IMPULSE BREAKDOWN OF ELECTROLYTES AT SHORT VOLTAGE EXPOSURE TIMES

A. T. Chepikov, B. V. Semkin, A. M. Mironov

(Presented by the scientific seminar of the Research Institute of High Voltages)

Volt-second characteristics of impulse breakdown of aqueous NaCl solutions were obtained in the voltage exposure-time interval \(8 \cdot 10^{-8} \div 5 \cdot 10^{-6}\) sec in a nonuniform electric field for a spacing of 5 mm. The specific resistance of the solution was varied from 10 to \(10^{5}\) ohm cm, while the resistance of the system varied correspondingly from 3.5 to \(3.5 \cdot 10^{4}\) ohm. It was established that, in the investigated time range, the electric strength is inversely proportional to the logarithm of the specific “low-voltage” resistance of the solution. At a voltage-pulse steepness of 1000 kV/μsec, the prebreakdown current in the gap was oscillographed. The maximum values of the power developed and of the energy released in the gap before breakdown were estimated as functions of the specific resistance of the solution.

Introduction

Most investigations of the impulse breakdown of electrolytes have been carried out with pulses of duration on the order of \(10^{-4}\) sec [1, 2, 3]. The available data on the impulse electric strength of electrolytes under pulses of microsecond duration are very limited [4, 5, 6].

In connection with the expansion of useful technical applications of pulsed electric discharge in liquid, it was of scientific and practical interest to investigate the electrical discharge characteristics of electrolytes as functions of their specific resistance under pulses of microsecond and nanosecond duration. It has been established [3] that the character of a “high-voltage” discharge depends mainly on the specific “low-voltage” electrical conductivity, and not on its chemical composition. Therefore, in the present work only aqueous NaCl solutions with a specific “low-voltage” resistance from 10 to \(10^{5}\) ohm cm were used.

In this work, the dependence of the impulse electric strength of the above-mentioned solutions on the voltage exposure time in a nonuniform field was studied experimentally. In order to obtain useful quantitative data, and also to explain the discharge mechanism, dependences were obtained of the impulse electric strength, the energy released in the gap, and the maximum power developed before breakdown on the specific resistance of the solution.

Experimental procedure

The source of the high-voltage impulse was a four-stage impulse-voltage generator rated at 480 kV, with a discharge capacitance \(C = 15600\) pF. The surge impedance of the generator discharge circuit was 36 ohms. The voltage across the gap under study was measured by means of a capacitive voltage divider and an OK 19-M2 electronic oscilloscope. The wave-front length was controlled by the shaping circuit \((L_{\mathrm{fr}}\) and \(C_{\mathrm{fr}})\) within the range \(8 \cdot 10^{-8}\)—\(7 \cdot 10^{-6}\) sec. Breakdown of the gap always occurred on the front of an exponential wave.

The current was measured by means of a coaxial shunt, the signals from which were fed through an RK-103 cable to the deflection plates of an OK19-2M oscilloscope tube. At the output of the RK-103 cable a matching resistance \(R_{\mathrm{v}} = 75\) ohms was installed.

The capacitive component of the current was determined by calculation and did not exceed 3% of the total current flowing through the shunt. The resistance of the shunt and its inductance were, respectively, \(R_{\mathrm{sh}} = 0.2\) ohm and \(L_{\mathrm{sh}} = 1.02 \cdot 10^{-9}\) H.

The studies were carried out for a “rod–plane” electrode system. Pulses of positive or negative polarity were applied to the “rod”; the plane electrode was grounded through the shunt resistance.

The high-voltage electrode was made of a copper rod 6 mm in diameter. To reduce the spreading of impulse currents, the rod was covered with polyethylene insulation 6 mm thick. The length of the uninsulated part of the rod was 12 mm, and the sharpening angle of the tip was \(30^\circ\).

The plane was a polished brass disk 120 mm in diameter. The distance between the electrodes was 5 mm. The electrode system was placed in an organic-glass tank measuring \(350 \times 320 \times 220\) mm. The specific resistance of the solution was varied by dissolving NaCl crystals in distilled water \((\rho = 3 \cdot 10^{5}\ \Omega\cdot\mathrm{cm})\).

The specific resistance of the solution was measured in a standard vessel with platinum electrodes, using a bridge circuit and a ZG-10 audio-frequency generator.

Results obtained and their discussion

Figures 1 and 2 show the dependences of the electric strength of aqueous NaCl solutions on the duration of voltage application in a sharply nonuniform field for positive and negative polarity of the “rod,” respectively. From the volt-second characteristics shown in Figs. 1 and 2, dependences were constructed for the breakdown voltage of the solution on its specific resistance at voltage application times of \(10^{-7}\) sec, \(2 \cdot 10^{-7}\) sec, \(5 \cdot 10^{-7}\) sec, and \(10^{-6}\) sec. These dependences are presented in Fig. 3. In the investigated interval of specific resistances of NaCl solutions \((10—10^{5}\ \Omega\ \mathrm{cm})\), for voltage application times \(5 \cdot 10^{-6}\div 8 \cdot 10^{-8}\) sec, the dependences of the breakdown voltage of the solution on its specific resistance, for any voltage application time, can be represented in the form

\[ U_{\mathrm{br}} = A_t + B_t \lg \rho, \tag{1} \]

where \(A_t\) and \(B_t\) are constants determined by the steepness of the applied voltage pulse;

\[ \rho \]

is the specific resistance of the solution, measured at low voltage.

We shall find the dependence of the breakdown voltage of an electrolyte on the concentration of dissociated molecules in it. According to [7]

\[ \rho=\frac{1}{e\left(g^{(+)}+g^{(-)}\right)\alpha N_0}, \tag{2} \]

where \(e\) is the magnitude of the ion charge;
\(g^{(+)}\) and \(g^{(-)}\) are the mobilities of positive and negative ions;
\(\alpha\) is the dissociation coefficient, defined as the ratio of the concentration of dissociated molecules to the concentration of solute molecules before its dissociation, \(N_0\),

\[ N=\alpha N_0 . \tag{3} \]

Fig. 1. Volt-second characteristics of aqueous solutions at a breakdown probability \(\varphi=5\%\) and positive polarity of the “rod”:

□ — \(\rho=10\ \Omega\cdot\text{cm}\);
△ — \(\rho=10^2\ \Omega\cdot\text{cm}\);
× — \(\rho=10^3\ \Omega\cdot\text{cm}\);
○ — \(\rho=10^4\ \Omega\cdot\text{cm}\);
● — \(\rho=10^5\ \Omega\cdot\text{cm}\).

Fig. 2. Same as in Fig. 1, but for negative polarity of the “rod.”

The mobility of ions does not depend on the voltage up to fields on the order of millions of volts per centimeter [7].

In the range studied, the specific electrical conductivity of the solution depends linearly on its concentration, and to a first approximation it may be assumed that the ion mobility does not depend on concentration. Therefore, for the investigated values, the specific resistivity is

\[ \rho=\frac{1}{\mathrm{const}\cdot N}. \tag{4} \]

Substituting (4) into (1), we obtain

\[ U_{\mathrm{br}}=A_t+B_t\lg\frac{1}{\mathrm{const}\cdot N}. \tag{5} \]

In [6], the electric strength of an aqueous NaCl solution was investigated as a function of the solution concentration \(N_0\) at times to breakdown of \(9\ \mu\text{s}\), \(3.9\ \mu\text{s}\), and \(0.1\ \mu\text{s}\); the interelectrode distance was \(2\ \text{mm}\). At \(t=9\ \mu\text{s}\) and \(t=3\ \mu\text{s}\), in the concentration range \(0.001\text{–}0.1\%\), the breakdown voltage varied inversely proportional to the logarithm of the solution concentration. Taking into account that, at high dilution of a strong electrolyte, \(\alpha \simeq 1\) and \(N \simeq U_0\),

the dependences obtained are in good agreement with (5). At \(t = 0.1\ \mu\text{sec}\), in the concentration range \(N_0 = 1 \div 10\%\), an increase in electric strength with increasing concentration was obtained. The authors explain this phenomenon by a possible change in the discharge mechanism.

A. I. Limasov [5] obtained dependences of the breakdown voltage of a solution of NaCl in water on its concentration, \(U_{\text{br}} = f(N_0\%)\), at \(t = 0.5 \cdot 10^{-6}\ \text{sec}\) and \(t = 2 \cdot 10^{-6}\ \text{sec}\) in a “rod–plane” field.

In the concentration range \(0.03 \div 1\%\), these dependences are described fairly satisfactorily by equation (5). When the concentration was increased above \(2\%\), the electric strength of the solution remained constant. From an analysis of the data obtained in the present work and given in [5, 6], it follows that the dependence of the electric strength of an aqueous solution, at high dilutions, on its “low-voltage” resistivity, for voltage exposure times \(10^{-7} \div 10^{-5}\ \text{sec}\) and distances between electrodes

Fig. 3. Dependence of the breakdown voltage of an aqueous NaCl solution on the logarithm of its resistivity for different exposure times:

• ● — \(t = 0.1\ \mu\text{sec}\);
• ○ — \(t = 0.2\ \mu\text{sec}\);
• × — \(t = 0.5\ \mu\text{sec}\);
• △ — \(t = 1\ \mu\text{sec}\);
• \(a\) — for positive polarity of the “rod”;
• \(b\) — for negative polarity of the “rod.”

Fig. 4. Dependence of the energy \(W\) dissipated in the gap, and of the maximum power \(P\) developed in the gap before breakdown, on the resistivity of an aqueous NaCl solution; steepness of the applied pulse \(1000\ \text{kV}/\mu\text{sec}\).

1 — \(W = f(\rho)\) — for positive polarity of the “rod”;
2 — \(W = f(\rho)\) — for negative polarity of the “rod”;
3 — \(P = f(\rho)\) — for positive polarity of the “rod”;
4 — \(P = f(\rho)\) — for negative polarity of the “rod.”

up to \(10\ \text{mm}\) is logarithmic in character. In strong solutions the character of the dependence changes. For an aqueous NaCl solution, the point of inflection corresponds to

\[ N_0 \approx 2\% \quad (\rho = 40\ \Omega\cdot\text{cm}). \]

The study of the currents preceding breakdown made it possible to estimate the energy dissipated in the gap before breakdown,

\[ W=\int\limits_{0}^{t_{\mathrm{br}}} U i\,dt, \tag{6} \]

and the maximum power developed in the gap before breakdown,

\[ P=U_{\mathrm{br}} i_{\mathrm{br}}, \tag{7} \]

where \(U_{\mathrm{br}}\) is the breakdown voltage;
\(i_{\mathrm{br}}\) is the instantaneous value of the current before breakdown.

Figure 4 presents the dependences of the dissipated energy and the maximum power developed in the gap before breakdown, at a voltage-pulse steepness of \(1000\ \mathrm{kV/\mu sec}\). Breakdown occurred at \(t_{\mathrm{br}}=(0.16\div0.28)\cdot10^{-6}\ \mathrm{sec}\). The dependences \(W=f(\rho)\) and \(P=f(\rho)\) shown were obtained by processing 20 oscillograms per point. As is seen from Fig. 4, for the function \(W=f(\rho)\), with different polarities of the “rod,” there are two characteristic regions. At \(\rho>3\cdot10^{2}\ \mathrm{ohm\,cm}\), the value of the energy released in the gap before its breakdown, for negative polarity of the “rod,” is higher than for positive polarity. This is explained, first, by the higher electric strength of the gap for negative polarity of the rod and, consequently, by the longer time to breakdown; second, by the higher value of the average prebreakdown current for negative polarity of the “rod” [10]. At \(\rho<3\cdot10^{2}\ \mathrm{ohm\,cm}\), the value of the energy released in the gap before its breakdown, for negative polarity of the “rod,” is lower than for positive polarity. This phenomenon agrees well with the lower electric strength of the solution for a negative “rod” at \(\rho<10^{2}\ \mathrm{ohm\,cm}\).

The maximum value of the power developed in the gap before its breakdown, for the positive “rod,” lies lower than for the negative one over the entire range of specific resistances studied.

Conclusions

1. It has been established that the impulse electric strength of aqueous dilute electrolyte solutions is determined by the concentration of dissociated molecules of the dissolved substance. The dependence of the impulse breakdown voltage of a dilute solution on its specific “low-voltage” resistance is logarithmic in character.

2. It has been shown that the polarity effect in impulse breakdown of an aqueous solution in a nonuniform field weakens with increasing electrical conductivity of the solution.

LITERATURE

1. N. P. Mel’nikov, G. A. Ostroumov, M. Yu. Stoyak. DAN SSSR, 148, 5, 1963.

2. N. P. Mel’nikov, G. A. Ostroumov, M. Yu. Stoyak. ZhTF, XXXIV 4, 1962.

3. N. P. Mel’nikov, G. A. Ostroumov, Shteinberg. DAN, 147, 4, 1962.

4. Torijama, Shinohara. Phys. Rev., 1937, 51, 580.

5. A. I. Limasov et al. Report on the topic: “Investigation of the impulse electric strength of certain solid dielectrics and liquids.” Siberian Scientific Research Institute of Power Engineering. Tomsk—Novosibirsk, 1963.

1. P. V. Ponomarev, K. S. Ponomareva et al. Report on topic 162 for 1956–1961: “Development of the theoretical foundations, methodology, and technology of drilling wells by means of the electrohydraulic effect.” VITR, Leningrad, 1962.

2. A. N. Matveev. Electrodynamics and the Theory of Relativity. Vysshaya shkola, 1964.

3. N. A. Izgaryshev, S. V. Gorbachev. A Course in Theoretical Electrochemistry. Goskhimizdat, 1951.

4. Edited by Prof. A. A. Vorob’ev. High-Voltage Testing Equipment and Measurements. Gosenergoizdat, 1960.

5. V. S. Komel’kov, DAN SSSR, 47, No. 4, 1945.