The effect of the plasma composition on characteristics of the d.c. arc—III

The effect of the plasma composition on characteristics of the d.c. arc-III Arc in carbon dioxide N. Faculty

IKONOMOV,

B.

PAVLO&,

V. VUKANOVIO)and N. RAKX~EVI~

of Sciences, Faculty of Technology and Metallurgy, and Institute Technology and Metallurgy, Beograd, Yugoslavia (Received

25 Octobm

of Chemistry,

1969)

A~s~aat-~he experimental and theoretical curves of radial temperature distribution of the arc burning in carbon dioxide, compared with corresponding curves in nitrogen, are considered. The theoretical curves are obtained by solving ELENBAAS-%OLLER energy balance equation according to Maecker. The model of the freely burning arc, under conditions usually applied in spectrochemical practice is used. Carbon dioxide exemplifies a plasma whose thermal conductivity as a function of temperature shows two maxima. In spite of one maximum being in approximately the same temperature interval as that of nitrogen, the presence of the second maximum causas the radial temperature distribution to become more abrupt in the luminous zone of the arc. I.NTE~~~TJOTI~N

THE RELATION between the radial temperature distribution and the thermal conductivity of the arc plasma has been discussed in [I]. The thermal conductivity depends markedly on the reaction energies of the components of the atmosphere. The temperature region in which recombination reactions occur determines the zone of increased thermal conductivity. For this temperature region the ELENBAASHELLER equation yields a relatively small gradient of the radial temperature distribution. When a thermal conductivity curve shows two maxima there are taking place at least two reactions with different energies [I]. IIere, the theory shows that smaller gradients of the radial temperature distribution in the temperature regions in which the reactions are taking place will be obtained, while between these two regions in which reactions are taking place, the temperature will decrease more quickly from one region to the other under the general conditions described in paper PI. The temperature function of the thermal conductivity for carbon dioxide is an example of a curve with two maxima. The theoretically calculated and experimentally obtained results of the radial temperature distribution of the arc burning in carbon dioxide are given. EXPERIMENTAL Our experiments were performed under conditions described in paper The experimentally obtained results of radial temperature distribution dioxide are plotted in Fig. 1, curve 1. In the same figure, this curve is with the radial temperature distribution curve 2, obtained under similar in pure nitrogen [I]. THEORETICAL

[l]. in carbon compared conditions

CALCULATION

The thermal and electrical conductivities were computed as functions of the temperature according to [I]. For the density of carbon dioxide, its composition [l] V. V~~ANOVI~,

N. kONOMOV

and 3. pAVLOTI6, 117

Spectrochim. Acta 26B, 109 (1971).

118

N. IKONOMOV, B. PAVLOVI& V. VUKANOVI~ and N. RAKI~EVI~

Fig.

1. Experimental radial temperature distribution in the arc: curve (1) arc burning in carbon dioxide; curve (2) arc burning in nitrogen.

Fig. 2. Diffusion coefficients of one type of particles into all others.

!Phe&feetof the plasma composition on ~h~ac~ristics

of the d-c. arc-III

119

I o-

T y

Q-5--

5

u v) 7,; u $ u “a x Y

2000

01

4ooc

8000

6000 T,

I0000

OK

I I 6k-

4-

2-

0

I 2000

I 6000

i 4000 T,

Fig. 3. Thermal

conductivity

I 8000

1 l0000

‘K

as a function of temperature (2) nitrogen.

(1) carbon dioxide;

and specific heat up to 7000°K we used the data of paper [2]. The following values for kinetic-theory cross-sections for collisions between neutral particles were used : l$“,:

= 37.5. 10-16cm2; 9:: = 32.8 ,10-16cm2; @$: = 28.7 .10-16cm2; Qg M Qg w 1543. lo-l6cm2; Q&O, M Q&, M 25.3 . lo-l6ema; Qgo m Q$o m 234 . lo-l6 cm2; Q& M Q& w 21.6 . lo-lacm2.

For the ~A~SAU~R

cross-sections

we used the approximate

Q$ m Qi M Q. w Qo m Q& M &eo m Q&

values:

= Q&, M 2 . lo-l5cm2.

On the basis of these data, as well as from the data for GVOZDOVER cross-sections, we calculated the mean free paths and diffusion coefficients. In Fig. 2, the calculated values of diffusion coefficients of one type of particles into all others are shown. Figure 3 shows the calculated thermal conductivity as a function of temperature [2]A. S. PLESHANOV and S. G. ZAICE~, E’izi&xkaja gawdinamika, teptoobnen gazov visokyh temperatur, Jedatel’stvo AN SSSR (1962).

i termochamika

120

N. IKONOMOV,

B. PAVLOVI~,

and N. RAKI~EVIO

V. VUKANOVI~

and at a pressure of p = 1 atm. Accordillgly, the thermal conductivity curve for carbon dioxide has two maxima. One of them corresponds to the reaction C + 0 --f CO, with a dissociation energy of 11-l eV, is situated at about 7000°K. The other maximum is at a temperature of about 3500°K and corresponds to the reactions co + 0 -+ CO, and 0 $- 0 -+ O,, with dissociation energies of 54 and 5.1 eV respectively. The thermal conductivity for nitrogen is also shown in Fig. 3. Figure 4 shows the electrical conductivity for carbon dioxide at different temperatures.

I

5

Fig. 4. Electrical conductivity

6

7

8

9

IO

of carbon dioxide as a function of temperature.

Applying MAECKER'S procedure for solving the energy balance equation of a cylindrically symmetric arc [l], we obtained the theoretical radial temperature distribution in carbon dioxide (Fig. 5, curve 1). In the same figure (curve 2) we show the theoretical curve for nitrogen. DISCUSSION

The radial temperature distribution in carbon dioxide is slightly more abrupt than that in nitrogen (Fig. 1). This difference can be interpreted on the basis of the difference in thermal conductivity. The temperature function of the thermal conductivity of carbon dioxide has two maxima and this means that there are at least two reactions with different energies taking place. One of these maxima is in approximately the same temperature region as the maximum for nitrogen. This temperature corresponds to the temperature in the arc axis, The second maximum is at 35W’K. It influences the radial temperature distribution too. Therefore,

The effect of the plasma composition on oharac~r~ti~s

of the d.c. arc-III

121

P Fig. 5. Theoretical radial temperature distribution of the arc plasma: curve (1) burning in carbon dioxide; curve (2) arc burning in nitrogen.

the gradient at a temperature of about 3500°K is smaller, but the radial temperature decline in the region between the two maxima and it is more abrupt. This is in agreement with the experimental result. In carbon dioxide, the core in the arc centre expands between 7000°K and 400O“K. Since the excitation processes of most elements occur in this central part of the arc, this core is of particular interest. The transport velocity of particles in an arc plasma depends on the radial temperature gradient. Therefore, if we consider the residence time of particles, a plasma with a small radial temperature gradient is more suitable for spectrochemical determinations than one with a steep distribution. From this point of view it can be expected that the residence time of particles of trace elements will be shorter in a carbon dioxide than in a nitrogen arc plasma.