Deformation and motion of bubbles at action of strong fields,
S. M. Korobeynikov* A. V. Melekhov**, V. G. Posukh**, V. M. Antonov**, Yu. N. Sinikh*
* Novosibirsk State Technical University
**Institute of Laser Physics, Siberian Branch of RAS
Bubble model of breakdown initiation allows explaining the main dependencies of the electric strength on the pulse duration, pressure, temperature and so on obtained experimentally. It is presumed here, that micro-bubbles initially exist on the surface of electrode, the breakdown is initiated from them, and the impact ionization in liquid could take place only under the action of high electric field greater than 10 MV/cm. The aim of this paper is the study of artificial bubbles at the action of strong field.
Experimental setup consists of: HV system with pulse voltage generator up to 100 kV with pulse rise 200 ns and pulse decay 50 ms; optical system of bubble visualization and photo registration with light pulse duration t~30 ns; system of bubbles generation on the surface of electrodes; the system of synchronization (Fig1).
The generation of microbubbles is carried out by pulse heating of quasi-needle electrode representing U-formed loop from nichrome wire by a diameter 0.2 mm, with radius of a bend of 0.5 mm. The wire is put to earth after the pulse of a current, opposite high-voltage electrode is a plane. Duration of pulses of a current by amplitude up to 3 A varies with the help of the relay of time in a range 0.1-5 s.
Bubbles are not in equilibrium in liquid and dissolve during some time duration ts. This time is proportional to squared radius r2 and depends on the level of air content C. Analyze shows that these data don't contradict model of dissolving of air bubble. This confirms by experiments in tap water, where bubble of 50 mm radius disappears during 6 min., while in slightly saturated water the same one disappears during several seconds. Computations of the threshold of bubble appearance are performed. Experimentally and by computing it is shown that 100-200 mm bubbles are appeared at the surface when the temperature near wire surface is more than boiling temperature.
Past appearance the size of bubble decreases very sharply during one second. After that at the surface of the quasi-needle there is long-lived slightly decreased microbubble by the size 10-100 mm. This bubble is ready for prebreakdown experiments. One should note that in degassed water there no bubbles at current up to 3 A and time duration up to 10 s.
After an establishment of temperature balance near to wire (~ 1 s), or after some period of time delay that necessary for reduction of the sizes too large bubble, to electrode system “quasi-needle - plane” applies a voltage pulse. In this experiments the quasi-needle electrode has "earth" potential, opposite electrode has positive or negative polarity. The intensity of an electrical field near to wire is necessary specially to compute, since for used electrode system there are no analytical decisions. The field at the tip very slightly depends on distance along surface. Field computation at the perpendicular plane leads to the same conclusion. As for as space distribution in vicinity of wire it can be estimate as cylindrical one.
1-test cell, 2- current supply, 3- relay,
The method of bubble behavior study consists of receiving of two pictures of bubbles on wire electrode: the first one before voltage action and the second one at the fixed moment during voltage exposure. Some results at the action of electric field on preexisted bubbles are shown on fig.2 (cathode), 3 (anode). Several formed bubbles of 35-60 mm are on electrode surface. Due to curvature of electrode in direction of laser beam, one can see full size of bubble only for those bubbles that are close to "visible" contour of electrode. One can see that bubbles: elongate in the direction of electric field; decrease in perpendicular direction; can divide on several bubbles (past 5-10 ms); the less bubble size – the more deformation; at the early stages bubble’s surface have some small scaled disturbances; the motion of bubbles at the times about 30-50 ms has EHD nature.
Fig.2. Bubbles configuration on cathode before and
past 4 ms of the action
of electric field
Emax = 300 kV/cm.
Fig.3. Bubbles configuration on anode before and
past 8 ms of exposure of
Emax = 200 kV/cm.
The main peculiarities of cathode bubbles are presented at pictures concerning anode bubbles. One should mention several differences. The first one is that come off bubble has spherical form and stayed part of bubble looks like spread disk or cone on the surface of electrode. These facts are shown on fig. 3. Bubbles number 1,2,3 that are situated close to the visible contour of electrode left flat rest on electrode past removing of the come off bubbles.
The deformation of unionized bubble depends on to radius and field intensity 
Here s is surface tension
coefficient. Relative decreasing of volume is 
Dielectrophoretic force due to difference of dielectric
permittivities of liquid and gas bubble appears in case of inhomogeneity of
electric field , that for axial case is:
where R - distance from the centerline of wire.
The third factor is partial discharges in
bubbles. According to bubble model of breakdown initiation [4,5], equivalent
pressure in the direction of electric field is
P = 3e0eE 2(mEt/r + 1)/2
where m is mobility of space charge in liquid, t - time duration of electric stress.
The last factor that should be considered is instability of
bubbles. There is instability of two kinds. Without electric field lower
frequency of bubble oscillation concerning elongation and dividing of bubble into
two or several bubble correspond
All above mention factors should
increase the frequency of bubble oscillation. Another variant is disturbances
due to instability of charged surface : In case of fully charged bubble
surface, as assumed in bubble model [4,5] its wavelength is
Let's compare the factors. Voltage across the bubbles of size 30-60 mm will be enough for discharge in bubble at the field intensity more than 100 kV/cm. Therefore discharges should be in all of registered bubbles. Coulomb force should be at least factor e (e=80) much more than the force that elongates uncharged bubble. Besides, deformation according (1) is proportional to r, so will lead to higher deformation of large bubbles. It contradicts to experimental data. The dielectrophoretic force in comparison with Coulomb force is less in factor R/r. In our case R/r ~ 4-8. Therefore Coulomb force is more suitable as source of bubble motion.
The comparison of computed and measured elongation is presented at fig. 4. Here it is chosen series of bubble recording at cathode with the bubble r=27±5 mm at field strength 100 kV/cm. On fig.4 it is rectangular marks. Curve 1 is obtained as computation according bubble discharge model. Coincidence of marks and curve 1 is not very good. It is clear that some factor is absent in model. One should note that in model it is assumed fully discharged bubble. It means that electric field in bubble after partial discharge equals zero. More realistic will be assumption that voltage across bubble will be supported at the level of breakdown voltage. In this case the surface charge past discharge in bubble is less approximately 1.5¸3 times. Figure depends on bubble size and field strength. More bubble and field - more surface charge.
Fig. 4. Comparison of computed (curve 1,2) and experimentally measured (rectangular marks) elongation of bubble 55 mm at cathode in electric field 100 kV/cm.
should obtain correct expression due to decreasing of surface charge.
Equivalent pressure that moves bubble wall along field will decrease too
where Up~300 V is Pashen's breakdown voltage. Computation of bubble's elongation according to corrected model is shown on fig. 8 as curve 2. Experimental marks well correspond to model.
As for as bubble's instability one can note a few moments. Bubble divides on two species in 5-10 ms. It is not contradict to expression (5). Observed disturbances have l at least 4-5 mm. Estimations according to (6) give l~0.1 mm. If expression (6) change by analogy with (7), estimation of l give 1-5 mm depending on E and r.
The behavior of artificial micro-bubble at the action of electric stress is studied. The main factors are partial discharges in bubbles at electrical stresses that will lead to surface charge appearance, Coulomb forces, pressure increase and bubble elongation. Bubble instability should be at the time duration more than 5-10 ms approximately. In this experiments electric field is not enough for breakdown initiation in liquid before bubbles dividing.
 Korobeynikov S.M. Deformation of bubbles in electric field. -Ingenerno-Physicheskii Journal, v.36, N5, pp.882-884, 1979 (in Russian).
 Jones T.B., Bliss G.W. Bubble dielectrophoresis. -J. Appl. Phys., V.48, 4, p.1412-1417, 1977.
 S.M. Korobeinikov, “The Role of Bubbles in the Electric Breakdown of Liquids: Prebreakdown processes”, High Temperature. V. 36, No. 3, pp. 362–367, 1998.
 S. M. Korobeynikov, “The Role of Bubbles in the Electric Breakdown of Liquids: Comparison with Experiment”, High Temperature. V. 36, No. 4, pp. 517–523, 1998.
 I.Alexeff, M.O. Pace, T.V. Blalock and A.I. Winterberg. Possible Models for the Earliest Prebreakdown Events in DC Stressed Hexane. Conf. Record of 10 ICDL, Grenoble, France, pp.387-391.
 Authors are grateful to RFBR and Ministry of Education for grants.