factor of 150.
In the combustion of ç + é mixtures at atmo-
relay
2
2
This large excess of k4 over k is due to the compar-
4
spheric pressure, the chain branching reaction
atively large value of the rate constant of reaction (I).
•
ç + é = éç + é
(I)
2
The smaller the extent of regeneration of chain car-
is in competition with the trimolecular formation of the
relay
riers, the smaller the difference between kr
and kr.
•
HO radical,
2
relay
r
By way of example, compare the k
and k values for
r
•
2
ç + é + å = HO + å,
(II)
•
2
HO adsorption,
2
which is unreactive in this system and mainly under-
goes recombination on the surface [3]. In reaction (II),
•
2
HO
(çé )
(V)
2 s
KINETICS AND CATALYSIS Vol. 49 No. 2 2008

ACCELERATED DIFFUSION OF CHAIN CARRIERS
181
for the combustion of 7% ç in air under the above con-
2
•
ditions. The HO diffusion coefficient in this mixture
2
at 293 K and 0.1 MPa is only slightly smaller than the
‡
2
é diffusion coefficient and is close to 0.25 cm /s [20,
2
•
2
2
1]. Since the HO diffusion coefficient at a constant
volume is proportional to T1.7 [21], DHO2 = 1.5 cm /s at
2
l
•
8
50 K. The rate-limiting step of HO regeneration is
2
reaction (III) because of its comparatively high activa-
tion energy. The rate constant of this reaction is 3 ×
1
3
3
–1 –1
1
0 Âı(–13100/T) cm mol s [22] (here, the activa-
tion energy is in kelvins). Hence, for T = 850 K, k =
.4 × 10 cm mol s . The initial ç concentration under
these conditions is 1.0 × 10 mol/cm . In the mixture
examined, which contains 7% ç , only part of the reac-
3
6
3
–1 –1
5
2
–6
3
b
2
tion (I) events actually cause chain branching. This is
due to the fact that, because of the small ç content,
2
•
part of the O atoms and éç radicals resulting from
reaction (I) have insufficient time to enter into the chain
propagation reactions
•
é + ç = éç + ç,
(VI)
2
•
éç + ç = ç é + ç
(VII)
2
2
and terminate the chain via the reaction opposite to
reaction (I),
Fig. 2. Schematic representation of (a) the combustion front
and (b) the cylindrical layer from which chain carriers have
time to reach the reactor surface.
•
é + éç = é + ç,
(–I)
2
and via adsorption on the walls. This is why the above
relay
coefficient accounting for the chain termination frac- fusing with the velocity Vδ = 380 cm/s will travel a
tion is between 1 and 2. In this calculation we take this
distance of ∆r ≈ 0.75 cm. Therefore, the H atoms sepa-
rated by a distance of ≤0.75 cm from the wall of the
cylindrical reactor will transfer their free valence to the
coefficient to be 1.5. Substituting the above values of D,
r, k , and ç concentration into expression (7) and
1
2
replacing the subscript “g” at the constants with the wall within the flame traveltime. In a reactor 12.6 cm in
relay
–
1
diameter, the volume of the cylindrical layer corre-
sponding to this distance is >20% of the reactor vol-
ume. Without relay-race diffusion, only the H atoms
subscript “5,” we obtain k5 ≈ 1.3 s . The rate con-
stant k calculated using expression (8) for d = 12.6 cm
5
relay
5
–
1
is 0.2 s , which is smaller than k
by a factor of 6.5. separated by 0.01 cm or a shorter distance from the wall
would reach the wall within the same period of time.
Chain Carrier Flux to the Surface
over the Flame Traveltime
The volume of the corresponding cylindrical layer is
below 0.5% of the reactor volume. Thus, without relay-
Obviously, the effect of the heterogeneous reactions race diffusion, the heterogeneous reactions cannot play
on combustion will be possible if the chain carriers any significant role in combustion.
have sufficient time to reach the surface area with
Similar calculations have demonstrated that, in the
which the traveling flame front is currently in contact.
mixture containing 7% ç , the flux of O atoms and
2
For this reason, let us determine the longest distance
from which the free valences propagating via reactions
of alternating hydrogen atoms can reach the walls of a
cylindrical reactor within the time taken by a laminar
flame front to travel the distance l equal to the thickness
of the combustion zone (Fig. 2). Substituting the values
of D, k , and é concentration into Eq. (5), we obtain
•
éç radicals to the surface is not lower than the flux of
H atoms.
For a reactor 5 cm in diameter (usual size), the vol-
ume of the cylindrical layer corresponding to the relay-
race diffusion distance ∆r ≈ 0.75 cm is above 50% of
the reactor volume and the effect of the surface proper-
ties is even stronger.
1
2
relay
Vδ
= 380 cm/s. The flame velocity in the mixture
Role of Heterogeneous Reactions in Combustion
at Atmospheric Pressure
examined is approximately equal to 50 cm/s [3], and
the combustion front thickness is l ≈ 0.1 cm. Hence, the
time taken by the flame to travel the distance l is 2 ×
The rate of the hydrogen combustion reaction (w)
−3
1
0 s. Within this period of time, the free valences dif- under self-heating conditions is described by the fol-
KINETICS AND CATALYSIS Vol. 49 No. 2 2008

1
82
AZATYAN et al.
lowing equation, which takes into account the homoge- pressure and luminescence. The signal from the piezo-
neous and heterogeneous chain termination reactions electric pressure gauge was amplified and was then
[
10, 12]:
recorded with an S9-8 dual-beam memory oscillo-
scope. The discretization time was 2 µs. Flame chemi-
luminescence between 300 and 600 nm was recorded
on an oscilloscope using an FEU-39 photomultiplier.
After each run, the reactor was pumped down to ~3 Pa.
This experimental procedure is detailed in an earlier
publication [23].
t
w/[O ] = k n exp {2k°[O ]β exp(–E /RT)
2
1
0
1
2
1
∫
(9)
t
0
relay
–
k [O ][M]η – k }dt,
2 2 4
where k° is the preexponential factor of the rate con-
Since the number of moles of the gas mixture
1
decreases steadily during H oxidation, the increase of
2
stant of reaction (1), E is the activation energy of this
1
pressure (∆P) observed during combustion is due only
to the increasing temperature. Obviously, the gas tem-
perature in the moving flame, which is the place where
heat is generated, is higher than the temperature of the
unburnt gas. Therefore, ∆P characterizes the tempera-
ture rise averaged over the reactor volume (and the
average temperature as well). This temperature rise is
determined by the ratio between the rate of heat gener-
ation due to combustion and the rate of heat removal
from the reactor. Thus, ∆P characterizes the rate of heat
generation and, accordingly, the rate of the combustion
•
reaction, β is the fraction of O atoms and éç radicals
participating in the chain propagation reactions (V) and
(
VI), k is the effective rate constant of reaction (II), t
2
0
is the point in time after which the role of the reaction
between the initial reactants is insignificant, n is the
0
chain carrier concentration at the point in time t (which
0
relay
is actually the combustion onset time), k4 is the rate
constant of heterogeneous chain termination, η is the
•
fraction of HO radicals that have not entered reaction
2
(
III) and will lead to chain termination, and T is temper- reaction. This is why the gas mixture pressure and the
ature.
chemiluminescence intensity increase synchronously
at an increasing rate (the initial portions of the kinetic
curves are concave upward) and reach their maxima
almost simultaneously.
It is clear from relationship (9) that the role of heter-
ogeneous chain termination in combustion is deter-
relay
mined by the balance between k4 and the difference
In order to elucidate the role of the heterogeneous
reactions, we varied the chemical properties of the sur-
face. For this purpose, the reactor surface in some
experiments was coated with a thin film of boric acid:
the reactor was rinsed with a boric acid solution and
then dried. To make sure that the data obtained are
reproducible, measurements for the boric acid–coated
surface were alternated with measurements for the
untreated surface in the same reactor. To remove the
boric acid coating, the reactor was rinsed with a sodium
carbonate solution and water and was then dried.
between the first two terms of the integrand:
2
k° [O ]βexp(–E /RT) – k [O ][M]η.
1
2 1 2 2
This difference is usually much smaller than either
term. Therefore, a change in the chemical properties of
relay
the surface that has an effect on k4
can cause an
appreciable change in the integrand and, accordingly, in
the overall process rate, particularly near the concentra-
tion limits of ignition, where the chain branching and
termination rates are similar.
Below, we will present an experimental verification
of the inference that the heterogeneous reactions of
chain carriers play a significant role in combustion at
atmospheric pressure.
Combustion of hydrogen-lean mixtures. The
lower hydrogen concentration limit for the propagation
of flame in hydrogen–air mixtures is known to be 5%.
The intensity of the combustion of 7 or 8% ç + air is
2
always much lower in the reactor treated with boric
acid than in the untreated reactor (Figs. 3, 4). Indeed,
the slope of the kinetic curve, which is a measure of the
rate of the combustion reaction, is always much smaller
in the boric acid–treated reactor. Furthermore, combus-
tion over boric acid stops earlier: the pressure peaks are
lower, and the areas under the kinetic curves are
smaller. The boric acid coating on the surface exerts a
similar effect on the luminescence curves.
EXPERIMENTAL PROCEDURE,
MEASUREMENTS, AND DISCUSSION
Reactions were carried out in an airtight, cylindri-
cal, stainless-steel reactor 12.6 cm in diameter and
5.2 cm in height. The components were mixed in the
reactor using a partial pressure–based method with a
relative accuracy of 1%. Before gas admission, the
reactor was pumped to 2 Pa. The initial mixture pres-
2
Furthermore, the treatment of the surface with boric
sure and temperature were 0.1 MPa and 293 K, respec- acid has an effect on the critical ignition and flame
tively. The mixture was ignited with a 3.6-J spark at the propagation conditions. In the reactor whose surface is
lower end of the reactor after the time necessary for the coated with boric acid, as distinct from the untreated
perfect mixing of the components (20 min). From the reactor, it is impossible to ignite a 6% ç + air mixture
2
ignition point until the completion of combustion, we at a spark energy of 3.6 J. Since the heat removal rate is
performed simultaneous rapid recording of the gas independent of the chemical properties of the reactor
KINETICS AND CATALYSIS Vol. 49 No. 2 2008

ACCELERATED DIFFUSION OF CHAIN CARRIERS
183
P, atm
.8
P, atm
2.5
1
1
1
1
1
1
.6
.4
.2
.0
4
1
2
2
1
.0
.5
3
7
4
6
5
3
8
5
2
6
1.0
0
500
1000
1500
t, ms
0
500
1000
1500
t, ms
Fig. 3. Combustion kinetics as pressure variation for a 7%
ç + air mixture: (1, 3, 4, 7) untreated reactor surface; (2, 5,
Fig. 4. Combustion kinetics as pressure variation for a 8%
ç + air mixture: (1, 2, 6) untreated reactor surface; (3–5)
2
2
6
, 8) reactor surface coated with boric acid. The curve num-
reactor surface coated with boric acid. The curve numbering
shows the order of runs.
bering shows the order of runs.
surface, it is quite obvious that the observed inhibition of near-stoichiometric mixtures. Furthermore, since the
of the combustion reaction by boric acid is due to the propagation rate of hydrocarbon–air flames normally
increased rate of the heterogeneous termination of reac- does not exceed the propagation rate of the 7% ç + air
2
tion chains. The results of these experiments, which flame [3], it is expected that the combustion of these
demonstrate that the ignition conditions at atmospheric organic compounds will also be dependent on the
pressure are primarily determined by the competition chemical properties of the surface because of the effect
between chain branching and termination rather than of the heterogeneous reactions of reactive species.
by the increasing self-heating, are in good agreement
Combustion of hydrogen-rich mixtures. Now let
with our earlier data [10–14]. The above data are also in
us consider the combustion of mixtures containing
good agreement with our data demonstrating the chain
overstoichiometric amounts of hydrogen. In this con-
character of hydrogen ignition in air at atmospheric
centration region, as distinct from the vicinity of the
pressure and illustrating the time lag between lumines-
lower concentration limit, the main chain carrier react-
cence rise curves and temperature rise curves during
ing on the surface is the H atom because nearly all of
combustion [11, 23].
•
the O atoms and éç radicals are involved in reactions
The conventional views of flame propagation, which (VI) and (VII). Since the heterogeneous reactions of H
disregard the chain character of this process, cannot atoms differ from the heterogeneous reactions of O,
•
2
explain the above observations.
•
éç , and HO , it was expected that boric acid would
The weakening of the effect of the boric acid coating
exert a different effect on the combustion of hydrogen-
rich mixtures. However, the data presented in Fig. 5
observed upon passing to the 8% ç + air mixture is due
2
to the following. As the ç concentration in the initial indicate that the boric acid coating on the reactor walls
2
•
mixture is raised, the fraction of O atoms and éç radi- does not exert any significant effect. This can be
cals participating in reactions (V) and (VI) increases explained by the fact that the mixture composition is far
(
i.e., β grows), resulting in a decrease in the contribution from the upper hydrogen concentration limit (75%). As
relay
relay
from kg
to the exponent in relationship (9). This is a consequence, k4 is so much smaller than the differ-
manifested as more intensive combustion. As a conse- ence between the first two terms of the integrand in
quence, the time taken by the flame to travel the distance relationship (9) that the contribution from the heteroge-
considered above (thickness of l = 0.1 cm) is shorter. neous reactions is smaller than in the case of the
Accordingly, the volume of the cylindrical layer from 7% ç + air mixture.
2
which H atoms reach the surface is smaller. As a conse-
The effect of the boric acid coating on the character-
quence, the difference between the combustion rates in
istics of combustion is unambiguous evidence that,
the untreated and boric acid–treated reactors is much
contrary to prevalent views, ignition and combustion at
smaller.
atmospheric pressure are caused by a chain avalanche
It follows from the above that, for reactors smaller and the reactions of atoms and radicals on the reactor
in diameter, the role of the heterogeneous reactions of walls play an important role in combustion. The signif-
chain carriers will also be significant in the combustion icant effect of the heterogeneous reactions on combus-
KINETICS AND CATALYSIS Vol. 49 No. 2 2008

1
84
P, atm
AZATYAN et al.
γv 2 Dk
[O ]
2
1
5
4
3
2
1
-
--- -- ≤ -------------------------- -- ,
(11)
d
r
1
relay
5
where the right-hand side is equal to k4 given by for-
mula (7).
3
4
2
Substituting the above parameters into relation-
relay
–3
ship (11) yields γ
≤ 6 × 10 . This value is more
than two orders of magnitude larger than the γ value
obtained without taking into account relay-race dif-
fusion. Note, however, that this value still seems to
be too small for the recombination of H atoms on
stainless steel. Some heterogeneous reactions of
atoms and radicals involve gaseous molecular reac-
tants and release new chain carriers into the gas
phase, implying heterogeneous chain propagation
0
25
50
t, ms
[
26–28]. In this case, in spite of the rate-limiting role
of diffusion in the access of H atoms to the surface,
the rate of heterogeneous chain termination depends
on the chemical properties of the surface [28].
Hydrogen atoms are also involved in the chemical
modification of the surface, which is due to the dis-
placement of metal atoms from solid salts into the
gas phase [29]. These reactions along with heteroge-
neous recombination are significant factors in com-
Fig. 5. Combustion kinetics as pressure variation for a 60%
ç + air mixture: (2, 4) untreated reactor surface; (1, 3, 5)
2
reactor surface coated with boric acid. The curve numbering
shows the order of runs.
tion under these conditions is due to the relay-race dif-
fusion of reactive intermediates.
Character of the heterogeneous reactions capa- bustion.
ble of affecting combustion. The observed depen-
Thus, because of the relay-race character of the dif-
dence of the characteristics of combustion at atmo-
spheric pressure on the chemical properties of the reac-
tor surface indicates that the rate of the heterogeneous
reactions is determined to a considerable extent by the
coefficient (probability) of adsorption of the intermedi-
ate species colliding against the surface. For this to be
the case, it is necessary that the rate constant of the cap-
ture of the intermediate by the surface be smaller than
the rate constant at which diffusion to the surface is the
rate-limiting process [1]. Without relay-race diffusion,
this condition is expressed as
fusion of chain carriers in the combustion of gases in
contact with a solid surface at atmospheric pressure, the
intensity and energetic parameters of this process, as
well as the concentration limits of flame propagation,
are determined to a large extent by the heterogeneous
reactions of the chain carriers. Obviously, the role of
the heterogeneous reactions is particularly significant
in filtration combustion, in which the gas–surface con-
tact area is very large.
ACKNOWLEDGMENTS
γv/d ≤ 23.2D/d2,
(10)
The authors are grateful to V.B. Kazanskii for help-
where v is the thermal velocity of the reactive species, ful discussions.
γ is the coefficient of capture of the species by the sur-
This study was supported by the Presidium of the
Russian Academy of Sciences (program no. 7P), the
Russian Foundation for Basic Research (project no. 05-
3-33050), INTAS (grant 05-1000005-7664), and
CRDF (grant RHT1-2686-MO-05).
face, and d is the diameter of the cylindrical reactor.
The right-hand side of Eq. (10) is equal to k , the rate
4
constant of diffusion-limited heterogeneous chain ter-
mination, which is given by formula (8) [1]. This for-
mula does not take into account relay-race diffusion.
0
Substituting the above values of the variables into
–
5
REFERENCES
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we examine a stainless steel reactor, this value is an
obvious underestimation, especially because the reac-
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of the smallness of the calculated γ value is that, as was
noted above, the right-hand side of Eq. (10) disregards
relay-race diffusion and is, therefore, an underestima-
tion. If relay-race diffusion is taken into account, the
condition for combustion depending on the properties
of the surface will be expressed as
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