Ozone decay in chemical reactor with the developed inner surface
The ozone decay was investigated in a chemical reactor with a developed inner surface on which it dissociates or absorbs. Ozone concentration behaves differently with time depending on where mainly decays ozone - in the volume or on the reactor surfaces. If ozone mainly decays on the reactor surface...
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irk-123456789-1221572017-06-29T03:02:53Z Ozone decay in chemical reactor with the developed inner surface Manuilenko, О.V. Golota, V.I. Низкотемпературная плазма и плазменные технологии The ozone decay was investigated in a chemical reactor with a developed inner surface on which it dissociates or absorbs. Ozone concentration behaves differently with time depending on where mainly decays ozone - in the volume or on the reactor surfaces. If ozone mainly decays on the reactor surface, the ozone concentration decreases with time as exp(-δt) , where δ is determined by the decay process at the inner surface of the reactor and its total area. If ozone decay occurs primarily in the volume, the ozone concentration decreases with time as 1/(1+σt), where σ is determined by the common process of ozone decay in the volume. Исследована кинетика распада озона в реакторе с развитой внутренней поверхностью, на которой может происходить его распад. В зависимости от того, какой из процессов распада является основным – распад в объёме, или распад на поверхности - концентрация озона ведёт себя по-разному со временем. Если распад озона происходит, в основном, на поверхности, то его концентрация уменьшается со временем пропорционально exp(-δt), где δ определяется процессом распада на внутренней поверхности реактора и её полной площадью. Если же распад озона происходит, в основном, в объёме, то его концентрация уменьшается со временем пропорционально 1/(1+σt), где σ определяется обычным процессом распада озона в объёме. Досліджено кінетику розпаду озону в реакторі з розвиненою внутрішньою поверхнею, на якій може відбуватися його розпад. Залежно від того, який із процесів розпаду є основним розпад в об'ємі або розпад на поверхні концентрація озону поводиться по-різному з часом. Якщо розпад озону відбувається, в основному, на поверхні, то його концентрація зменшується з часом пропорційно exp(-δt), де δ визначається процесом розпаду на внутрішній поверхні реактора та її повною площею. Якщо ж розпад озону відбувається, в основному, в об'ємі, то його концентрація зменшується з часом пропорційно 1/(1+σt), де σ визначається звичайним процесом розпаду озону в об'ємі. 2017 Article Ozone decay in chemical reactor with the developed inner surface / О.V. Manuilenko, V.I. Golota // Вопросы атомной науки и техники. — 2017. — № 1. — С. 148-151. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 52.75.-d, 52.77.Fv, 52.80.Hc, 52.90.+z, 81.20.-n http://dspace.nbuv.gov.ua/handle/123456789/122157 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии |
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Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии Manuilenko, О.V. Golota, V.I. Ozone decay in chemical reactor with the developed inner surface Вопросы атомной науки и техники |
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The ozone decay was investigated in a chemical reactor with a developed inner surface on which it dissociates or absorbs. Ozone concentration behaves differently with time depending on where mainly decays ozone - in the volume or on the reactor surfaces. If ozone mainly decays on the reactor surface, the ozone concentration decreases with time as exp(-δt) , where δ is determined by the decay process at the inner surface of the reactor and its total area. If ozone decay occurs primarily in the volume, the ozone concentration decreases with time as 1/(1+σt), where σ is determined by the common process of ozone decay in the volume. |
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Article |
| author |
Manuilenko, О.V. Golota, V.I. |
| author_facet |
Manuilenko, О.V. Golota, V.I. |
| author_sort |
Manuilenko, О.V. |
| title |
Ozone decay in chemical reactor with the developed inner surface |
| title_short |
Ozone decay in chemical reactor with the developed inner surface |
| title_full |
Ozone decay in chemical reactor with the developed inner surface |
| title_fullStr |
Ozone decay in chemical reactor with the developed inner surface |
| title_full_unstemmed |
Ozone decay in chemical reactor with the developed inner surface |
| title_sort |
ozone decay in chemical reactor with the developed inner surface |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2017 |
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Низкотемпературная плазма и плазменные технологии |
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http://dspace.nbuv.gov.ua/handle/123456789/122157 |
| citation_txt |
Ozone decay in chemical reactor with the developed inner surface / О.V. Manuilenko, V.I. Golota // Вопросы атомной науки и техники. — 2017. — № 1. — С. 148-151. — Бібліогр.: 11 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT manuilenkoov ozonedecayinchemicalreactorwiththedevelopedinnersurface AT golotavi ozonedecayinchemicalreactorwiththedevelopedinnersurface |
| first_indexed |
2025-07-08T21:15:50Z |
| last_indexed |
2025-07-08T21:15:50Z |
| _version_ |
1837114960068476928 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2017. №1(107)
148 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2017, № 1. Series: Plasma Physics (23), p. 148-151.
OZONE DECAY IN CHEMICAL REACTOR WITH THE DEVELOPED
INNER SURFACE
О.V. Manuilenko, V.I. Golota
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: ovm@kipt.kharkov.ua
The ozone decay was investigated in a chemical reactor with a developed inner surface on which it dissociates or
absorbs. Ozone concentration behaves differently with time depending on where mainly decays ozone - in the
volume or on the reactor surfaces. If ozone mainly decays on the reactor surface, the ozone concentration decreases
with time as )exp( t , where is determined by the decay process at the inner surface of the reactor and its total
area. If ozone decay occurs primarily in the volume, the ozone concentration decreases with time as )1/(1 t ,
where is determined by the common process of ozone decay in the volume.
PACS: 52.75.-d, 52.77.Fv, 52.80.Hc, 52.90.+z, 81.20.-n
INTRODUCTION
Ozone is an environmentally friendly oxidant [1]. It
can be used in a wide range of plasma-chemical
technologies in various fields of human activity, such as
medicine and veterinary medicine [2], agriculture [3],
food production and storage, waste recycling [4-6] and
other. This paper is devoted to the usage of ozone in
food storage.
The development of ozone technologies includes
solution of the three major problems: the problem of
energy efficient ozone production, the problem of ozone
delivery, with minimal loss, to the interaction point, and
the problem of the chemical interaction of ozone with
the substance to be treated. The first problem was
solved with the help of barrier-free ozonizer [7] based
on the streamer discharge [8-11]. The paper is devoted
to the solution of the second problem.
The ozone decay in the refrigerated container for the
transportation of perishable products is investigated.
The loaded container can be considered as a chemical
reactor with a developed inner surface on which the
ozone dissociates or absorbs. Ozone is synthesized in
the barrier-free streamer discharge ozonizer with the
high-speed air-flow. Only a given part of the circulating
cooling air flow is passed through the ozonizer. After
switching ozonizer off, the ozone concentration in
reactor decreases with time as a result of the ozone
decay in the volume and on the inner surfaces of
reactor. It was found that ozone concentration behaves
differently with time depending on where mainly decays
ozone - in the volume or on the reactor surfaces. If
ozone mainly decays on the reactor surface, the ozone
concentration decreases with time proportional to
)exp( t , where is determined by the decay process
at the inner surface of the reactor and its total area. If
ozone decay occurs primarily in the volume, the ozone
concentration decreases with time as )1/(1 t , where
is determined by the common process of ozone
decay in the volume. The analytical expressions for
ozone concentration in the reactor have been obtained as
function of time and parameters, such as the initial
ozone concentration, the reaction rate constants,
temperature, humidity, the reactor volume and its inner
surface. It is shown that the analytical results are in
good agreement with the experimental data.
THEORY, EXPERIMENT AND DISCUSSION
Most of the known data on the ozone decomposition
can be explained in terms of the simple atomic
mechanism [1]:
OOO
f
k
rk
23
,
23
2OOO
O
f
k
. (1)
In the equations (1) = {N2, O2, H2O, O3, CO2, He,
Ar, N2O}. )(Tk
f
is the rate constant of the forward
reaction. It depends on the temperature T like the rest
of the reaction rate constants. )(Tk
r
is the reverse
reaction rate constant, )(Tk O
f
is a forward reaction rate
constant. The forward reaction in first equation of (1)
shows unimolecular ozone decay. This reaction is not
elementary. It consists of a multi-stage process which
includes activation and decay of the excited molecule
through the activated complex. The reverse reaction is
also not elementary. It flows in two biomolecular
stages: formation of excited ozone with subsequent
relaxation. The second reaction in (1) is exothermic.
The excess energy is distributed over the vibrational
degrees of freedom of the oxygen molecule. As a rule,
vibrationally excited oxygen relaxes to the ground state.
The system of kinetic equations describing the ozone
decay mechanism (1), if = {N2, O2, H2O, O3},
generally is the following:
OO
O
frOOfO
O
CCkCkCCCkC
dt
dC
323
3
, (2)
OO
O
frOOfO
O
CCkCkCCCkC
dt
dC
323
2 2
, (3)
OO
O
frOOfO
O CCkCkCCCkC
dt
dC
323
, (4)
where )(tC
is a concentration of . For = {N2,
H2O}, the density of particles )(tC
may depend on time
only through the initial conditions. Therefore,
2N
C =
const, OH
C
2
= const. The following equation can be
obtained using the method of steady-state concentrations
for O:
ISSN 1562-6016. ВАНТ. 2017. №1(107) 149
)()()(
)()(
)(
32
3
tCktCktC
tCktC
tC
O
O
frO
fO
O
. (5)
It is convenient to introduce the following notations:
)()(),( tCTkTtF
f
,
)()(),( tCTkTtG
r
. (6)
The equations (2), (3) may be presented in a simple
form:
2
3
32
3 2
O
O
O
fO
O
fO
C
CkGC
Fk
dt
dC
, (7)
2
3
32
2 3
O
O
O
fO
O
fO
C
CkGC
Fk
dt
dC
. (8)
The numerical estimations of F and G , using the rate
constants of the corresponding reactions from [1], for the
ozone-air mixture at the atmospheric pressure and the
temperature T ~ 300 К, for the mass ozone
concentration
3O
MC < 20 g/m
3
and water concentration
OH
MC
2
< 25 g/m
3
, show that the main input to F will be
achieved due to ozone decay at the collision with
nitrogen. Ozone collision with oxygen and water gives
the input to F by several times lower. Ozone collision
with ozone gives the input by two orders lower than the
ozone decay on nitrogen. This allows highly accurate
calculation of F in accordance with the initial densities
of nitrogen, water and oxygen – F
2
2 )(
N
N
f
CTk +
OH
OH
f
CTk
2
2 )( +
2
2 )(
O
O
f
CTk . A similar analysis can be
carried out for G . As a result, G with high accuracy, as
well as F , does not depend on time and is defined by
the initial bulk densities of nitrogen, water and oxygen –
G
2
2 )(
N
N
r
CTk +
OH
OH
r
CTk
2
2 )( +
2
2 )(
O
O
r
CTk .
The equations (7) and (8) show that in general case
the ozone decay is described by the variable order
kinetics, from the 1-st to the 2-nd order depending on
the parameters of the problem. If
23 OO
O
f
GCCk , ozone
decay is described by the first order kinetics:
O
fO
O
fO
kFCkdtdC /2/
33
. In the opposite case, if
23 OO
O
f
GCCk , ozone decay is described by the second
order kinetics:
233
/2/ 2
OO
O
fO
GCFCkdtdC .
By comparing
3
)(
O
O
f
CTk and
2O
CG , for the
parameters of ozone-air mixture presented above, it can
be found that
2O
CG is higher that
3
)(
O
O
f
CTk by more
than two orders, i.e.
3
)(
O
O
f
CTk can be neglected in the
equations (7), (8):
2
3
2
3 2
O
O
O
fO
C
GC
Fk
dt
dC
, 2
3
2
2 3
O
O
O
fO
C
GC
Fk
dt
dC
, (9)
i.e. ozone decay is defined by the second order kinetics.
By defining
2
/
O
O
f
GCFkk , the equations (9) can be
easily integrated:
tkC
C
C
O
O
O *
3
*
3
3 21
,
tkC
tCk
CC
O
O
OO *
3
2*
3*
22 21
3
, (10)
where *
33
)0(
OO
CtC , *
22
)0(
OO
CtC are the initial
conditions. At t 0)(
3
tC
O
, *
22
)(
OO
CtC
*
3
5.1
O
C . If the set of experimental points for )(
3 kO
tC is
built in the coordinates {
k
t , 1/ )(
3 kO
tC }, a straight line
with the tangent ratio equal to k2 can be obtained:
1/ )(
3
tC
O
= 1/ *
3O
C + kt2 . (11)
It can be shown that the system of equations (9)
corresponds to the following ozone decay scheme:
23
32 OO
k
, where the effective «reaction rate constant»
k is obviously dependant on the initial densities of
nitrogen, water and oxygen as well as on the reaction
rate constants which are included in the scheme (1).
The ozone decay on the surface can be included in
the equations (7), (8). To do this, the continuity
equations should be integrated over the volume:
2
3
32
3
3 2)(
O
O
O
fO
O
f
O
O
C
CkGC
Fk
div
t
C
, (12)
2
3
32
2
2 3)(
O
O
O
fO
O
f
O
O
C
CkGC
Fk
div
t
C
, (13)
where
3O
,
2O
are the ozone and oxygen fluxes. As a
result, the following equations can be obtained:
VC
CkGC
Fk
Sd
dt
dN
O
O
O
fO
O
f
S
O
O 2
3
32
3
3 2
, (14)
VC
CkGC
Fk
Sd
dt
dN
O
O
O
fO
O
f
S
O
O 2
3
32
2
2 3
. (15)
Here, V is a vessel volume where ozone decay takes
place, S is a surface limiting the volume V ,
3O
N ,
2O
N
are the number of particles in volume V . The fluxes of
particles to the surface S can be estimated in the
following way:
3333
)(
OOTO
Cvv
O
,
2222
)(
OOTO
Cvv
O
, (16)
where
3OT
v
,
2OT
v
are the thermal particle velocities,
3O
v
,
2O
v
are the convective velocities. After the
integration over the container surface the following
expression can be obtained for a number of particles
reaching the container surface:
SCvN
OOO 333
, SCvN
OOO 222
, (17)
where
3O
v ,
2O
v are particle velocities, is a coefficient
considering the problem geometry. By introducing the
probability of the particle decay on the surface
3O
,
2O
,
the equations (14), (15) can be presented in the
following way:
333
2
3
32
3 2
OOOO
O
O
fO
O
fO
C
V
S
vC
CkGC
Fk
dt
dC
, (18)
222
2
3
32
2 3
OOOO
O
O
fO
O
fO
C
V
S
vC
CkGC
Fk
dt
dC
. (19)
Further, only the equation (18) will be considered. In
accordance with the calculations for the ozone-air
mixture at the atmospheric pressure and the initial mass
concentrations of ozone
3O
MC 20 g/m
3
,
32
/
O
O
fO
O
f
CkGCFkK does not depend on time and is
defined by the initial concentration of reagents. This
150 ISSN 1562-6016. ВАНТ. 2017. №1(107)
allows integration of the equation (18) using substitution
))(2exp()(
3 dttCKtu
O
:
0
2
2
dt
du
V
S
dt
ud
, (20)
where
33 OO
v . The solution of (20) can be
presented in the following way:
)/exp()(
21
VStCCtu . After simple
transformations for )(
3
tC
O
, the following expression
may be obtained:
)exp(
)exp(
2
1
)(
21
2
3
t
V
S
CC
t
V
S
V
S
C
K
tC
O
. (21)
Taking into consideration that at the initial time
*
33
)0(
OO
CtC , after substitution in (21), the following
expression can be obtained:
)/()( *
3
*
321 OO
bCabCCC , (22)
where Kb 2 , VSa / . This allows rewriting the
solution (21) in the following way:
)]exp(1[
)exp(
)(
*
3
*
3
3 atbCa
ataC
tC
O
O
O
. (23)
The solution (23), where ozone decay in volume and on
the surface is taken into consideration, differs from the
solution (10), where ozone decay is considered to be
only in volume. In (23), the multiplier )exp( at
appeared. The multiplier is defined only by the decay on
the walls. If it is dominant, ozone decay is determined by
the decay on the walls, but not by the decay in the
volume. The limiting cases should be analyzed. The
expression (23) can be rewritten as:
)]exp(1[1
)exp()(
*
3
*
3
3
at
a
bC
at
C
tC
OO
O
. (24)
Let us assume that 1/*
3
abC
O
. This means either
small initial ozone concentrations or large surface areas
in relation to the volume, or both at the same time:
1*
3
O
C , 1/ VS . As the denominator of (24) has
the product abCat
O
/)]exp(1[ *
3
in which
1/*
3
abC
O
, and 1)]exp(1[ at ,
)/)]exp(1[1/(1 *
3
abCat
O
may be expanded as
xx 1)1/(1 . The following expression may be
obtained:
)exp(
)(
*
3
3 at
C
tC
O
O
. (25)
It is shown that ozone decay is defined only by the decay
on the surface.
Let us assume that 1/*
3
abC
O
. This means either
large initial ozone concentrations or small surface areas
in relation to the volume, or both at the same time.
Under large initial ozone concentrations, the expression
(24) cannot be applied, as it considers that K does not
depend on time and is defined by the initial
concentrations of reagents. In this case, the equations
(18), (19) should be solved numerically. Therefore, let
us analyze the case 1a , taking into consideration
that K does not depend on time. In (24), )exp( at
may be expanded:
tbC
at
tbCC
tC
OOO
O
*
3
*
3
*
3
3
11
1)(
. (26)
The first term in the right part (26) is the solution (10)
for the ozone decay in the vessel volume, and the second
term defines a small influence of the wall.
If the set of experimental points for )(
3 kO
tC is built
in the coordinates {
k
t , ))(/ln(
33
*
kOO
tCC }, the curve
))(/ln(
33
*
kOO
tCC = ]/))exp(1(1ln[ *
3
aatbCat
kOk
will be obtained. At
k
t = 0, it starts from
))0(/ln(
33
*
OO
CC = 0, and at
k
t it is almost straight:
]1ln[))(/ln(
*
3
3
*
3 a
bC
attCC
O
kkOO
. (27)
Thus, there are two limiting modes of ozone decay
in the vessel. The first mode considers small initial
ozone concentrations, or large surface areas in relation
to the volume, or both at the same time. This mode can
be called the surface dominated ozone decay mode. In
this case, ozone concentration decreased in accordance
with the exponential law )exp()( *
33
tCtC
OO
, where
the exponent is determined by the surface – VS / .
The second mode can be called the volume dominated
ozone decay mode. This mode is realized when the
surface areas are small in relation to the volume, and
ozone concentrations are not too large. In this case
)1/()( *
33
tCtC
OO
, and the ozone decay is determined
by the decay in the vessel volume.
Figure shows ozone decay in the empty and
differently filled container for perishable products
transportation.
Ozone decay in the empty and differently filled
container. Concentration vs time, as well as its
approximation using (10), (23). The empty container
corresponds to the volume dominated ozone decay
mode, and the filled container corresponds to the
surface dominated ozone decay mode
The ozone concentrations vs time at given
temperature and humidity are presented in Figbre a. The
initial ozone concentrations are little bit different. The
approximations of experimental data by (10) and (23)
for empty container are also shown in Figure a. The
equation (23) was used for approximation of
experimental data in the filled container (see Figure a).
It is clear that equations (10) and (23) are good
approximations for ozone decay in empty and filled
b
a c
ISSN 1562-6016. ВАНТ. 2017. №1(107) 151
containers. Figure b shows ozone concentration vs time
for empty container in the coordinates {
k
t , 1/ )(
3 kO
tC },
and its approximation by (10) and (23) with sufficiently
small a . This is the volume dominated ozone decay
mode. Figure c show ozone concentration vs time for
differently filled container in the coordinates {
k
t ,
))(/ln(
33
*
kOO
tCC }, and its approximation by (24). This is
the surface dominated ozone decay mode. Due to
increase of the container filling, the decay of ozone on
its inner surface increases. This leads to an increase of
the parameter a in (24), (25), (27), as can be seen from
the Figure, c.
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Article received 25.11.2016
РАСПАД ОЗОНА В ХИМИЧЕСКОМ РЕАКТОРЕ С РАЗВИТОЙ ВНУТРЕННЕЙ ПОВЕРХНОСТЬЮ
О.В. Мануйленко, В.И. Голота
Исследована кинетика распада озона в реакторе с развитой внутренней поверхностью, на которой может
происходить его распад. В зависимости от того, какой из процессов распада является основным – распад в
объёме, или распад на поверхности концентрация озона ведёт себя по-разному со временем. Если распад
озона происходит, в основном, на поверхности, то его концентрация уменьшается со временем
пропорционально )exp( t , где определяется процессом распада на внутренней поверхности реактора и
её полной площадью. Если же распад озона происходит, в основном, в объёме, то его концентрация
уменьшается со временем пропорционально )1/(1 t , где определяется обычным процессом распада
озона в объёме.
РОЗПАД ОЗОНУ В ХІМІЧНОМУ РЕАКТОРІ З РОЗВИНЕНОЮ ВНУТРІШНЬОЮ ПОВЕРХНЕЮ
О.В. Мануйленко, В.І. Голота
Досліджено кінетику розпаду озону в реакторі з розвиненою внутрішньою поверхнею, на якій може
відбуватися його розпад. Залежно від того, який із процесів розпаду є основним розпад в об'ємі або розпад
на поверхні концентрація озону поводиться по-різному з часом. Якщо розпад озону відбувається, в
основному, на поверхні, то його концентрація зменшується з часом пропорційно )exp( t , де
визначається процесом розпаду на внутрішній поверхні реактора та її повною площею. Якщо ж розпад озону
відбувається, в основному, в об'ємі, то його концентрація зменшується з часом пропорційно )1/(1 t , де
визначається звичайним процесом розпаду озону в об'ємі.
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