Journal o f E lec t ros ta t ics , 2 ( 1 9 7 6 ) 1 7 5 - - 1 8 6 175 © Elsevier Scient i f ic Publ i sh ing C o m p a n y , A m s t e r d a m - - P r i n t e d in The Ne the r l ands

THE INFLUENCE OF ELECTRODE SEPARATION, GEOMETRY AND AN APPLIED MAGNETIC FIELD UPON CURRENT CONDUCTION IN SILICONE OIL

ALAN WATSON and SAMIR S. GIRGIS

Faculty of Engineering Science and Centre for Chemical Physics, The University of Western Ontario, London, Ontario N6A 5B9 (Canada)

(Received September 1, 1975; in revised form January 5, 1976)

Summary

The characteristic variation of pre-breakdown conduction current with voltage has been investigated in L45 silicone oil when the potential was applied as a time-varying linear ramp function with a growth rate of 19 kV/s up to 52 kV. Copper and aluminum electrodes with hemispherical or Bruce profile were employed. Two sharply divided portions of the high field conduction regime displayed a linear relationship between the logarithm of the current and of the voltage while the ultimate slope varied with gap separation according to the conductance law

d( ln V) / d ( ln I ) = C 2 + C2d

The pa rame te r s C2 and C 2 varied w i th the e lec t rode geomet ry for c o p p e r e lec t rodes , bu t a l u m i n u m e lec t rodes d isp layed no t r ans i t i on to this regime. A weak magne t i c f ield o f 3.4 x 10 -3 T ac t ing t ransverse to t he ro t a t i ona l s y m m e t r y axis of the e lec t rodes was suf f ic ien t to raise the value o f the der ivat ive given above for gap sepa ra t ions b e t w e e n 0.6 cm and 1.0 cm, b u t lowered it f r om t h e n on up to 1.4 cm.

The c o n d u c t a n c e law has been s h o w n to be cons i s t en t w i th a m o d e l involving Fowle r - - N o r d h e i m emiss ion f r o m a c a t h o d e site in to a vo r t ex cell wh ich enlarges w i t h t he rising voltage.

1. Introduction

Current conduction and breakdown through liquid dielectrics is a well investigated phenomenon, the complexities of which have been frequently reviewed. Many variables contribute to the variety of the outcome of an experiment, including the geometry and material composition of the electrodes, their surface condition, as well as the nature, purity, and external pressure acting upon the liquid [ 1 ]. The present investigation has concentrated upon the detection of a magnetic influence upon conduction in silicone oil while defining the significance of electrode geometry, material, gap separation and time variant voltage application as determinant factors.

The strongly non-linear nature of the pre-breakdown current versus voltage characteristic in liquid dielectrics has been well known since its description in

176

the early work of Nikuradse [2] . A division of the characteristic is conveniently made into low, intermediate, and high field regions, the latter being at tr ibuted to the injection of charge carriers from the cathode into the liquid. The division is more clearly evident from the log--log plot of the characteristic in which the high field port ion is linear. Analysis of the experimental results of several workers was made by Ostroumov [3] who showed from theoretical considerations that when the liquid is in laminar e lectrohydrodynamic motion induced by charge injection the current should vary as the cube of the voltage. The high field por t ion of the logarithmic current plot was hence shown to have the required slope and, moreover, to revert on occasion to a value of two, indicating the transition to turbulent flow.

Certainly very little at tention has been given to the possible influence of an applied magnetic field upon the conduct ion or breakdown process due to the obvious dominance of other factors. A definite at tenuation of the conduc- tivity was, however, reported by Saveanu and Mondescu in the polar liquids water and ethyl alcohol between 2.0 and 3.0 × 10 -2 T [4] , the effect being undetectable below this as well as in the non-polar liquids benzene and trans- former oil. Further work was carried out by Gallagher [5] who reported small positive increases in the direct breakdown voltage of sphere---sphere and point--sphere copper and aluminum electrode configurations at 100 p separation in pure n-hexane. More significant, however, was the observation of almost no influence upon the pre-breakdown current except when the electric stress was initially applied. This suggests that the rate of growth of electrode processes might be a contributing factor. Secker and Hilton [6] have investigated the magnetic influence upon the breakdown voltage of brass spheres in hexane using a ramp voltage generator with a growth rate of 0.625 kV/s. The results of this were quite definite, indicating that for 100 and 150

gap separations the breakdown voltage increased with magnetic field strength by a maximum of 2.8% or 4% respectively, thereafter decreasing and becoming a negative influence beyond either 0.11 T or 0.15 T, as the cas may be. No comprehensive explanation of these phenomena was proposed except in terms of the probable modifications to electron trajectories within the liquid due to the Lorentz force.

The present investigation of the influence of magnetic fields upon the con- duction current in dielectric liquids has been carried out in L45 silicone off with long gap separations from 0.6 to 1.4 cm. A voltage growth rate of 10 kV/s was provided by a ramp generator with which current versus voltage characteristics were obtained with a fixed magnetic field strength at five different gap separations. The magnetic influence upon the conduct ion current was hence investigated under steadily timevarying conditions when it would seem to be most evident. In addition to complementing the work of Secker and Hilton [6] , this s tudy investigates the importance of the gap separation, in particular the manner in which this defines the magnitude and sign of the influence of a weak magnetic field.

1 7 7

2. Experimental technique and results

Tests were carried out in an acrylic chamber with an internal diameter of 2.25 in. standing 3.5 in. high, the positive electrode protruding from the base as shown schematically in Fig. 1. The negative electrode, attached to a fixed cylindrical stem extending from a corona-free bushing, dipped into the liquid under test and the gap separation was shortened by raising the chamber. A hollow stem screwed to the protruding lower electrode passed through a thick acrylic base to which it was clamped and housed the probe of a Hall effect gaussmeter. Resting upon the base was a four-port cast steel chamber with two mild steel polepieces of 4 in. diameter intruding from steel plates blanking off the two side ports. Internal coils were wound upon spools on the pole- pieces which provided a horizontally directed magnetic field over a distance of 4 in. within which the test chamber was situated. The corona-free bushing was supported from the remaining upper port.

Hemispherically tipped short cylinders of copper were machined to screw on to the bushing and chamber stems. The surface preparation was by mechanical polishing with fine emery cloth (number 320 grade), cleaning with petroleum ether, and final immersion in boiling silicone oil. Preparatory

. o . o

M x YJ Ioo~ i

R CIRCUIT

I H.V.D.C. i~.~ $ U PPLY ~ - II .olo,.,sEo

F i g . 1. G e n e r a l schematic diagram o f e x p e r i m e n t a l equipment. B - 7 5 k V corona free bushing C - magnetic excitation coils M - c a s t steel magnetic y o k e a n d outer chamber O - s i l i c o n e o i l , c h a m b e r a n d test electrodes P - p o l e p i e c e s

178

vacuum filtration of the L45 silicone oil was carried ou t through a 1.2 ~ pore size Millipore filter.

Preliminary experiments using a chart recorder verified that the conduct ion current decayed from its initial value upon voltage application in times of the order of one minute after which no magnetic effect was discernible from the randomly fluctuating signal. This absence of an effect was thought to be the result of the development of electrode surface processes and occurred similarly in carbon tetrachloride. Continued voltage application with the latter liquid led to chemical attack of the electrodes, rendering it unsuitable for reliable measurements.

After preparation of the oil and electrodes as described above, each set of tests was begun with an initial conditioning procedure by setting the maximum voltage excursion at 10 kV and running the voltage up and down in 15 successive complete cycles. This was repeated in 10 kV steps up to 50 kV and then at 52 kV, an arbitrarily chosen safe maximum with minimum likelihood of sparking and subsequent contamination of the liquid by jelly and particulate matter. At 52 kV a set of 15 consecutive plots of current versus voltage were recorded, superimposed upon each other on graph paper with the x--y recorder (Fig. 2). This permitted an estimate to be made of the statistical scatter of the data due to short term stress conditioning. The liquid was subjected to 50 further cycles wi thout recording data and then a second set of 15 recordings were made. In this manner four sets of 15 superimposed data plots were made

0p I :°V/./"'

.-.or/ ./-

0 1 2 3 4 5

I x Io ' AMP

Fig. 2. Voltage v e r s u s current characteristics for fifteen consecutive stress cycles. (1) Voltage rising; (2) voltage falling.

179

with 50 interspersed cycles in each case wi thout record. This permit ted an estimate to be made of reproducibility over longer intervals of stress conditioning.

The appearance of Fig. 2 shows that the measured current differs according to whether the voltage is rising or falling in time, the difference being due to the fact that the displacement current in the system reverses on the return half of the cycle. In order to separate the conduct ion current from this data it is only necessary, therefore, to plot the average current for any particular applied voltage, as indicated by the intermediate dots in Fig. 2. Assuming that conditioning has no significant influence upon the conduct ion from one half of a cycle to another, this is a valid procedure. Some confidence in the veracity of this assumption is gained by observation of the relatively good reproducibility over 15 cycles. After extraction of the conduct ion current in this way the results were replotted in logarithmic form as a function of the logarithm of the applied voltage as shown in Fig. 3 (the Ostroumov plot).

4 . 0

2 - 0

f'O n :E

0.5 ®o

X

0'2

C ~ ' , ~ / E S T 1 /3// HEMISPHERICAL COPPER

/ / GAP O-6¢m ~ ~ A I ZERO TESLA

I 1 L I I I

2 5 tO 20 50 1OO V, KV

Fig. 3. The Ostroumov plots for hemispherical copper and aluminiura electrodes.

This procedure was carried out for five different gap separations varying from 0.6 cm through to 1.4 cm in 0.2 cm intervals. The data showed in all cases that there were low and intermediate field conduct ion regions with no apparent features wor thy of at tention from the standpoint of this investigation. A distinct and quite sharply defined division of the high field conduct ion region was, however, evident in every test, the curve being composed of two intersecting linear portions of different slope. The slope of the final port ion was observed to vary with the gap separation and its inverse value is shown plotted as a function of gap separation in the curves of Fig. 4, all 4 of which were obtained from four sets of tests with no applied magnetic field. Each

180

(1)

1-01.10-9 . ~ . ~ . . . o ~

¢ " ~ O ' S

~ ( c • 0E. :ROF/LEm cOPPER 0 ' 6

O . 5 I I I I I

o 0-4 o.e ~.2 ~.6 2.0 d , cm

d(ln V) Fig. 4. - - for copper as a func t ion o f gap separat ion for hemispherical and Bruce

d(ln I) profi le electrodes.

of the four curves indicates an accurately linear relationship between the slope representing the derivative d(In V)/d(ln I) and the gap separation. A linear relationship appeared in each case, bu t with the slopes and the ordinate intercepts varying somewhat. Of particular interest is the fact that each point on any line was obtained from a particular range of 15 test cycles, the four being from cycle numbers 1--15, 65--80, 130--145, or 195--210 after the initial short conditioning procedure.

The complete procedure described in the preceding paragraph was carried out with an applied magnetic field of 3.4 × 10 -3 T and after data reduction the slopes representing the exponent d(ln V)/d(ln I) appeared as shown in Fig. 5. In this case the linear relationship between the slope d(ln V)/d(ln I) and the gap separation had disappeared, giving way to a set of curves which were always concave to the abscissa. These data were in fact obtained in the residual field due to remanence in the equipment iron circuit, a coercive force being necessary to obtain the data under strictly non-magnetic conditions.

The slopes of the initial linear port ion of the high field region demonstrated no obvious relationship to the gap separation or magnetic field strength and varied by a factor of two or more from test to test. The slopes were generally lower for larger gap separations (Fig. 6).

181

1 " 0

0 . 9

>J1'-40.8

0 . 7

0.6

/ / / / /

IN .-"

/ / /

HEMISPHERICAL COPPER GAP 0 " 6 - - 1 . 4 ¢ m 0.0034 TESLA

0 " 5 I__ [ _ _ _ I __ [

o o~ o,o 1-z 1.6 d ,cm

d(ln V) Fig. 5. as a function of gap scparation for four successive sets o f 15 recordings in

d(ln I) the presence of a weak magnetic field. The broken line indicates comparative curve in the absence of a magnetic field (reproduced from Fig. 4 for comparison).

--=--=20 "~1"o

1 . 0

0 1

0 - 4

d o n V)

"1 o 2

" 3 = 4

1 1 1 l

0'8 1"2 l"S d

Fig. 6. for the initial linear portion of the high field conduction regime illustrating d(ln I)

no obvious relationship to the gap separation. Numbered points illustrate successive sets of 15 consecutive stress cycles.

182

The pre-breakdown conduct ion characteristic for a pair of hemispherical aluminum electrodes pretreated in the manner described above was investigated in the same liquid. Only one linear port ion of the high field conduct ion regime was observed, as shown in Fig. 3.

3. Discussion and theory

3.1 General comments After reviewing the results of the first reported data by Saveanu and

Mondescu [4] , Gallagher proceeded in this investigation [5] to extend the range of measurements to greater magnetic field strengths as high as 0.22 T. Secker and Hilton, on the other hand, measured the magnetic perturbation of the breakdown voltage to as low a flux density as 1.5 X 10 -2 T at which the effect seemed to be most prominent [6] . Each of these studies were carried out in hexane with electrode materials as diverse as brass, copper, and aluminum without , however, positively confirming the existence of a magnetic perturbation of the conduct ion process itself. The results of the investigation presented here confirm the existence of such an effect, bu t assert its presence down to magnetic flux densities as low as 3.4 X 10 -3 T. In magnitude and sign, moreover, the perturbation is strongly dependent upon the gap separation, the range of which is much wider than those investigated in hexane which, like silicone oil, is nompolar. The "conduct ivi ty" , if this is represented by the conductance exponent d(ln I)/d(ln V), is at tenuated for low electrode separations, but the perturbation is reversed for longer gaps. In the initially reported experiments [4] only an attenuation of the conductivity was dis- covered and, moreover, solely in polar fluids. In general agreement with Gallagher's experience, no effect was discernible with direct voltage application after the initial decay of conduct ion current to its steady state average value. The successful detect ion of a magnetic perturbation followed upon application of a ramp voltage in the manner reported by Secker and Hilton [6] , suggesting that it was attributable to processes occurring during the approach to a steady state.

Phenomena at tendant upon the approach to steady state conduct ion have been studied by Croitoru [1] in monochlorobenzene using the electro-optical Kerr effect. Initially it was found that the electric field strength at both electrodes was reduced, indicating the injection of charges at each electrode of the same sign as that of the electrode itself. This phenomenon was ex- tensively studied by Guizonnier and co-workers, whose results have been re- viewed [ 1 ]. Certain highly viscous dried oils, to which group silicones belong, were considered prone to exhibiting this behaviour and were classified as being "homocharge liquids". Croitoru discovered that the rate of growth of the cathode space charge due to electron injection was higher than that of positive charges at the anode and quickly masked its influence as the fluid proceeded to the steady state in a few seconds. It seems more appropriate,

183

therefore, to view the magnetic perturbation of conduction processes from the standpoint of the Guizonnier classification of liquid dielectrics as opposed to grouping them into the polar or non-polar categories.

The linear graphs in Fig. 4 indicate that the conduction law in the ultimate high field regime may be expressed by the equation

d(ln V)/d(ln I) = C1 + C2d (1)

where d is the gap separation and C1, C2 are constants which have average values for hemispherically tipped cylindrical electrodes of 0.71 and 0.17 cm -1 respectively.Thus it appears that conduction is determined by two terms, only one of which is dependent upon the gap length. The statistical scatter of the data is surprisingly low for each graph of d(ln V)/d(ln I) as a function of gap separation in view of the much greater standard deviation of the overall average. Only two points in four lines fall outside of one overall standard deviation from the line itself. This testifies to the level of repro- ducibility attainable with the technique, moreover indicating that a level of conditioning is achieved according to the number of stress cycles which have been sustained. In the same manner a level of confidence is achieved in the reproducibility of the data when a magnetic field is present. No comparable confidence can be placed in the reproducibility of the slopes of the lower linear portion of the high field conduction regime, as shown in Fig. 6, from which it must be concluded that a degree of control is required beyond that which is possible with the existing procedures.

A set of data was also obtained with a pair of copper electrodes with Bruce profile in *~he manner outlined above and the average straight line was obtained relating d(ln V)/d(ln I) with d. The results were similarly accurate, but the slope and ordinate intercept differed in each case as is evident from Fig. 4. The values of C1 and C2 in this case were 0.95 and 0.09 cm -~ respec- tively.

3.2 Theoretical considerations The behaviour expressed by the equation above may be accounted for

in terms of the Fowler--Nordheim equation for field emission of electrons into the liquid dielectric. Conduction current may be assumed to consist wholly of electrons injected in this way from an emission site on the cathode with area ~ and where the local field strength Es in a uniform field system is given by -~ V/d, ~ being the field intensification factor. Thus

I = ~AEs 2 exp(-S /Es) (2)

where A and B are the Fowler--Nordheim constants. Changes in this current occur when the voltage is raised and hence

d l n / _ d In Es 2 1 + (3)

d i n V d l n V

184

This may be approximately given as

d l n I - \ d l n V 1 + d (4) 2 ~ V

where Es is given by -~ V/d. This equation is of the form of eqn. (1) under the following conditions:

d In Es 2 . . . . const. (5) d l n V

~V = const. (6)

Electrons may be considered to be emitted radially from the centre of curvature of the tip of a cathode protrusion with radius rs and over an area

= 2~(1 - cos 0 ) which is defined within a conical sector of half angle 0 [7] . Fluid is furthermore considered to flow in a vortex cell enclosing a steady irrotational funnel flow through i t score as shown in Fig. 7. Negative charge is trapped in the moving core of liquid dielectric and the space charge is contained laterally by the tendency of the vortex ring to resist stretching by the outward component of the electrostatic Maxwell stress.

Upon raising the applied voltage the Maxwell stress from this space charge will increase and extend the vortex. If the consequent rate of change of vorticity ~ is slow the Navier--Stokes equation reduces to a diffusion equation in vorticity [8] . The funnel consequently expands into the stationary fluid

CATHODE

i

ANODE

Fig. 7. Schemat i c i l lus t ra t ion of cu r r en t and f luid f low conf igura t ion . V o r t e x w i th s t r eng th w creates a cu r r en t c o l u m n expans ion to d i ame te r k a f te r emiss ion f r o m a c a t h o d e pro- t rus ion . The i nne r cyl indr ical c o l u m n i l lust ra tes c u r r e n t channe l be fore the vor t ex is developed. The funne l w i d t h and d e p t h are s h o w n to be equal so t h a t k /2 appears a rb i t ra r i ly equa l to the radius rf of the m o u t h .

185

at a rate dx2/dt which is equal to the dynamic viscosity 77. Liquid flows into the funnel across its boundary at the cathode with velocity v and laterally outward at the mouth , bu t the inertial stress, proport ional to the vector cross product ~ X ~ , is oppositely directed at the two locations. The axial Maxwell stress gradient in equilibrium with this is hence also oppositely directed at the cathode and the funnel mouth , signifying the presence of opposing potential gradients if the space charge to mass ratio is fixed. The funnel mouth may hence become a virtual cathode and Es can be redefined in terms of the reduced gap separation x = d - X/2 (Fig. 7} so that/3V is equal to Esx. Fluid flows away from the tip upon charge injection so that dx /d t is equal to the drift velocity Ud = bEs where b is the electronic mobili ty. Thus

- ~ V = Esx = (Es/Ud)(~/2) = ~?/2b (7)

and the assumption of eqn. (6) is validated. At the funnel mouth with area ~r~, the current I drifting to the anode is

given by ltr~ PeV/x where Pe is the charge density and rf is the funnel mouth radius. Equating this with the Fowler--Nordheim expression in eqn. (2) and replacing Es 2 by 2Pe V/e, it follows that

br~ 2A ( 2 B b x ) - x e x p - - ~ - , (8)

2rs 2 (1-cos0) e

Thus, if rf and rs sin0 are equal, the funnel is a simple cylinder and no vortex will exist, as shown in Fig. 7. A critical value xc may be found from above to make the left hand side of eqn. (8) equal to b(sin0 ) /2(1-cos0 ), being defined only by the physical constants of the dielectric fluid and the protrusion para- meters. Thus below a characteristic gap separation, Ohmic conduct ion persists, with no virtual cathode, and d(ln I)/d(ln V) is unity so that eqn. (4) becomes

d(ln E~)/d(ln V) = 1 + (Bb/~)x c (9)

and the assumption of eqn. (5) is validated.

4. Conclusions

The model given above for the charge transport mechanism will adequately account for the linear variation of the derivative d(ln V)/d(ln I} with gap separation for uniform field electrodes stressed by a voltage rising linearly in time. For sufficiently low values of applied potential the/~V product can no longer be constant, since the field enhancement factor will possess an upper limit imposed by the protrusion geometry when the retarding space charge field has totally declined. There is, hence, a low voltage limit below which a virtual cathode cannot exist and upon exceeding it the vortex cell is fully developed. This will account for the presence of sharply differentiated portions of the high field regime observed in the Ostroumov plot.

When a weak magnetic field is applied transverse to the axis of rotational

186

symmetry of the electrode system, the derivative d(ln V)/d(ln I) no longer varies linearly with gap separation. The experiments of Secker and Hilton [6] indicate a perturbat ion of the breakdown voltage value for liquid hexane in a magnetic field under similar conditions. Evidence exists moreover that the static breakdown voltage of copper electrodes in vacuum is perturbed in quite an analogous manner [9] , presumably suggesting that these effects originate in the field emission mechanism itself rather than in the intervening dielectric.

Acknowledgements

The work presented here was carried out under a grant from the National Research Council of Canada.

Nomenclature

Vector quantities are denoted by the tilde (~) written below the symbol, e.g. vorticity is given by ~.

The vector cross product of vorticity and velocity is written as ~ × ~.

References

1 A.A. Zaky and R. Hawley, Conduction and Breakdown in Mineral Oil, Peter Peregrinus Ltd., on behalf of the Inst. Electr. Eng., London, 1973.

2 A. Nikuradse, Das Flussige Dielectrikum, Springer-Verlag, Heidelberg, 1934. 3 G.A. Ostroumov, Results of measurements of the electrical conductivity of insulating

liquids, Soy. Phys.-JETP, 14 (1962) 317. 4 L. Saveanu and D. Mondescu, Phenomenes de conduction dans les liquides isolants,

Grenoble, 1968, p. 385. 5 T.J. Gallagher, The influence of a magnetic field on the breakdown of a liquid, Proc. 4th

Int. Conf. on Conduction and Breakdown in Dielectric Liquids, Dublin, 1972, p. 210. 6 P.E. Secker and K.J. Hilton, Measurement of breakdown stress in hexane subjected to

a transverse magnetic field, Proc. 4th Int. Conf. on Conduction and Breakdown in Dielectric Liquids, Dublin, 1972, p. 206.

7 P.A. Chatterton, Theoretical study of field emission initiated vacuum breakdown, Proc. Phys. Soc., 88 (1966), 231.

8 D.E. Rutherford, Fluid Dynamics, University Mathematical texts, Oliver & Boyd, Edin- burgh, 1959.

9 A. Watson, Magneto surface effects in vacuum breakdown, Proc. 4th Int. Syrup. on Dis- charges and Breakdown in Vacuum, Waterloo, 1970, p. 18.