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Corona from bursting bubbles
Atmospheric Research, 26 ( 1991 ) 329-338
329
Elsevier Science Publishers B.V., Amsterdam
Corona from bursting bubbles M. Khaleeq-ur-Rahman a and C.P.R. Saunders b ~Physics Department, University of Engineering and Technology, Lahore-31, Pakistan bDepartment of Pure and Applied Physics, UMIST, P.O. Box 88, Manchester M60 1QD, UK (Received July 13, 1990; revised and accepted December 10, 1990 )
ABSTRACT Khaleeq-ur-Rahman, M. and Saunders, C.P.R., 1991. Corona from bursting bubbles. Atmos. Res., 26: 329-338. The phenomenon of bubble bursting in the presence of high electric fields has been studied with the intent of determining the critical field for corona initiation. Various bubble sizes were produced in a solution of sodium chloride in order to model conditions under oceanic thunderstorms. The results show that the corona threshold is inversely dependent on the bubble diameter. The quantity of charge transferred during a corona event was measured and was found to depend on the bubble size and the electric field strength. This process could be one of the effective charge transfer mechanisms over the oceans under thunderclouds.
RI~,SUMI~
On 6tudie le ph6nom~ne d'6clatement d'une bulle en pr6sence de champs 61ectriques 61ev6s en vue de d6terminer la valeur critique n6cessaire au d6clenchement de l'effet couronne. Afin de se placer dans des conditions d'orage maritimes, on produit des bulles de diff6rentes dimensions dans une solution de chlorure de sodium. Les r6sultats montrent que le seuil critique de l'effet couronne est en relation inverse avec le diam~tre de la bulle. La quantit6 de charge transf6r6e lors d'un effet couronne a 6t6 mesur6e, et on trouve qu'elle d6pend de la dimension de la buUe et de l'intensit6 du champ 61ectrique. Ce processus pourrait constituer un m6canisme efficace de transfert de charge au-dessus des oc6ans sous les orages.
INTRODUCTION
M a n y research workers have made both experimental and theoretical studies of bubble bursting phenomena and have examined its importance as a
0169-8095/91/$03.50
© 1991 - - Elsevier Science Publishers B.V.
330
M, K H A L E E Q - U R - R A H M A N A N D ( '.P.R. S A U N D E R S
source of large airborne salt particles in the atmosphere. Woodcock et al. (1953), Blanchard ( 1955, 1963), and Joraide (1976) have also discussed the contribution of bursting bubbles towards the charge transfer between the oceans and the atmosphere, the bursting bubble produces a jet which breaks up into droplets ejected from the tip and also into film droplets ejected from the sides of the jet. The droplets ejected from the tip carry a positive charge whose source is the electrical double layer on the water surface. The presence of a substantial electric field in the atmosphere will induce additional electric charge in the ejected droplets. Latham ( 1975 ) has suggested that corona discharges from bursting bubbles may also be one of the effective charge transfer mechanisms over the oceans under thunderclouds. He suggested that corona may be produced at the tips of jets resulting from the bursting of bubbles and he emphasised the need for further work. This paper presents results of an investigation into the conditions under which corona is produced from bursting bubbles and the charge transferred during corona events. Bubbles of seven different sizes in the range 2-13 m m diameter were produced by forcing air through glass capillaries of different diameters. The capillaries were placed in sodium chloride solution of sea-salt concentration, (0.6 mole/l ), so that the individual bubble production mechanism at the air-water interface was representative of bubble phenomena on the open sea. APPARATUS The experimental set-up for the present study is shown in Fig. 1. It includes a metal enclosure, a hide, and a bubble production mechanism. The enclosure, hide, and all other metal parts were earthed to form an electrostatic shield in order to minimise electrical noise. The metal enclosure was made from a steel drum, 0.91 m in diameter and 1.83 m high painted black on the inside to aid the photography of the bursting bubbles. An earthed wire mesh on conducting foil was placed both on the floor and at the top of the d r u m to provide
observer's hide etectrode ....
~uid:
to charge detector and oscilloscope
:-~!.
cameras and photornu|tip[ier
power supply oir input
screened cage
Fig. 1. The bubble production and bursting apparatus,
CORONA FROM BURSTING BUBBLES
331
electrostatic shielding. Inside the enclosure, a black plastic bucket of 31 cm upper diameter and 23.5 cm lower diameter was placed on an insulating block and was filled with the target liquid to a depth of 24.3 cm. A copper wire passed through the side of the bucket to provide an effective electrical connection to the positive terminal of a high-voltage power supply placed outside the enclosure. A copper disc of 22 cm diameter formed the upper electrode which was m o u n t e d on insulators 10 cm above the salt water surface. The edges of the upper plate were covered with insulating rubber to avoid any corona discharges, this upper electrode was connected to a storage oscilloscope through a charge detection circuit which were both placed outside the enclosure. Thus the direction of the electric field is the same as is found under thunderstorms. A hide was built around the experimental area to contain the corona detection equipment, the cameras and the observer. The hide was lined with blackout cloth and was covered with conducting foil to provide electrostatic shielding. A photomultiplier, placed inside the hide, was used to confirm the occurrence of luminous activity associated with the corona discharges from bursting bubbles. The photomultiplier assembly contained an EMI 9558 type multiplier tube and an amplifier with a variable gain. The photomultiplier tube was a 5 cm diameter, fiat faced, end window tube with a 44 m m cathode and 11 dynodes having CsSb secondary emitting surfaces. As the photomultiplier was affected by fields, the whole assembly was placed in a metal cylinder to provide an electrostatic shield. A lens was fitted at one end of the cylinder, facing both the cathode of the photomultiplier tube and the region under observation. The output from the photomultiplier was fed into an oscilloscope which was placed outside the hide. Bubbles were produced by supplying filtered air from a compressed air cylinder placed outside the hide, to a glass capillary. The air supply was controlled through a fine valve to provide pressures in the range 2 X 104-5 × 104 Pa so that single bubbles could be produced at the desired rate of one every eight seconds. The capillaries had previously been drawn into fine points of various diameters. Bubbles smaller than 4.75 m m diameter were produced by keeping the capillary tips immersed in the liquid at a depth of 12 cm in the upward direction as shown in Fig. 1. However, for larger bubbles, open-ended glass tubes of various diameters were immersed in the liquid in the downward direction. The diameters of the bubbles produced by the above mechanism were measured by photography. An arrangement for this purpose included a perspex tank which temporarily replaced the black vessel so that the bubbles could be viewed through the side. Bubbles of various diameter were produced and illuminated by diffused light while a 35 m m camera fitted with a zoom lens was used to determine their size which was in the range 2-13 m m diameter. A charge detection amplifier was used to measure the charge transferred
332
M. KHALEEQ-UR-RAHMAN AND C.P.R. SAUNDERS
during the corona events. Connected to an operational integrator, the signal went directly to the inverting input which was a virtual earth. Therefore, the arrival of charge q at the input will give an output voltage of magnitude q/C where C is the feedback capacitor. An advantage of using the virtual earth of an operational amplifier is that any stray capacitance is negligible and that the input device itself does not "see" the output voltage pulse since the latter appears at the opposite side of the virtual earth. A C-MOS 7611 was used, having an input impedance of 1012 ohms with low input bias current; values of R, the feedback resistor, and C were 108 ohms and 100 pF respectively. A chart recorder was used to record the charge transferred. OBSERVATIONS AND RESULTS
The bubble bursting phenomenon is too rapid to observe with the naked eye. However, the droplets produced from the resulting jet at the top of their trajectories were quite visible. The formation of a jet during bubble bursting is the principal mechanism by which droplets are ejected into the air, as suggested by Stuhlman ( 1932 ) and confirmed by Kientzler et al. ( 1954 ), using high-speed photography. Observations clearly revealed that the physical behaviour of bubbles is very much similar to that described by the earlier workers. The surface life of the bubbles before bursting, was found to vary from 0.5 to several seconds, depending upon their size. Measurements of the maximum height of the top droplet from disintegrating jets due to bursting bubbles were also made. This was done by moving the upper plate up and down until the top jet droplet just touched and was captured by the plate, this was repeated several times for each bubble size. It was found that as the bubble size increased beyond 2 mm diameter, the corresponding maximum droplet height decreased. In the present case, only ejecting heights up to a bubble size of 4.75 m m were measured because larger bubbles produced jets which did not break up into droplets. Results of the maximum top jet droplet heights for bubbles of three different sizes are shown in Fig. 2, together with a compilation of data by Blanchard ( 1963 ) from several sources. Stroboscopic observations confirmed the presence of film droplets as reported by earlier workers. In the absence of an electric field, these tiny droplets, produced due to the shattering of a bubble film, were found not to move upward by a substantial amount. Blanchard and Syzdek ( 1988 ) showed that film droplet production showed a maximum production rate for bubbles in the range 2-2.5 mm diameter. The corona threshold (Ec) for a bubble of diameter (D) is designated as the field strength at which 20% of the bursting bubbles resulted in corona as detected by the photomultiplier. In order to rely on the photomultiplier signals, great care was taken to check the insulation of the system and the dark-
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ness in the hide; the bubble production was stopped and high electric fields were applied across the gap in order to detect stray corona. After making sure that there was no signal from the photomultiplier, the experiments were continued. So, the present experimental arrangement proved to be more reliable than that of earlier workers: Blanchard ( 1963 ) mentioned the inadequacy of his system for the study of bursting bubbles in high electric fields while he was studying the induction charging of jet droplets from bursting bubbles. Visual observations of corona discharges produced at the tip of a jet due to a bursting bubble revealed that these are of the same nature as noted by Khaleeq-ur-Rahman and Saunders ( 1988 ) in their studies of corona from splashing water drops. As the field was further raised above the corona threshold, a stage was reached where corona, both from smaller and larger bubbles, could be seen with a dark adapted eye. Observations were made by applying electric fields between 1 and 3 kV c m - 1. The electric field caused bubbles to remain for a longer time, depending on their diameter, at the liquid surface and their surface life increased with increase in the electric field. Drops both from disintegrating jets and shattering films were found to move upward to considerable heights while levitated by the electric field. In the case of a bubble of 4.75 m m diameter, the m a x i m u m top jet droplet height increased from 3.8 cm (in the absence of field) to a height of 8 cm in the presence of an electric field of 1 kV c m - ~. By further increasing the field to a value of 2 kV c m - 1, the top droplet reached a height of 15 cm. No measurements regarding the top droplet height for smaller
3 34
M. KHALEEQ-U R-RAHMAN A N D C.P.R. SAU NDERS
bubbles were made as it was not possible to raise the top electrode further. For larger bubbles for which, in the absence of an electric field, there were no jet droplets observed, a number of small droplets were found to reach the upper plate (kept at 10 cm) in the presence o f an electric field o f I kV c m - l . The life-time of bubbles on the surface, for constant size and field, varied between/min and/max. For a particular field value,/max increased with the bubble diameter. Figure 3 represents such variations in/max with bubble diameter at three field values. The corona thresholds (Ec) for bubbles o f different diameters were found to vary inversely with the bubble diameter as shown in Fig. 4. All the mea15
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335
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surements were made from the bursting of single bubbles of each size. It was found that the gap between the upper plate and the liquid surface did not affect Ec showing that the field was uniform. Measurements of charge transferred during each corona event at a field strength E ( > Ec), showed a range of values. So, for each bubble diameter, charge transferred during 50 corona events was measured at each value of field. Plots of the mean charge as a function of the electric field for bubbles of different diameters are shown in Fig. 5. For all the bubble diameters, it is evident from the plots that the mean charge transferred varies exponentially with electric field. Some measurements of charge transfer below Ec were also made for different bubble diameters which revealed only small charges on the small droplets produced by the disintegrating jets and shattering films. The droplets were levitated by the field and reached the upper plate even for large plate separations. It was found that at each field value the a m o u n t of charge transferred increased with the surface life of a bubble. With increase in electric field, coalescence between bubbles on the surface also increased, which resulted in a single bubble of a larger diameter giving rise to increased charge transfer. DISCUSSION
The behaviour of a bubble on a liquid surface is affected by the field. In the absence of any field, when a bubble reaches the liquid surface, it develops a thin cap which drains, thins, and bursts to leave a cavity. Fragments of the film are thrown out and are dragged upward by the air escaping from the bubble orifice along with the droplets from a disintegrating jet. Now, in an electric field, in addition to the upward directed buoyancy force, there is also
336
M. KHALEEQ-UR-RAHMANAND C.P.R, SAUNDERS
an upward force due to the field acting on the induced charges which will prevent the film cap draining and thinning. So, a longer time will be required for the surface tension forces to overcome these forces, after which a bubble finally bursts releasing charged droplets which are levitated in the field. In disturbed weather conditions, high electric fields associated with thunderstorms and perhaps show showers at sea would induce high positive charges on the ejected fragments due to bubble bursting (Blanchard, 1963 ). The fragments may then be carried by the turbulent mixing and convective updraughts into the positive regions of the storm, thus increasing the amount of positive charge in the 'core'. This may cause an increase in the electric field at the cloud surface as suggested by Vonnegut ( 1955 ). Wilson and Taylor ( 1925 ), and Macky (1930), have studied the bursting of isolated soap bubbles, not floating bubbles, resting on a plate in the presence of uniform electric fields, they found that the critical field required to produce disruption of a bubble is proportional to (surface tension/bubble radius) °5. In the present case, an inverse dependence of Ec on D was also noted and is shown in Fig. 4. However, a linear relationship is a best fit to the data, given by an empirical relationship, Ec X 1 0 - 5 = 3 . 4 8 5 - 0 . 1 1 2 D
( 1)
where Ec is in V m - ~and D is in mm. The above relationship between corona threshold and bubble diameter is in accordance with the prediction made from the theory of bursting bubbles. When a bubble bursts, a jet rises which then disintegrates into droplets. Many research workers, including Hayami and Toba ( 1958 ), and Blanchard ( 1963 ), have reported that the efficiency of droplet production decreases as the bubble diameter increases, while Knelman et al. (1954), Mason (1954), Blanchard (1963), Day (1964) have confirmed that for large bubbles ( > 4.75 mm, from the present experiments), the jet is formed but does not disintegrate into droplets. The jet height increases with bubble diameter and so the tall jet from a large bubble will lead to considerable field intensification at the tip and so will require a smaller field to initiate corona. The resulting jet from a small bubble ( <4.75 m m ) after disintegration, will be of a lesser height which in turn will require a higher field to initiate corona. This is all commensurate with the observed inverse dependence of critical field on bubble diameter. The aim of the present study was to investigate the electric fields needed to initiate corona from bursting bubbles of different diameters and to measure the associated charge transferred. The results reveal the occurrence of corona discharges along with the charge transfer for bubbles of diameter 2-13 mm. Blanchard and Woodcock (1957) obtained bubble distribution data from white caps near the shore which do not represent the bubble spectrum over the open sea. It would be most revealing, as suggested by Blanehard ( 1963 ),
CORONA FROM BURSTING BUBBLES
337
if bubble distribution data could be obtained on the open sea as a function of wind speed and as a function of time after a white cap has formed. He also suggested that the bubble spectrum for high winds would be significantly altered in shape from that for low winds. An estimate of the global importance of these results may be made by use of the calculations of Blanchard ( 1963 ) who estimated the ocean-air current due to charged droplets produced by bubble bursting. He determined a worldwide current of order 100 Amps caused by positive charge on the droplets. Due to the electric field under thunderstorms, some droplets become additionally positively charged by induction and the world-wide effect of this was calculated to be of order 10 Amps. For this latter calculation Blanchard performed experiments in which the charge on droplets produced by bubbles bursting in a field was determined. His field strength was below the critical field required for corona breakdown. Induced charges may be represented by an equation of the form q = k E r z where k = 8.8 X 10-10 from Blanchard's data, with q in Coulombs, E in volts per metre and r in metres. Blanchard ( 1989 ) showed that a 2 m m diameter bubble produces a 150 a m radius droplet for which the theoretical induced charge in a field of 2 × 105 V m - ~ is 4 pC. The present results show that the charges measured during the bursting of 2 m m bubbles in a field of 2 × 105 V m - i , a r e around 1.5 pC. Thus, it appears that the small drops in these experiments are receiving a charge due to breakdown of the same order of magnitude as the induced charge. The most important drop sizes for their effect on global charge transfer over the oceans, are in the range 10-100 p m (Blanchard, 1963 ). Thus for these sizes, it seems that calculations based on the induced charges are adequate and so Blanchard's estimate of the global charge effects due to bubble bursting under thunderstorms requires no revision from his value of 10 Amps. However, for bubbles larger than 4.75 m m diameter which do not break up into droplets, there will be no induced charge transfer; the corona discharge mechanism does apply to these large bubbles and substantial charge is released as can be seen from Fig. 5. However, there is a lack of evidence regarding the actual distribution of bubbles on the open sea as a function of various factors, without which no meaningful estimate of the total charge transferred during corona from bursting bubbles at the ocean surface can yet be made. Large bubbles may be present at the ocean surface during disturbed weather conditions. Both the present study and that made by Hallett and Christensen (1984), reveal that during splashing of large water drops ( > 2 m m diameter), about 50% of the splashes result in the formation of bubbles of a few centimetres diameter. These bubbles remain at the surface for a few seconds. So, the present results have relevance to the initiation of corona discharges from large bubbles produced due to the splashing of large rain drops at the ocean surface. In the light of the above discussion, it is suggested that corona from burst-
338
M. KHALEEQ-UR-RAHMANANDC.PR. SAUNDERS
ing b u b b l e s m a y b e a n a d d i t i o n a l s o u r c e o f c h a r g e at t h e sea s u r f a c e u n d e r o c e a n i c t h u n d e r s t o r m s w h e r e h i g h v a l u e s o f e l e c t r i c field a r e p r e s e n t . ACKNOWLEDGEMENTS Khaleeq-ur-Rahman wishes to thank the Ministry of Education, Government of Pakistan for financial support and the University of Engineering and Technology, Lahore, for leave of absence.
REFERENCES Blanchard, D.C., 1955. Electrified droplets from the bursting of bubbles at an air-sea water interface. Nature, 175: 334-336. Blanchard, D.C., 1963. The electrification of the atmosphere by particles from bubbles in the sea. Progr. Oceanogr., 1: 7 t-202. Blanchard, D.C., Woodcock, A.H., 1957. Bubble formation and modification in the sea and its meteorological significance. Tellus, 9 (2): 145-158. Blanchard, D.C. and Syzdek, L.D., 1988. Film drop production as a function of bubble size. J. Geophys. Res., 93: 3649-3654. Blanchard, D.C., 1989. The size and height to which jet drops are ejected from bursting bubbles in seawater. J. Geophys. Res., 94:10999-11002. Day, J.A., 1964. Production of droplets and salt nuclei by the bursting of air bubble films. Q. J. R. Meteorol. Soc., 90: 72-78. Hallett, J. and Christensen, L., 1984. Splash and Penetration of drops in water. J. Rech. Atmos., 18(4): 225-242. Hayami, S. and Toba, Y., 1958. Drop production by bursting of air bubbles on the sea surface ( 1 ). Experiments at still sea water surface. J. Ocean Soc. Jap., 14:145-150. Joraide, A.A., 1976. The electrification and size of jet droplets from bursting bubbles at an airwater interface. Thesis, Univ. Durham. Khaleeq-ur-Rahman and Saunders, C.P.R., 1988. Corona from splashing water drops. J. Atmos. Terr. Phys., 50: 545-555. Kientzler, C.F., Arons, A.B., Blanchard, D.C. and Woodcock, A.H., 1954. Photographic investigation of the projection of droplets by bubbles bursting at a water surface. Tellus, 6 ( 1 ): 1-7. Knelman, F.H., Drombrowski, N. and Newitt, D.M., 1954. Mechanism of the bursting of bubbles. Nature, 173: 261. Latham, J., 1975. Possible mechanisms of electrical discharge involved in biogenesis. Nature, 256: 34-35. Macky, W.A., 1930. The deformation of soap bubbles in electric fields. Philos. Soc. Proc., 26: 421-428. Mason, B.J., 1954. Bursting of air bubbles at the surface of sea water. Nature, 174:470-471. Stuhlman, O., 1932. The mechanics of effervescence. Physics, 2: 457-466. Vonnegut, B., t955. Possible mechanism for the formation of thunderstorm electricity. Proc. Int. Conf. Atmos Elec. Portsmouth N.H. Geophys. Res. Pap., 42:169-181. Wilson, C.T.R. and Taylor, G.I., 1925. The bursting of soap bubbles in a uniform electric field. Proc. Cambridge Philos. Soc., 22: 728-730. Woodcock, A.H., Kientzler, C.F., Arons, A.B. and Blanchard, D.C., 1953. Giant condensation nuclei from bursting bubbles. Nature, 172:1144-145.
329
Elsevier Science Publishers B.V., Amsterdam
Corona from bursting bubbles M. Khaleeq-ur-Rahman a and C.P.R. Saunders b ~Physics Department, University of Engineering and Technology, Lahore-31, Pakistan bDepartment of Pure and Applied Physics, UMIST, P.O. Box 88, Manchester M60 1QD, UK (Received July 13, 1990; revised and accepted December 10, 1990 )
ABSTRACT Khaleeq-ur-Rahman, M. and Saunders, C.P.R., 1991. Corona from bursting bubbles. Atmos. Res., 26: 329-338. The phenomenon of bubble bursting in the presence of high electric fields has been studied with the intent of determining the critical field for corona initiation. Various bubble sizes were produced in a solution of sodium chloride in order to model conditions under oceanic thunderstorms. The results show that the corona threshold is inversely dependent on the bubble diameter. The quantity of charge transferred during a corona event was measured and was found to depend on the bubble size and the electric field strength. This process could be one of the effective charge transfer mechanisms over the oceans under thunderclouds.
RI~,SUMI~
On 6tudie le ph6nom~ne d'6clatement d'une bulle en pr6sence de champs 61ectriques 61ev6s en vue de d6terminer la valeur critique n6cessaire au d6clenchement de l'effet couronne. Afin de se placer dans des conditions d'orage maritimes, on produit des bulles de diff6rentes dimensions dans une solution de chlorure de sodium. Les r6sultats montrent que le seuil critique de l'effet couronne est en relation inverse avec le diam~tre de la bulle. La quantit6 de charge transf6r6e lors d'un effet couronne a 6t6 mesur6e, et on trouve qu'elle d6pend de la dimension de la buUe et de l'intensit6 du champ 61ectrique. Ce processus pourrait constituer un m6canisme efficace de transfert de charge au-dessus des oc6ans sous les orages.
INTRODUCTION
M a n y research workers have made both experimental and theoretical studies of bubble bursting phenomena and have examined its importance as a
0169-8095/91/$03.50
© 1991 - - Elsevier Science Publishers B.V.
330
M, K H A L E E Q - U R - R A H M A N A N D ( '.P.R. S A U N D E R S
source of large airborne salt particles in the atmosphere. Woodcock et al. (1953), Blanchard ( 1955, 1963), and Joraide (1976) have also discussed the contribution of bursting bubbles towards the charge transfer between the oceans and the atmosphere, the bursting bubble produces a jet which breaks up into droplets ejected from the tip and also into film droplets ejected from the sides of the jet. The droplets ejected from the tip carry a positive charge whose source is the electrical double layer on the water surface. The presence of a substantial electric field in the atmosphere will induce additional electric charge in the ejected droplets. Latham ( 1975 ) has suggested that corona discharges from bursting bubbles may also be one of the effective charge transfer mechanisms over the oceans under thunderclouds. He suggested that corona may be produced at the tips of jets resulting from the bursting of bubbles and he emphasised the need for further work. This paper presents results of an investigation into the conditions under which corona is produced from bursting bubbles and the charge transferred during corona events. Bubbles of seven different sizes in the range 2-13 m m diameter were produced by forcing air through glass capillaries of different diameters. The capillaries were placed in sodium chloride solution of sea-salt concentration, (0.6 mole/l ), so that the individual bubble production mechanism at the air-water interface was representative of bubble phenomena on the open sea. APPARATUS The experimental set-up for the present study is shown in Fig. 1. It includes a metal enclosure, a hide, and a bubble production mechanism. The enclosure, hide, and all other metal parts were earthed to form an electrostatic shield in order to minimise electrical noise. The metal enclosure was made from a steel drum, 0.91 m in diameter and 1.83 m high painted black on the inside to aid the photography of the bursting bubbles. An earthed wire mesh on conducting foil was placed both on the floor and at the top of the d r u m to provide
observer's hide etectrode ....
~uid:
to charge detector and oscilloscope
:-~!.
cameras and photornu|tip[ier
power supply oir input
screened cage
Fig. 1. The bubble production and bursting apparatus,
CORONA FROM BURSTING BUBBLES
331
electrostatic shielding. Inside the enclosure, a black plastic bucket of 31 cm upper diameter and 23.5 cm lower diameter was placed on an insulating block and was filled with the target liquid to a depth of 24.3 cm. A copper wire passed through the side of the bucket to provide an effective electrical connection to the positive terminal of a high-voltage power supply placed outside the enclosure. A copper disc of 22 cm diameter formed the upper electrode which was m o u n t e d on insulators 10 cm above the salt water surface. The edges of the upper plate were covered with insulating rubber to avoid any corona discharges, this upper electrode was connected to a storage oscilloscope through a charge detection circuit which were both placed outside the enclosure. Thus the direction of the electric field is the same as is found under thunderstorms. A hide was built around the experimental area to contain the corona detection equipment, the cameras and the observer. The hide was lined with blackout cloth and was covered with conducting foil to provide electrostatic shielding. A photomultiplier, placed inside the hide, was used to confirm the occurrence of luminous activity associated with the corona discharges from bursting bubbles. The photomultiplier assembly contained an EMI 9558 type multiplier tube and an amplifier with a variable gain. The photomultiplier tube was a 5 cm diameter, fiat faced, end window tube with a 44 m m cathode and 11 dynodes having CsSb secondary emitting surfaces. As the photomultiplier was affected by fields, the whole assembly was placed in a metal cylinder to provide an electrostatic shield. A lens was fitted at one end of the cylinder, facing both the cathode of the photomultiplier tube and the region under observation. The output from the photomultiplier was fed into an oscilloscope which was placed outside the hide. Bubbles were produced by supplying filtered air from a compressed air cylinder placed outside the hide, to a glass capillary. The air supply was controlled through a fine valve to provide pressures in the range 2 X 104-5 × 104 Pa so that single bubbles could be produced at the desired rate of one every eight seconds. The capillaries had previously been drawn into fine points of various diameters. Bubbles smaller than 4.75 m m diameter were produced by keeping the capillary tips immersed in the liquid at a depth of 12 cm in the upward direction as shown in Fig. 1. However, for larger bubbles, open-ended glass tubes of various diameters were immersed in the liquid in the downward direction. The diameters of the bubbles produced by the above mechanism were measured by photography. An arrangement for this purpose included a perspex tank which temporarily replaced the black vessel so that the bubbles could be viewed through the side. Bubbles of various diameter were produced and illuminated by diffused light while a 35 m m camera fitted with a zoom lens was used to determine their size which was in the range 2-13 m m diameter. A charge detection amplifier was used to measure the charge transferred
332
M. KHALEEQ-UR-RAHMAN AND C.P.R. SAUNDERS
during the corona events. Connected to an operational integrator, the signal went directly to the inverting input which was a virtual earth. Therefore, the arrival of charge q at the input will give an output voltage of magnitude q/C where C is the feedback capacitor. An advantage of using the virtual earth of an operational amplifier is that any stray capacitance is negligible and that the input device itself does not "see" the output voltage pulse since the latter appears at the opposite side of the virtual earth. A C-MOS 7611 was used, having an input impedance of 1012 ohms with low input bias current; values of R, the feedback resistor, and C were 108 ohms and 100 pF respectively. A chart recorder was used to record the charge transferred. OBSERVATIONS AND RESULTS
The bubble bursting phenomenon is too rapid to observe with the naked eye. However, the droplets produced from the resulting jet at the top of their trajectories were quite visible. The formation of a jet during bubble bursting is the principal mechanism by which droplets are ejected into the air, as suggested by Stuhlman ( 1932 ) and confirmed by Kientzler et al. ( 1954 ), using high-speed photography. Observations clearly revealed that the physical behaviour of bubbles is very much similar to that described by the earlier workers. The surface life of the bubbles before bursting, was found to vary from 0.5 to several seconds, depending upon their size. Measurements of the maximum height of the top droplet from disintegrating jets due to bursting bubbles were also made. This was done by moving the upper plate up and down until the top jet droplet just touched and was captured by the plate, this was repeated several times for each bubble size. It was found that as the bubble size increased beyond 2 mm diameter, the corresponding maximum droplet height decreased. In the present case, only ejecting heights up to a bubble size of 4.75 m m were measured because larger bubbles produced jets which did not break up into droplets. Results of the maximum top jet droplet heights for bubbles of three different sizes are shown in Fig. 2, together with a compilation of data by Blanchard ( 1963 ) from several sources. Stroboscopic observations confirmed the presence of film droplets as reported by earlier workers. In the absence of an electric field, these tiny droplets, produced due to the shattering of a bubble film, were found not to move upward by a substantial amount. Blanchard and Syzdek ( 1988 ) showed that film droplet production showed a maximum production rate for bubbles in the range 2-2.5 mm diameter. The corona threshold (Ec) for a bubble of diameter (D) is designated as the field strength at which 20% of the bursting bubbles resulted in corona as detected by the photomultiplier. In order to rely on the photomultiplier signals, great care was taken to check the insulation of the system and the dark-
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ness in the hide; the bubble production was stopped and high electric fields were applied across the gap in order to detect stray corona. After making sure that there was no signal from the photomultiplier, the experiments were continued. So, the present experimental arrangement proved to be more reliable than that of earlier workers: Blanchard ( 1963 ) mentioned the inadequacy of his system for the study of bursting bubbles in high electric fields while he was studying the induction charging of jet droplets from bursting bubbles. Visual observations of corona discharges produced at the tip of a jet due to a bursting bubble revealed that these are of the same nature as noted by Khaleeq-ur-Rahman and Saunders ( 1988 ) in their studies of corona from splashing water drops. As the field was further raised above the corona threshold, a stage was reached where corona, both from smaller and larger bubbles, could be seen with a dark adapted eye. Observations were made by applying electric fields between 1 and 3 kV c m - 1. The electric field caused bubbles to remain for a longer time, depending on their diameter, at the liquid surface and their surface life increased with increase in the electric field. Drops both from disintegrating jets and shattering films were found to move upward to considerable heights while levitated by the electric field. In the case of a bubble of 4.75 m m diameter, the m a x i m u m top jet droplet height increased from 3.8 cm (in the absence of field) to a height of 8 cm in the presence of an electric field of 1 kV c m - ~. By further increasing the field to a value of 2 kV c m - 1, the top droplet reached a height of 15 cm. No measurements regarding the top droplet height for smaller
3 34
M. KHALEEQ-U R-RAHMAN A N D C.P.R. SAU NDERS
bubbles were made as it was not possible to raise the top electrode further. For larger bubbles for which, in the absence of an electric field, there were no jet droplets observed, a number of small droplets were found to reach the upper plate (kept at 10 cm) in the presence o f an electric field o f I kV c m - l . The life-time of bubbles on the surface, for constant size and field, varied between/min and/max. For a particular field value,/max increased with the bubble diameter. Figure 3 represents such variations in/max with bubble diameter at three field values. The corona thresholds (Ec) for bubbles o f different diameters were found to vary inversely with the bubble diameter as shown in Fig. 4. All the mea15
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surements were made from the bursting of single bubbles of each size. It was found that the gap between the upper plate and the liquid surface did not affect Ec showing that the field was uniform. Measurements of charge transferred during each corona event at a field strength E ( > Ec), showed a range of values. So, for each bubble diameter, charge transferred during 50 corona events was measured at each value of field. Plots of the mean charge as a function of the electric field for bubbles of different diameters are shown in Fig. 5. For all the bubble diameters, it is evident from the plots that the mean charge transferred varies exponentially with electric field. Some measurements of charge transfer below Ec were also made for different bubble diameters which revealed only small charges on the small droplets produced by the disintegrating jets and shattering films. The droplets were levitated by the field and reached the upper plate even for large plate separations. It was found that at each field value the a m o u n t of charge transferred increased with the surface life of a bubble. With increase in electric field, coalescence between bubbles on the surface also increased, which resulted in a single bubble of a larger diameter giving rise to increased charge transfer. DISCUSSION
The behaviour of a bubble on a liquid surface is affected by the field. In the absence of any field, when a bubble reaches the liquid surface, it develops a thin cap which drains, thins, and bursts to leave a cavity. Fragments of the film are thrown out and are dragged upward by the air escaping from the bubble orifice along with the droplets from a disintegrating jet. Now, in an electric field, in addition to the upward directed buoyancy force, there is also
336
M. KHALEEQ-UR-RAHMANAND C.P.R, SAUNDERS
an upward force due to the field acting on the induced charges which will prevent the film cap draining and thinning. So, a longer time will be required for the surface tension forces to overcome these forces, after which a bubble finally bursts releasing charged droplets which are levitated in the field. In disturbed weather conditions, high electric fields associated with thunderstorms and perhaps show showers at sea would induce high positive charges on the ejected fragments due to bubble bursting (Blanchard, 1963 ). The fragments may then be carried by the turbulent mixing and convective updraughts into the positive regions of the storm, thus increasing the amount of positive charge in the 'core'. This may cause an increase in the electric field at the cloud surface as suggested by Vonnegut ( 1955 ). Wilson and Taylor ( 1925 ), and Macky (1930), have studied the bursting of isolated soap bubbles, not floating bubbles, resting on a plate in the presence of uniform electric fields, they found that the critical field required to produce disruption of a bubble is proportional to (surface tension/bubble radius) °5. In the present case, an inverse dependence of Ec on D was also noted and is shown in Fig. 4. However, a linear relationship is a best fit to the data, given by an empirical relationship, Ec X 1 0 - 5 = 3 . 4 8 5 - 0 . 1 1 2 D
( 1)
where Ec is in V m - ~and D is in mm. The above relationship between corona threshold and bubble diameter is in accordance with the prediction made from the theory of bursting bubbles. When a bubble bursts, a jet rises which then disintegrates into droplets. Many research workers, including Hayami and Toba ( 1958 ), and Blanchard ( 1963 ), have reported that the efficiency of droplet production decreases as the bubble diameter increases, while Knelman et al. (1954), Mason (1954), Blanchard (1963), Day (1964) have confirmed that for large bubbles ( > 4.75 mm, from the present experiments), the jet is formed but does not disintegrate into droplets. The jet height increases with bubble diameter and so the tall jet from a large bubble will lead to considerable field intensification at the tip and so will require a smaller field to initiate corona. The resulting jet from a small bubble ( <4.75 m m ) after disintegration, will be of a lesser height which in turn will require a higher field to initiate corona. This is all commensurate with the observed inverse dependence of critical field on bubble diameter. The aim of the present study was to investigate the electric fields needed to initiate corona from bursting bubbles of different diameters and to measure the associated charge transferred. The results reveal the occurrence of corona discharges along with the charge transfer for bubbles of diameter 2-13 mm. Blanchard and Woodcock (1957) obtained bubble distribution data from white caps near the shore which do not represent the bubble spectrum over the open sea. It would be most revealing, as suggested by Blanehard ( 1963 ),
CORONA FROM BURSTING BUBBLES
337
if bubble distribution data could be obtained on the open sea as a function of wind speed and as a function of time after a white cap has formed. He also suggested that the bubble spectrum for high winds would be significantly altered in shape from that for low winds. An estimate of the global importance of these results may be made by use of the calculations of Blanchard ( 1963 ) who estimated the ocean-air current due to charged droplets produced by bubble bursting. He determined a worldwide current of order 100 Amps caused by positive charge on the droplets. Due to the electric field under thunderstorms, some droplets become additionally positively charged by induction and the world-wide effect of this was calculated to be of order 10 Amps. For this latter calculation Blanchard performed experiments in which the charge on droplets produced by bubbles bursting in a field was determined. His field strength was below the critical field required for corona breakdown. Induced charges may be represented by an equation of the form q = k E r z where k = 8.8 X 10-10 from Blanchard's data, with q in Coulombs, E in volts per metre and r in metres. Blanchard ( 1989 ) showed that a 2 m m diameter bubble produces a 150 a m radius droplet for which the theoretical induced charge in a field of 2 × 105 V m - ~ is 4 pC. The present results show that the charges measured during the bursting of 2 m m bubbles in a field of 2 × 105 V m - i , a r e around 1.5 pC. Thus, it appears that the small drops in these experiments are receiving a charge due to breakdown of the same order of magnitude as the induced charge. The most important drop sizes for their effect on global charge transfer over the oceans, are in the range 10-100 p m (Blanchard, 1963 ). Thus for these sizes, it seems that calculations based on the induced charges are adequate and so Blanchard's estimate of the global charge effects due to bubble bursting under thunderstorms requires no revision from his value of 10 Amps. However, for bubbles larger than 4.75 m m diameter which do not break up into droplets, there will be no induced charge transfer; the corona discharge mechanism does apply to these large bubbles and substantial charge is released as can be seen from Fig. 5. However, there is a lack of evidence regarding the actual distribution of bubbles on the open sea as a function of various factors, without which no meaningful estimate of the total charge transferred during corona from bursting bubbles at the ocean surface can yet be made. Large bubbles may be present at the ocean surface during disturbed weather conditions. Both the present study and that made by Hallett and Christensen (1984), reveal that during splashing of large water drops ( > 2 m m diameter), about 50% of the splashes result in the formation of bubbles of a few centimetres diameter. These bubbles remain at the surface for a few seconds. So, the present results have relevance to the initiation of corona discharges from large bubbles produced due to the splashing of large rain drops at the ocean surface. In the light of the above discussion, it is suggested that corona from burst-
338
M. KHALEEQ-UR-RAHMANANDC.PR. SAUNDERS
ing b u b b l e s m a y b e a n a d d i t i o n a l s o u r c e o f c h a r g e at t h e sea s u r f a c e u n d e r o c e a n i c t h u n d e r s t o r m s w h e r e h i g h v a l u e s o f e l e c t r i c field a r e p r e s e n t . ACKNOWLEDGEMENTS Khaleeq-ur-Rahman wishes to thank the Ministry of Education, Government of Pakistan for financial support and the University of Engineering and Technology, Lahore, for leave of absence.
REFERENCES Blanchard, D.C., 1955. Electrified droplets from the bursting of bubbles at an air-sea water interface. Nature, 175: 334-336. Blanchard, D.C., 1963. The electrification of the atmosphere by particles from bubbles in the sea. Progr. Oceanogr., 1: 7 t-202. Blanchard, D.C., Woodcock, A.H., 1957. Bubble formation and modification in the sea and its meteorological significance. Tellus, 9 (2): 145-158. Blanchard, D.C. and Syzdek, L.D., 1988. Film drop production as a function of bubble size. J. Geophys. Res., 93: 3649-3654. Blanchard, D.C., 1989. The size and height to which jet drops are ejected from bursting bubbles in seawater. J. Geophys. Res., 94:10999-11002. Day, J.A., 1964. Production of droplets and salt nuclei by the bursting of air bubble films. Q. J. R. Meteorol. Soc., 90: 72-78. Hallett, J. and Christensen, L., 1984. Splash and Penetration of drops in water. J. Rech. Atmos., 18(4): 225-242. Hayami, S. and Toba, Y., 1958. Drop production by bursting of air bubbles on the sea surface ( 1 ). Experiments at still sea water surface. J. Ocean Soc. Jap., 14:145-150. Joraide, A.A., 1976. The electrification and size of jet droplets from bursting bubbles at an airwater interface. Thesis, Univ. Durham. Khaleeq-ur-Rahman and Saunders, C.P.R., 1988. Corona from splashing water drops. J. Atmos. Terr. Phys., 50: 545-555. Kientzler, C.F., Arons, A.B., Blanchard, D.C. and Woodcock, A.H., 1954. Photographic investigation of the projection of droplets by bubbles bursting at a water surface. Tellus, 6 ( 1 ): 1-7. Knelman, F.H., Drombrowski, N. and Newitt, D.M., 1954. Mechanism of the bursting of bubbles. Nature, 173: 261. Latham, J., 1975. Possible mechanisms of electrical discharge involved in biogenesis. Nature, 256: 34-35. Macky, W.A., 1930. The deformation of soap bubbles in electric fields. Philos. Soc. Proc., 26: 421-428. Mason, B.J., 1954. Bursting of air bubbles at the surface of sea water. Nature, 174:470-471. Stuhlman, O., 1932. The mechanics of effervescence. Physics, 2: 457-466. Vonnegut, B., t955. Possible mechanism for the formation of thunderstorm electricity. Proc. Int. Conf. Atmos Elec. Portsmouth N.H. Geophys. Res. Pap., 42:169-181. Wilson, C.T.R. and Taylor, G.I., 1925. The bursting of soap bubbles in a uniform electric field. Proc. Cambridge Philos. Soc., 22: 728-730. Woodcock, A.H., Kientzler, C.F., Arons, A.B. and Blanchard, D.C., 1953. Giant condensation nuclei from bursting bubbles. Nature, 172:1144-145.