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The effect of the plasma composition on characteristics of the d.c. arc—II
Spectrochimica Acta,Vol.26B, pp.109to 115. Pergamon Press1971.Printed
in NorthernIreland
The effect of the plasma composition on characteristics of the d.c. arc-II Arc in argon and arc in nitrogen with water vapour Faculty
B. PAVLOVI~, V. VUKANOVI~ and N. IKONOMOV of Technology and Metallurgy, Faculty of Sciences, and Institute of Chemistry, Technology and Metallurgy, Beograd, Yugoslavia (Received
28 October 1969)
Abstract-The experimental and theoretical curves of the radial temperature distribution of the arc burning in argon, are compared with the corresponding curves in nitrogen. The theoretical curves are obtained by solving the ELENBAAS-HELLER energy balance equation according to Maecker. The model of the freely burning arc, under conditions usually applied in spectrochemical praxis, is considered. In accordance with theory and in comparison with the arc burning in pure nitrogen, the brilliant zone of ares burning in argon has a steeper radial temperature distribution. If water vapour is added to an arc burning in nitrogen, the arc plasma is narrowed and the temperature increased. These experimental data can be interpreted theoretically from the solution of the energy balance equation. INTRODUCTION of chemical reactions taking place in the arc and their influence on the arc characteristics and hence, on spectrochemical analysis. It has been shown that chemical reactions chiefly determine the radial
IN PAPER [l] we pointed
temperature
distribution
out the importance
in the arc.
The temperature region in which reactions occur is a zone of higher thermal conductivity and lower radial temperature gradient in the arc. The theory has shown that if the temperature in this zone differs from that in the arc axis, a core of higher temperature is formed in the arc centre. In order to investigate such possible cases and, in general, to investigate further the plasma energy balance we shall now observe: (1) The atmosphere concerning (2) The
shape of the radial temperature distribution curve in the arc burning in where reactions practically do not occur, e.g. argon. Our observations are the freely burning arc. influence of added water vapour on the arc burning in nitrogen. EXPERIMENTAL
The general experimental conditions were the same as in paper [I]. The radial temperature distribution of the plasma of the arc burning in argon is shown in Fig. 1, curve 1. The addition of water vapour to nitrogen was performed by evaporation of water from an electrically heated vessel placed around the lower electrode. As the water begins to evaporate no changes in the plasma are visible. After that, when larger quantities of water vapour are present in the atmosphere, the arc plasma becomes narrower and the temperature in the arc axis considerably increases. The radial temperature distribution corresponding to such a plasma is given in Fig. 2, curve 1. In Figs. 1 and 2, we have shown for comparison the experimental curve for the radial temperature distribution in nitrogen (curve 2). [l] V. VUKANOVI~,
N. IKONOMOV
and B. PAVLOV& 109
Spectrochim.
acta
26B, 95 (1971).
a. PAVLO~~, V.
110
and N. bONOMOV
VVHANOVI~!
8000
4ooc
0.5
I
I
!,O
8
I5
I
2.0 f.
P5
8
3.0
3.5
I
40
mm
Fig. 1. Experimental radial temperature distribution in the arc plasma: burning in argon. (2) Arc burning in nitrogen.
THEORIZWXL
(1) Arc
CALCULATIONS
The theoretical procedure applied is described in paper [I]. Using the literature data [2] for the dependence of thermal and electrical conductivity of argon on temperature, we solved the ELENBAAS-HELLER equation. The theoretical curve of the radial temperature distribution in argon, corresponding to a temperature at the arc axis 5Y0= 7100”K, as determined by experiment, is represented by curve 1 in Fig. 3. It is compared with the calculated radial temperature distribution in nitrogen (curve 2). Curves are shown as functions of p = r/R. To describe the effect of the addition of water vapour to nitrogen, we considered theoretically the case of pure water vapour. Basic data for water vapour composition, specific heats and densities as a function of temperature were taken from [3]. The following values for kinetic theory cross-sections for collisions between neutral particles used : &II BHz = 4.8 . lo-l6
cm2;
Qozo~ = 7 . 10-l” cm2;
Q$$jQonoH
QHIT w Qoo C=ZG QIio w 1.56 . lo-i5 cm2. [2] CF.
KHOPP
[3]F. BXJRZORX
and A.B. CANFEL, and R. WIENECKE,
Phy~, _F%'lui& 9,988 11966). 2. Ylqs.Chem. 215, 255 (1960).
1 . iOkl” cm2;
The effect of the plasma composition
xJX
9000
BOO0
-
7000
-
on characteristics
of the d.c. arc--II
/X-T-X<
“‘x N,+ H,O \X \ (I) x
Y *
.x-x~--p_ x---p+
1x._ X. x..+
Nz ‘Gx
EOOO
‘4.,x
-
-x,
AX.
(2)
‘cxNx
5000
I 3.0
i 2.0
i I.0 r.
1 4.0
mm
Pig. 2. Experimental radial temperature distribution in the am: (1) Arc burning in nitrogen to which water vapour is added. (2) Arc burning in nitrogen alone.
Fig. 3. Theoretical radial temperature distribution in the arc: (1) Arc burning in argon (T, 7XO0°K). (2) Are in nitrogen (T, = 6800%).
111
B. PAVLOVI~,V. VUEAXOVI~ and N. IEONOMOV
112
The RAMSAUER cross-sections
for elastic collisions between electrons and neutral
particles were : Q
em QH,i w 1.2 . lo-15 cm”;
Qne m QHi C-X1.3 . lo-i4 cm2;
Qo” m QIr m QOHe M QOHi M Qo,” M Qo,i M QkZo w Q&o = 2 . lo-l5 cme. We calculated the mean free paths and the diffusion coefficients from these crossFigure 4 shows the calculated diffusion sections and G~OZDOVER cross-sections.
220 200 -
/ 80 -160 T : 140In ?J E U 120d
100 60 60 40 20 I
2000
I 4000
I 6000 T.
I 8000
I
10000
OK
Fig. 4. Diffusion coefficients of one type of particles into all others.
coefficients of one type of particles into all others. Figure 5 shows the calculated thermal and Fig. 6 electrical conductivities of water vapour as functions of temperature. Solving the energy balance equation we obtained the radial temperature
distri-
bution with a temperature T, = 9300°K at the arc axis (curve 1, Fig. 7). This curve agrees with the theoretical ones described in the paper [l], when T, is essentially In these cases, the core of higher temperature in the axis of the different from T,,,,. arc plasma is obtained with a very steep gradient of the radial temperature bution towards the zones in which reaction occurs.
distri-
The effect of the plasma composition on characteristics of the d.c. arc-11
T.
Fig. 6. Thermal conductivity
OK
of water vapour as a function of temperature.
T
r 0
-0 x
b
T. Fig. 0. Electrical
conductivity
“K
of water vapour
as a function
of temperature.
113
114
B. PAVLOVI& V. VUKANOVI~ and N. IKOXOMOV
c:
4-
\
\
3-
l.
-.
----_
----_
2I --
0
0.1
0.2
0.3
0.4
0.5
0.7
0.8
0.9
I.0
P Fig. 7. Theoretical radial temperature distribution of the arc plasma for the temperature T, = 9300’K at the arc axis: (1) Arc burning in water vapour. (2) Arc burning in nitrogen.
For the same temperature in pure nitrogen is calculated
T, in the arc axis, the radial temperature distribution using basic data from paper [l] (curve 2, Fig. 7). DISCUSSION
Considering the plasma energy balance described in paper [l], we concluded that the shape of the calculated radial temperature distribution in the arc plasma depends on two temperatures: the temperature T, in the arc axis and the temperature T,,,, where conditions of equilibrium and energy of chemical reactions determine the maximal value of the thermal conductivity. This is the temperature of maximum thermal conductivity. Under the conditions described in [l], these two temperatures were approximately equal and we obtained a relatively broad plasma in which the temperature decreases relatively slowly from the centre of the arc towards the peripheral zones. But in the case of argon, the increase of the thermal conductivity, in the considered temperature interval, is only a consequence of normal thermal conductivity, but not of the transport of reaction energy. Namely, the temperature in the observed arc does not become high enough for ionization. The theoretical curve of radial temperature distribution does not show the plateau in either central part, as is the case in the central zone in nitrogen, or in the periphery zones in water vapour. Consequently, in the case when chemical reactions do not occur in the arc atmosphere, the radial temperature distribution must decrease uniformely from the axis to the periphery of the arc. The experimental curve of radial temperature
The effect of the plasma composition on characteristics of the d.c. are--II
115
distribution in argon is much more abrupt than the curve of distribution in nitrogen (Fig. I), as is also the case with the theoretical curve (Fig. 3). From the point of view of spectrochemical determinations, only with regard to the transport velocity of traces from the plasma, such a steeper distribution of temperature in argon is less convenient, with respect to nitrogen. If larger quantities of water vapour are added, the plasma is immediately If we compare the theoretical curve narrowed and the temperature increased. obtained for pure water vapour (curve 1, Fig. 7), with the theoretical curve for pure nitrogen (curve 2, Fig. 7), it is seen that the experimental curve no longer follows the theoretical curve for nitrogen but approaches the theoretical curve for water vapour, although there are still considerable deviations because a mixture of water vapour and nitrogen instead of pure water vapour is added. The fact that the plasma will be narrowed is evident also from the curves described in paper [l] which show the effect of the chemical reactions on the plasma and imply a core of increased temperature in the arc axis. The temperature around the core may be so low that we no longer observe light from this zone. As is seen from Figs. 2 and 7, the theory of plasma energy balance gives a good interpretation of the effect of plasma narrowing when water vapour is added, which does not exclude that the arc periphery is possibly cooled by the water vapour.
in NorthernIreland
The effect of the plasma composition on characteristics of the d.c. arc-II Arc in argon and arc in nitrogen with water vapour Faculty
B. PAVLOVI~, V. VUKANOVI~ and N. IKONOMOV of Technology and Metallurgy, Faculty of Sciences, and Institute of Chemistry, Technology and Metallurgy, Beograd, Yugoslavia (Received
28 October 1969)
Abstract-The experimental and theoretical curves of the radial temperature distribution of the arc burning in argon, are compared with the corresponding curves in nitrogen. The theoretical curves are obtained by solving the ELENBAAS-HELLER energy balance equation according to Maecker. The model of the freely burning arc, under conditions usually applied in spectrochemical praxis, is considered. In accordance with theory and in comparison with the arc burning in pure nitrogen, the brilliant zone of ares burning in argon has a steeper radial temperature distribution. If water vapour is added to an arc burning in nitrogen, the arc plasma is narrowed and the temperature increased. These experimental data can be interpreted theoretically from the solution of the energy balance equation. INTRODUCTION of chemical reactions taking place in the arc and their influence on the arc characteristics and hence, on spectrochemical analysis. It has been shown that chemical reactions chiefly determine the radial
IN PAPER [l] we pointed
temperature
distribution
out the importance
in the arc.
The temperature region in which reactions occur is a zone of higher thermal conductivity and lower radial temperature gradient in the arc. The theory has shown that if the temperature in this zone differs from that in the arc axis, a core of higher temperature is formed in the arc centre. In order to investigate such possible cases and, in general, to investigate further the plasma energy balance we shall now observe: (1) The atmosphere concerning (2) The
shape of the radial temperature distribution curve in the arc burning in where reactions practically do not occur, e.g. argon. Our observations are the freely burning arc. influence of added water vapour on the arc burning in nitrogen. EXPERIMENTAL
The general experimental conditions were the same as in paper [I]. The radial temperature distribution of the plasma of the arc burning in argon is shown in Fig. 1, curve 1. The addition of water vapour to nitrogen was performed by evaporation of water from an electrically heated vessel placed around the lower electrode. As the water begins to evaporate no changes in the plasma are visible. After that, when larger quantities of water vapour are present in the atmosphere, the arc plasma becomes narrower and the temperature in the arc axis considerably increases. The radial temperature distribution corresponding to such a plasma is given in Fig. 2, curve 1. In Figs. 1 and 2, we have shown for comparison the experimental curve for the radial temperature distribution in nitrogen (curve 2). [l] V. VUKANOVI~,
N. IKONOMOV
and B. PAVLOV& 109
Spectrochim.
acta
26B, 95 (1971).
a. PAVLO~~, V.
110
and N. bONOMOV
VVHANOVI~!
8000
4ooc
0.5
I
I
!,O
8
I5
I
2.0 f.
P5
8
3.0
3.5
I
40
mm
Fig. 1. Experimental radial temperature distribution in the arc plasma: burning in argon. (2) Arc burning in nitrogen.
THEORIZWXL
(1) Arc
CALCULATIONS
The theoretical procedure applied is described in paper [I]. Using the literature data [2] for the dependence of thermal and electrical conductivity of argon on temperature, we solved the ELENBAAS-HELLER equation. The theoretical curve of the radial temperature distribution in argon, corresponding to a temperature at the arc axis 5Y0= 7100”K, as determined by experiment, is represented by curve 1 in Fig. 3. It is compared with the calculated radial temperature distribution in nitrogen (curve 2). Curves are shown as functions of p = r/R. To describe the effect of the addition of water vapour to nitrogen, we considered theoretically the case of pure water vapour. Basic data for water vapour composition, specific heats and densities as a function of temperature were taken from [3]. The following values for kinetic theory cross-sections for collisions between neutral particles used : &II BHz = 4.8 . lo-l6
cm2;
Qozo~ = 7 . 10-l” cm2;
Q$$jQonoH
QHIT w Qoo C=ZG QIio w 1.56 . lo-i5 cm2. [2] CF.
KHOPP
[3]F. BXJRZORX
and A.B. CANFEL, and R. WIENECKE,
Phy~, _F%'lui& 9,988 11966). 2. Ylqs.Chem. 215, 255 (1960).
1 . iOkl” cm2;
The effect of the plasma composition
xJX
9000
BOO0
-
7000
-
on characteristics
of the d.c. arc--II
/X-T-X<
“‘x N,+ H,O \X \ (I) x
Y *
.x-x~--p_ x---p+
1x._ X. x..+
Nz ‘Gx
EOOO
‘4.,x
-
-x,
AX.
(2)
‘cxNx
5000
I 3.0
i 2.0
i I.0 r.
1 4.0
mm
Pig. 2. Experimental radial temperature distribution in the am: (1) Arc burning in nitrogen to which water vapour is added. (2) Arc burning in nitrogen alone.
Fig. 3. Theoretical radial temperature distribution in the arc: (1) Arc burning in argon (T, 7XO0°K). (2) Are in nitrogen (T, = 6800%).
111
B. PAVLOVI~,V. VUEAXOVI~ and N. IEONOMOV
112
The RAMSAUER cross-sections
for elastic collisions between electrons and neutral
particles were : Q
em QH,i w 1.2 . lo-15 cm”;
Qne m QHi C-X1.3 . lo-i4 cm2;
Qo” m QIr m QOHe M QOHi M Qo,” M Qo,i M QkZo w Q&o = 2 . lo-l5 cme. We calculated the mean free paths and the diffusion coefficients from these crossFigure 4 shows the calculated diffusion sections and G~OZDOVER cross-sections.
220 200 -
/ 80 -160 T : 140In ?J E U 120d
100 60 60 40 20 I
2000
I 4000
I 6000 T.
I 8000
I
10000
OK
Fig. 4. Diffusion coefficients of one type of particles into all others.
coefficients of one type of particles into all others. Figure 5 shows the calculated thermal and Fig. 6 electrical conductivities of water vapour as functions of temperature. Solving the energy balance equation we obtained the radial temperature
distri-
bution with a temperature T, = 9300°K at the arc axis (curve 1, Fig. 7). This curve agrees with the theoretical ones described in the paper [l], when T, is essentially In these cases, the core of higher temperature in the axis of the different from T,,,,. arc plasma is obtained with a very steep gradient of the radial temperature bution towards the zones in which reaction occurs.
distri-
The effect of the plasma composition on characteristics of the d.c. arc-11
T.
Fig. 6. Thermal conductivity
OK
of water vapour as a function of temperature.
T
r 0
-0 x
b
T. Fig. 0. Electrical
conductivity
“K
of water vapour
as a function
of temperature.
113
114
B. PAVLOVI& V. VUKANOVI~ and N. IKOXOMOV
c:
4-
\
\
3-
l.
-.
----_
----_
2I --
0
0.1
0.2
0.3
0.4
0.5
0.7
0.8
0.9
I.0
P Fig. 7. Theoretical radial temperature distribution of the arc plasma for the temperature T, = 9300’K at the arc axis: (1) Arc burning in water vapour. (2) Arc burning in nitrogen.
For the same temperature in pure nitrogen is calculated
T, in the arc axis, the radial temperature distribution using basic data from paper [l] (curve 2, Fig. 7). DISCUSSION
Considering the plasma energy balance described in paper [l], we concluded that the shape of the calculated radial temperature distribution in the arc plasma depends on two temperatures: the temperature T, in the arc axis and the temperature T,,,, where conditions of equilibrium and energy of chemical reactions determine the maximal value of the thermal conductivity. This is the temperature of maximum thermal conductivity. Under the conditions described in [l], these two temperatures were approximately equal and we obtained a relatively broad plasma in which the temperature decreases relatively slowly from the centre of the arc towards the peripheral zones. But in the case of argon, the increase of the thermal conductivity, in the considered temperature interval, is only a consequence of normal thermal conductivity, but not of the transport of reaction energy. Namely, the temperature in the observed arc does not become high enough for ionization. The theoretical curve of radial temperature distribution does not show the plateau in either central part, as is the case in the central zone in nitrogen, or in the periphery zones in water vapour. Consequently, in the case when chemical reactions do not occur in the arc atmosphere, the radial temperature distribution must decrease uniformely from the axis to the periphery of the arc. The experimental curve of radial temperature
The effect of the plasma composition on characteristics of the d.c. are--II
115
distribution in argon is much more abrupt than the curve of distribution in nitrogen (Fig. I), as is also the case with the theoretical curve (Fig. 3). From the point of view of spectrochemical determinations, only with regard to the transport velocity of traces from the plasma, such a steeper distribution of temperature in argon is less convenient, with respect to nitrogen. If larger quantities of water vapour are added, the plasma is immediately If we compare the theoretical curve narrowed and the temperature increased. obtained for pure water vapour (curve 1, Fig. 7), with the theoretical curve for pure nitrogen (curve 2, Fig. 7), it is seen that the experimental curve no longer follows the theoretical curve for nitrogen but approaches the theoretical curve for water vapour, although there are still considerable deviations because a mixture of water vapour and nitrogen instead of pure water vapour is added. The fact that the plasma will be narrowed is evident also from the curves described in paper [l] which show the effect of the chemical reactions on the plasma and imply a core of increased temperature in the arc axis. The temperature around the core may be so low that we no longer observe light from this zone. As is seen from Figs. 2 and 7, the theory of plasma energy balance gives a good interpretation of the effect of plasma narrowing when water vapour is added, which does not exclude that the arc periphery is possibly cooled by the water vapour.