On the influence of copper impurities on the transport properties of thermal water plasma
The influence of copper impurities on the transport properties of multicomponent thermal plasma is considered in the ambient atmosphere of water vapors. The calculations are carried out on the base of Grad’s method, and it is shown that a small amount of metal causes the essential changes in the val...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
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nasplib_isofts_kiev_ua-123456789-1122032025-02-09T22:38:24Z On the influence of copper impurities on the transport properties of thermal water plasma Про вплив домішок міді на транспортні властивості термічної водяної плазми О влиянии примесей меди на транспортные свойства термической водной плазмы Porytskyy, P.V. Приложения и технологии The influence of copper impurities on the transport properties of multicomponent thermal plasma is considered in the ambient atmosphere of water vapors. The calculations are carried out on the base of Grad’s method, and it is shown that a small amount of metal causes the essential changes in the values of transport coefficients in comparison with the case of pure water plasma. It is considered the influence of the model of cross-section for electron collisions with atomic copper on transport properties. Розглянуто вплив домішок міді на транспортні властивості багатокомпонентної плазми в атмосфері водяної пари. Проведені розрахунки ґрунтувалися на методі моментів Ґреда. Показано, що невелика кількість металевих домішок може суттєво змінити величини транспортних коефіцієнтів порівняно із випадком чистої водяної пари. Розглянуто вплив моделі перерізу зіткнень електрона з атомом міді на транспортні властивості термічної плазми. Рассмотрено влияние примесей меди на транспортные свойства многокомпонентной плазмы в атмосфере водяного пара. Проведенные расчеты основывались на методе моментов Грэда. Показано, что незначительное количество примесей металла может существенно изменить величины транспортных коэффициентов в сравнении со случаем чистого водяного пара. Рассмотрено влияние модели сечения столкновений электрона с атомом меди на транспортные свойства термической плазмы. 2015 Article On the influence of copper impurities on the transport properties of thermal water plasma / P.V. Porytskyy // Вопросы атомной науки и техники. — 2015. — № 4. — С. 335-337. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.25.Fi, 52.25.Vy, 52.25.Ya, 52.27.Cm, 52.77.Fv, 52.50.Nr, 52.80.Mg https://nasplib.isofts.kiev.ua/handle/123456789/112203 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Приложения и технологии Приложения и технологии |
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Приложения и технологии Приложения и технологии Porytskyy, P.V. On the influence of copper impurities on the transport properties of thermal water plasma Вопросы атомной науки и техники |
| description |
The influence of copper impurities on the transport properties of multicomponent thermal plasma is considered in the ambient atmosphere of water vapors. The calculations are carried out on the base of Grad’s method, and it is shown that a small amount of metal causes the essential changes in the values of transport coefficients in comparison with the case of pure water plasma. It is considered the influence of the model of cross-section for electron collisions with atomic copper on transport properties. |
| format |
Article |
| author |
Porytskyy, P.V. |
| author_facet |
Porytskyy, P.V. |
| author_sort |
Porytskyy, P.V. |
| title |
On the influence of copper impurities on the transport properties of thermal water plasma |
| title_short |
On the influence of copper impurities on the transport properties of thermal water plasma |
| title_full |
On the influence of copper impurities on the transport properties of thermal water plasma |
| title_fullStr |
On the influence of copper impurities on the transport properties of thermal water plasma |
| title_full_unstemmed |
On the influence of copper impurities on the transport properties of thermal water plasma |
| title_sort |
on the influence of copper impurities on the transport properties of thermal water plasma |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2015 |
| topic_facet |
Приложения и технологии |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/112203 |
| citation_txt |
On the influence of copper impurities on the transport properties of thermal water plasma / P.V. Porytskyy // Вопросы атомной науки и техники. — 2015. — № 4. — С. 335-337. — Бібліогр.: 7 назв. — англ. |
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Вопросы атомной науки и техники |
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ISSN 1562-6016. ВАНТ. 2015. №4(98) 335
ON THE INFLUENCE OF COPPER IMPURITIES ON THE TRANSPORT
PROPERTIES OF THERMAL WATER PLASMA
P.V. Porytskyy
Institute for Nuclear Research of NASU, Kiev, Ukraine
The influence of copper impurities on the transport properties of multicomponent thermal plasma is considered
in the ambient atmosphere of water vapors. The calculations are carried out on the base of Grad’s method, and it is
shown that a small amount of metal causes the essential changes in the values of transport coefficients in comparison
with the case of pure water plasma. It is considered the influence of the model of cross-section for electron collisions
with atomic copper on transport properties.
PACS: 52.25.Fi, 52.25.Vy, 52.25.Ya, 52.27.Cm, 52.77.Fv, 52.50.Nr, 52.80.Mg
INTRODUCTION
Copper is widely used in plasma devices and in-
dustrial electronic plants. Sometimes they are doped
with other materials to lower the work function of the
cathode material. At operation the process of erosion
leads to the evaporation of the metal impurities into
the discharge region that causes the change of plasma
properties. Also, the plasma created from water vapors
is widely applied in applications. It is the thermal
plasma mixture of both the copper and water vapors is
considered below.
The improvement in controlling plasma processing
needs for accurate numerical modeling. Transport
properties are indispensable input data for the model-
ing. At weakly ionization the Lorentzian theory is suit-
able to calculate the properties of multicomponent
thermal plasma [1]. But at increasing of ionization
processes a number of collision processes are known
to be included into consideration. Because of that it is
the many processes are needed to take into account in
the calculation procedure.
In this paper, the transport coefficients for multi-
component water plasma with copper impurities are
calculated on the base of the Grad’s method [2 - 4]. It
is shown that the impurities have an influence on the
transport properties of thermal plasma.
1. METHOD OF CALCULATION
It should be noted that the present state of the
theory of gas mixtures, as well as multicomponent
plasma, is characterized by the lack of a unified ap-
proach to the description of transport processes. The
reason for this is a very complex nature of depend-
encies of the properties of gas mixtures and plasma
on the properties of pure gases and concentrations of
the components.
Thus, the coefficient of thermal conductivity is cal-
culated as the sum
inth e ri rdλ λ λ λ λ λ= + + + + , (1)
where hλ is the translational thermal conductivity of
heavy particles, eλ is the thermal conductivity of elec-
trons, intλ is the thermal conductivity due to the trans-
fer among the internal degrees of freedom, riλ is the
reactive thermal conductivity due to ionization, rdλ is
the reactive thermal conductivity due to dissociation.
In turn, the coefficient of viscosity is calculated as
the sum of additions from heavy particle hη and elec-
trons eη :
h eη η η= + . (2)
It should be underlined that, now, the Grad’s
method of moments [2, 3] is an unique alternative in
spite of the most developed Chapman-Enskog’ method
[4 - 8] to solve the kinetic Boltzmann equation. Both
the methods are based on the formalism of Chapman-
Cowling kinetic integrals
( ) ( )2
1 2
2 3
02
llr rkT e Q dς
αβ αβ
αβ
ς ς ς
πµ
∞
+ −
Ω =
∫ , (3)
where k is Boltzmann constant, T is temperature,
αβµ is a reduced mass of collided species of α and
β , ( )1 2
2kT gαβς µ= , g is the relative velocity,
and transport cross-section of order l is determined as
( ) ( ) ( )
0
2 , 1 cos sinl lQ g g d
π
αβ αβπ σ χ χ χ χ= −∫ ,
where χ is scattering angle, ( ),gαβσ χ is differen-
tial scattering cross-section.
In the 13-moments (13M) approximation of the
Grad’s method the translational transport coefficients
are calculated as the sum of effective coefficients for
each species
h hα
α
η η= ∑ , (4)
h hα
α
λ λ= ∑ . (5)
The effective coefficients are calculated on the
base of combination of the Chapman-Cowling inte-
grals (3).
The studies of electronic transport coefficients are
known to need using of higher approximations. In that
way for electronic viscosity, electrical conductivity
σ , and electronic conductivity one can be write [3],
respectively,
( )1 225 2
2e e e
p
n m kT
p
η π
′
= , (6)
1 2
2 23 2
2 e
e
q
n e
m kT q
πσ
′
=
, (7)
ISSN 1562-6016. ВАНТ. 2015. №4(98) 336
1 2
275 2
8e e
e
qkTn
m q
πλ
′′
= ′
. (8)
Here em is the mass of electron, en is electronic
density, the elements of determinants nkp and nkq
are the functions of the above pointed Chapman-
Cowling integrals. Script denotes the absence of el-
ements with indexes 0 and 1.
The peculiarity of the Grad’ method is that the val-
ues have the same dimensions at all of stages in calcu-
lation procedure due to the control of calculation pro-
cedure may be improved.
2. RESULTS AND DISCUSSION
The calculations are carried out at assumption of
local thermodynamic equilibrium, and the following
16 species have been taken into account: e-, H2O,
H2O+, H2, H2
+, O2, O2
+, OH ,OH+, H, H+, O, O+, Cu,
Cu+, Cu2+. The results of calculation ns for the case of
pure water are shown in Figs. 1-4.
Fig. 1. Electrical conductivity of thermal plasma
for the equimolar mixtures of water vapors with cop-
per (pressure p =1 bar). Curves 1 − pure water;
2 − H2O-Cu (99.99:0.01); 3 − H2O-Cu (99.7:0.3);
4 − H2O-Cu (95:5); 5 − H2O-Cu (70:30). The transport
cross-section for e-+Cu collision according to [5]
One can see that the properties of multicomponent
plasma have a pronounced non-monotone character with
sharp pikes in certain temperature and pressure ranges.
The pikes are appeared due to the dissociation, ioniza-
tion and from others effects connected with metal im-
purities.
Fig. 2. Thermal conductivity of thermal plasma
for the equimolar mixtures of water vapors with cop-
per ( p =1 bar). Curves 1 − pure water; 2 − H2O-Cu
(99.9:0.1); 3 − H2O-Cu (99.7:0.3); 4 – H2O-Cu (99:1);
5 − H2O-Cu (95:5); 6 − H2O-Cu (70:30); 7 − H2O-Cu
(10:90). The transport cross-section for e-+Cu colli-
sion according to [5]
Fig. 3. Electrical conductivity of thermal plasma
for the equimolar mixtures of water vapors with cop-
per H2O-Cu (10:90) ( p =1 bar). Curves 1 – pure
water; 2 – the transport cross-section for e-+Cu colli-
sion according to [6]; 3 – one is [5]; 4 – one is [7]
Fig. 4. Electrical conductivity of thermal plasma
for the equimolar mixtures of water vapors with cop-
per ( p =1 bar). Curves 1 − pure water; 2 − H2O-Cu
(99.99:0.01); 3 − H2O-Cu (95:5); 4 − H2O-Cu (95:5);
5 – H2O-Cu (70:30). The transport cross-section for
e-+Cu collision according to [5]
The appearance of copper impurities causes the es-
sential changing of transport properties with compari-
son to the case of pure water. That is needed to take
into account under studies of discharges with copper
electrodes.
It should be noted that under scattering of electron
on an atomic copper the various models are known to
be exist (see for details [5 - 7]). The influence of the
different cross-sections on the properties takes place
with the strong character (see Figs. 3-4). Thus, the
calculations based on the novel model [5] are very
different from widely used one [6].
CONCLUSIONS
Thus, a small amount of copper causes the essen-
tial changes in the values of transport coefficients of
thermal plasma in comparison with the case of pure
water.
The properties of thermal plasma mixture are
strongly depended on the character of electron-atom
collision cross-sections.
Furthermore, the problem of inequality of transport
properties calculation takes place for plasma mixtures
containing copper due to the existing of various mod-
els describing the electron-atom collision cross section
for copper.
ISSN 1562-6016. ВАНТ. 2015. №4(98) 337
REFERENCES
1. P. Porytsky, I. Krivtsun,V. Demchenko, U. Reis-
gen, O. Mokrov, A. Zabirov. On the application of
the theory of Lorentzian plasma to calculation of
transport properties of multicomponent arc plasmas
// European Phys. Journ. D. 2010, v. 57, № 1,
p. 77-85.
2. H. Grad. On the kinetic theory of rarefied gases //
Comm. Pure and Appl. Math. 1949, v. 2, p. 331-
407.
3. V.M. Zhdanov. Transport Processes in Multicom-
ponent Plasma. NY: “Taylor&Francis”, 2002.
4. P. Porytsky, I. Krivtsun, V. Demchenko, et al.
Transport properties of multicomponent thermal
plasma: Grad method versus Chapman-Enskog
method // Phys. Plasmas. 2013, v. 20, p. 023504.
5. O. Zatsarinny, K. Bartschat. Electron collisions
with copper atoms: Elastic scattering and electron
impact excitation of the (3 d 10 4 s) 2S -> (3 d 10
4 p) 2P resonance transition // Phys. Rev. A. 2010,
v. 82, p. 062703.
6. K.F. Scheibner, A.U. Hazi, R.J.W. Henry. Elec-
tron-impact excitation cross sections for transitions
in atomic copper // Phys. Rev. A. 1987, v. 35,
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7. B. Chervy, O. Dupont, A. Gleizes, P. Krenek. The
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Article received 28.04.2015
О ВЛИЯНИИ ПРИМЕСЕЙ МЕДИ НА ТРАНСПОРТНЫЕ СВОЙСТВА
ТЕРМИЧЕСКОЙ ВОДНОЙ ПЛАЗМЫ
П.В. Порицкий
Рассмотрено влияние примесей меди на транспортные свойства многокомпонентной плазмы в атмо-
сфере водяного пара. Проведенные расчеты основывались на методе моментов Грэда. Показано, что незна-
чительное количество примесей металла может существенно изменить величины транспортных коэффици-
ентов в сравнении со случаем чистого водяного пара. Рассмотрено влияние модели сечения столкновений
электрона с атомом меди на транспортные свойства термической плазмы.
ПРО ВПЛИВ ДОМІШОК МІДІ НА ТРАНСПОРТНІ ВЛАСТИВОСТІ
ТЕРМІЧНОЇ ВОДЯНОЇ ПЛАЗМИ
П.В. Порицький
Розглянуто вплив домішок міді на транспортні властивості багатокомпонентної плазми в атмосфері во-
дяної пари. Проведені розрахунки ґрунтувалися на методі моментів Ґреда. Показано, що невелика кількість
металевих домішок може суттєво змінити величини транспортних коефіцієнтів порівняно із випадком чис-
тої водяної пари. Розглянуто вплив моделі перерізу зіткнень електрона з атомом міді на транспортні влас-
тивості термічної плазми.
О ВЛИЯНИИ ПРИМЕСЕЙ МЕДИ НА ТРАНСПОРТНЫЕ СВОЙСТВА ТЕРМИЧЕСКОЙ ВОДНОЙ ПЛАЗМЫ
П.В. Порицкий
Рассмотрено влияние примесей меди на транспортные свойства многокомпонентной плазмы в атмосфере водяного пара. Проведенные расчеты основывались на методе моментов Грэда. Показано, что незначительное количество примесей металла может существенно измени...
П.В. Порицький
Розглянуто вплив домішок міді на транспортні властивості багатокомпонентної плазми в атмосфері водяної пари. Проведені розрахунки ґрунтувалися на методі моментів Ґреда. Показано, що невелика кількість металевих домішок може суттєво змінити величини тр...
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