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Corona from splashing water drops
0
~21-9169/8~ $3.00+ ‘00 1988 Pergamon Press plc
Corona from splashing water drops M. K~L~Q-~-RA~AN Department of Physics, University of Engineering and Technology, Lahore-3 1Pakistan and C. P. R. SAUNDERS
Department of Pure and Applied Physics, UMIST, PO Box 88, Sackville Street, Manchester M60 lQD, U.K. (Received in firm/form
15Derember 1987)
Abstract-The splashing of water drops of raindrop sizes on to a water or sea-water surface has been studied ; the nature of the splash is surface dependent and, with drops at terminal velocity, a secondary splash jet is noted. In the presence of an electric field, the jet tip provides space charge by means of a corona discharge. The critical field strength for corona is found to be considerably below that reported in earlier studies and this leads to greater effectiveness of smail drops in providing space charge beneath oceanic thunderstorms.
1. INTRODUCTION The splashing of raindrops upon the ocean surface beneath thunderclouds will cause the release ofcorona charge from the tips of the jets thrown up by the splash. Such jets were initially studied by WORTHINGTON (1908), while GRIFFITHS et al. (1973) and PHELPSet al. (1973) investigated the corona produced by splashing drops. Above a critical electric field value, a splashing drop produces a Worthington jet which has a sufficiently enhanced field, due to the high curvature at the jet tip, to produce corona. Under a typical thunderstorm, the charge released will be positive and may become involved in further electri~~ation of the thundersto~ (VONNEGUT,19.55). In general, however, the production of corona over the ocean surface is more difficult than over land (where a large number of sharp points are available to initiate corona). Thus, it is important to know the conditions under which corona may be initiated over the ocean in order to determine the available current density. Experiments were performed in the laboratory to investigate the splashing of raindrop sized water drops falling at terminal velocity onto a water or salt water surface in the presence and absence of a vertical electric field. The luminous phenomena associated with the splash in an electric field were observed by eye and with a sensitive photomultiplier, in order to determine the critical field strength required to initiate corona discharge. The experiments follow those of GRIFFITHS et al. (1973) and are felt to be worth reporting because 545
of the lower values of critical fields found here, which will have implications for thundercloud processes. 2. APPARATUS The experimental set up shown in Fig. 1 is similar to that used by PHELPSet al. (1973). It comprised a metal enclosure (a hide), a drop production mechanism, a liquid surface, an electric field region in which splashing took place, a splash and corona observation and detection system and a charge transfer detector. The metal enclosure consisted of a steel drum of 0.91 m diameter and 1.83 m height inside which observations of drop splashing were made. The inside of the drum was painted black to improve contrast for observation and photography. A wire mesh on thin conducting foil was placed both on the floor and at the top of the drum to provide a complete, earthed, electrostatic shield. Inside the enclosure, the target liquid was held in an insulated container of depth 26 cm and diameter 30 cm and the liquid was connected to the positive terminal of a high voltage power supply placed outside the enclosure. A copper disc of 22 cm diameter, having a hole in the centre, formed the other electrode and was connected to storage oscilloscope through a charge detection circuit, which were both placed outside the enclosure. Water drops in the radius range 1.462.05 mm fell from hypodermic needles of various diameter through the centre of a vertical earthed metal tube. After falling 2.5 m through the hole in the centre of the upper electrode, they impacted the liquid surface at a
.. ::;t: P
546
M. K~ALEEQ-UR-OMAN
-.‘:
water tank
hypodermic needle
observer’s hide cameros and photomultiplier
---
I
+ screened cage Fig. 1. Experimental set-up for studying corona from splashing water drops.
velocity within a few per cent of their terminal velocity, which was around 7 m s- I. A video camera operating at 25 frames sP ‘, together with a recorder and monitor, were used to view and record the splash events. Higher resolution with a higher framing rate was obtained with a high speed camera running between 100 and 11,000 frames s- ‘. Backlighting through a ground glass screen provided suitable illumination. A sensitive photomultiplier, placed inside the hide, was used to confirm the occurrence of luminous activity associated with the corona discharges from splashing water drops. A lens focused the splash region onto the photomultiplier tube, and the output was fed into an oscilloscope placed outside the hide. Any charge transfer occurring in the electric tield region was detected with a charge amplifier connected between the upper electrode and a storage oscilloscope. The use of a virtual earth configuration meant that the output voltage was simply proportional to the charge induced on the upper electrode. 3. SPLASHING-IN
THE ARSENCE
ELECTRIC
OF AN
FiELD
When a 2.05 mm radius drop impacts on a tap water surface, a crater is formed whose depth increases with
and C. P. R. SAUNDERS
increase in drop size. Five milliseconds after impact, a crown is formed, having thin, almost vertical walls. Then a number of spray jets, which break up into small droplets, are ejected from the upper rim of the crown. When the crown is fully developed, its walls become thicker and higher; the height depends upon the size of the impacting drop, being greater for greater drop sizes. Smaller spray droplets are sometimes captured by the upper electrode plate, which is at 12 cm above the water surface, while the larger drops return towards the water surface Forty-five milliseconds after impact, the crown completely collapses and a cavity is formed whose depth is greater for larger drop sizes. As the cavity starts to collapse, the liquid which was forced outward returns to form a central jet, which starts rising at 65 ms to reach a height of over 3 cm at I15 ms. Then the jet starts collapsing, during which it may pinch off to form one or more large droplets, or remain intact before collapsing completely. A graph of jet height against time was not symmetrical, with the time taken for the jet to collapse being longer than the rise time by 25 ms, indicating that fluid continues to flow up the jet after it has reached its maximum height. The development of a secondary jet is then observed. As the main jet completely collapses, a cavity is formed at 205 ms and, about 30 ms later, another jet starts rising, which rises to about a centimetre at 265 ms. The development of the secondary jet has been observed only in the case of large drops and has not been reported before for drops of the sizes studied here, possibly because in previous studies the water tank was not so deep. It was observed that jets produced by a series of drops, all of the same size, were not alike in respect of height and shape at their maximum position. So, there is a natural variability in the measurements, which could be attributed to drop oscillations and the spiral motion of the falling drops due to drag effects, which may cause the impact on the water surface to be at some angle. The time taken by the whole splashing event also depends upon the drop size, taking longer in the case of large drops. The characteristics of the jets are summrised in Table 1. Sometimes, in the case of large drops, instead of a jet, a bubble was formed, which remained for a long time at the point of impact on the surface. If the next drop hit the bubble, the resulting surface disturbance led to the release of very small droplets into the air. Experiments were also performed to study the splashing of water drops of 2.05 mm in radius onto a solution of sodium chloride of concentration 0.6 mole I- ‘, which corresponds to the salinity of sea water. The sequence ofjet formation in this case is essentially the same as described in the previous section, but
Corona from splashing water drops
547
Table 1. Characteristics of the jets for different drop sizes Radius of drop (mm)
1.46 1.66 1.75 1.85 2.05
Height of jet (cm)
No. of small spray jets from crown
No. of small spray jets when jet is at maximum position
Time for whole splashing event (s)
Diameter of the jet at its widest point (mm)
3.0+0.15 3.1 kO.1 3.3kO.l 3.4kO.l 3.45kO.15
5 I I 8 9
34 56 56 6 6
0.28 0.40 0.44 0.48 0.56
5.00 6.00 7.00 7.05 8.00
there are slight variations in the physical characteristics of the jet, such as the rise and collapse times and the height, diameter and shape of the main jet. The number of spray jets drawn out from the upper rim of the crown is less than for tap water. The main jet in this case develops as a column of liquid having nearly the same diameter along its length. The jet reaches its maximum height 155 ms after the impact, which is 40 ms later than for pure water. Forty per cent of the splashes go to the maximum height of 3.7 cm and 10% to a height of 3.1 cm. The diameters of the jets lie in the range 5.5f0.5 mm, depending on the jet height, being smaller for higher jets and vice versa; this is considerably narrower than for tap water. The sequence of the collapsing jet is similar to that described in the previous section. However, the total time taken by the splashing events is about 50 ms longer than for tap water. The development of a secondary jet also takes place in the present case; it collapses back to form a cone with a drop at the apex which then separates from the collapsing secondary jet. The splashing of water drops on the salt solution also results in the production of very small spray droplets which move upward and are hardly visible. Their presence is confirmed by observing the upper plate; the small droplets carry salt which can be seen as a deposit on the plate after evaporation. The production of these very small droplets due to the splashing of water drops on the sea surface may be of atmospheric importance in providing a source of small salt particles which will be carried aloft. The observations and results mentioned above reveal that the nature of the target liquid has influenced the various characteristics of the splashing events. thus, it can be inferred that the physical parameters of the target liquid, such as surface tension and density, may affect the nature of the splash. 4. SPLASHING-IN
THE PRESENCE
ELECTRIC
OF AN
FIELD
In this section, the effects of an electric field on the characteristics of the jet due to the splashing of water
drops onto tap water and sodium chloride solution are described. In order to ascertain whether the field is uniform in the 12 cm gap, with no edge effect distortions reaching the splash sites, a subsidiary experiment was performed with a 6 cm gap which would have produced a more uniform field. It was found that there was no difference in the characteristics of the jet in the presence of the same field values for both the gaps, which suggests that the field was sufficiently uniform in the 12 cm gap. When a drop splashes onto tap water in the presence of an electric field, the sequence of the jet formation is mainly the same as described earlier. However, the presence of an electric field causes some changes in the physical chracteristics of the jets, as noted by GRIFFITHS et al. (1973). High speed photographs of the splashing of water drops of 2.05 mm radius in the presence of an electric field of 2.5 x lo5 V mm ’ were analysed. It was observed that some time after the onset of a jet, its upper end becomes pointed when reaching its maximum position. The presence of an electric field also causes the jet to rise higher, with a corresponding decrease in the width of the jet. The number of filaments drawn out from the developing jet also increases with increase of field intensity. These filaments are found to disintegrate into numerous small droplets, some of which are levitated by the field for a short while before falling back to the water surface. Measurements regarding the time taken by different splashing events revealed that there is an increase produced by the field to a value of 155 ms for the jet to reach its maximum height, compared with 115 ms in the absence of an electric field. Similarly, the shape of the collapsing jet is slightly different ; the jet remains pointed for a long time during its collapse and simultaneously it becomes thinner with decreasing height, whereas, in the absence of an electric field, it collapses as a whole without losing thickness. When the jet is near to complete collapse it starts disintegrating into a number of small droplets, some of which are levitated by the field. The splashing events finish 245 ms after the drop impact.
548
M. KHALEEQ-UR-RAHMAN and C. P. R. SAUNDERS
It was also observed during the frame by frame observations of high speed film that the jet splits up into two or three parts when it is near to its maximum height. The upper portion is pulled by the electric field and becomes pointed while the other parts show similar behaviour. The portions are rejoined when the collapse starts. The maximum jet height was noted for a range of values of electric field for all the drop sizes investigated. The effect for all drop sizes was similar, with the jet height increasing from around 3 cm at zero field to about 5 cm at a field of 3.5 x 10’ V mm ‘. The increase of jet height with field was linear, indicating an increasing upward force on the jet with field. The splashing of water drops of radius 2.05 mm on to sodium chloride solution of 0.6 mole I-’ concentration in the presence of an electric field of 2.5 x 10’ V rn- ’ is described in this section. Figure 2 shows a time sequence of a splash event from the high speed camera. The presence of an electric field causes the resulting jet to have distinctive characteristics. The jet starts rising 85 ms after the drop impact, and it becomes pointed only 15 ms later. The jet starts rising 20 ms later and becomes pointed 40 ms earlier than the jet in the tap water case. The jet is at its maximum height 180 ms after the drop impact and achieves a height of 4.7 cm in the field, whereas in the absence of a field it reaches only 3.7 cm. The jet shape is quite distinctive, being long and thin as compared with the jet shape described in the tap water case, and it does not disintegrate into parts. There are fewer filaments drawn out from the developing jet. The main jet starts collapsing in a similar fashion to the field-free case. It remains pointed for a longer time, about 80 ms after the initiation of the collapse, whereas with tap water it remained pointed for only 65 ms. The collapsing jet also does not disintegrate into drops before complete collapse, as it does in the case of tap water. It collapses completely 295 ms after the drop impact. As mentioned earlier, the above observations indicate that the nature of the target liquid, such as surface tension and density, possibly affect the nature of the splash. The results now suggest that the conductivity of the liquid also plays a significant role in the splashing phenomena occurring in the presence of an electric field.
5. CORONA AND ASSOCIATED CHARGE TRANSFER
Observations and results presented in this section are related to the electrically induced hydrodynamic instability at the tip of a jet, which results in corona and charge transfer. Such a hydrodynamic instability
is independent
of polarity
1969 ; F’HELPSet al., 1973)
(TAYLOR, 1964 ; DAWSON,
; the present study is made
with the water at a positive potential. Normally, a run of 100 drops was made for each set of observations. Both tap water and a prepared solution of sodium chloride were used. Visual observations of corona were made inside a well darkened hide after waiting for more than 1 h, so that the eyes became dark-adapted. The drops were allowed to fall continuously while the electric field was steadily increased. The experimental sequence is as follows. Initially, there are no signals on the oscilliscopes linked to the photomultiplier and the charge measuring circuit. Application of an electric field results in a very small signal on the oscilloscope from the charge measuring circuit, but no signal from the photomultiplier, indicating that some very small charged droplets due to the mechanics of the splash are levitated by the field to such an extent that they are captured by the upper plate. When the field is further raised, a stage is reached at which the photomultiplier, along with the charge measuring circuit, detects small signals, evidence that charge transfer and some type of luminous phenomena of very weak intensity are occurring which are not visible to the dark-adapted eye. At this moment, charge in the range of lo- 9 C is being transferred. The electric field at which this occurs is almost the same for all drop sizes used at about 10’ V mm ‘. As the field is raised beyond this point, a critical stage is reached at which both the photomultiplier and charge measuring circuit detect large signals. A very feeble, yellow luminosity, which can just be seen with well dark-adapted eyes, is observed around the point where the jet is estimated to be at its maximum height, and is accompanied by a low intensity audible hiss. These manifestations reveal the onset of a corona discharge from the tip of the disrupting jet. However, at this field strength, corona occurs for only some of the splashing events. The field strength for which 10% of the splashes produce corona is called the critical field strength (E,.), or the threshold field strength for a splashing drop of radius r, and it increases as the drop radius decreases. When the field is increased by about 0.2 x IO5 V mm’ above EC (typically 1.6 x 10’ V mm’ for tap water), nearly every splashing event results in corona discharge. These discharges are of positive streamers with characteristic branched filamentary structure (like a paint brush) with a yellow coloured stem and a purple coloured flare; they are accompanied by relatively large amounts of charge transfer. However, for drops of a given size the luminosity varies, and the corresponding amounts of charge transferred also vary, being greater in the case of a
Corona from splashing water drops
Fig. 2. High speed photoaaphs of drops of radius 2.05 mm splashing into sodium chloride solution in an electric field of 2.5 kV cm-‘ ‘. Time sequence : (a) 85 ms jet onset ; (b) I00 ms pointed jet rising ; (c) 115ms developing jet ; (d) I80 ms jet at maximum height, 47 cm ; (e) 240 ms pointed jet collapsing; (f) 290 ms jet just before complete collapse.
549
551
Corona from splashing water drops
highly luminous discharge. These observations can be attributed to the range of jet heights for the same drop size, as already described. So, these corona discharges can be classified as strong, medium and weak, depending upon their associated luminosities and corresponding charge transfer. At and around 0.34x 10’ V m-’ above E,, the resulting corona streamers are highly luminous and can easily be seen with the naked eye in a darkened room. Their lateral spread and length also increase with increase in field intensity. At higher field strengths a glow is also observed near the upper plate, which may be a corona discharge from the drop surface as it approaches the upper plate. Further increase of the field strength results in the production of very strong streamers from the tip of the jet, which cover nearly all the gap. These are highly luminous, being violet colour in the outer regions and blue in the central regions, with a relatively large amount of charge being transferred. These are very similar to the pre-breakdown streamers which are observed in metal point to plane gaps. A further increase in the field results in the production of more intense streamers, being predominantly blue in colour with a very bright conducting channel. At this stage, some splashes resulted in a complete breakdown of the gap, producing a spark ; these may be regarded as breakdown streamers. The field strength at which 10% of the splashes due to drops of radius r resulted in complete breakdown is designated as the breakdown field strength Eb for a particular gap length, and has a value around 3.5 x 10’ V rn- ‘. Measurements reveal that for a particular drop size it varies with the gap length, and for a particular gap length it varies inversely with the drop radius. Visual observations made during the different stages of corona discharge from the tip of a jet have established that these are of the same nature as those produced from pointed metal electrodes, as described by L~EB (1965). The yellow luminosity observed by eye at the threshold is also observed during pulsed streamer discharge from a pointed electrode, and is indicative of the presence of the first positive bands system of nitrogen. It also implies a low field condition at the tip. The observed violet and blue colours at higher fields represent the presence of the second positive bands of nitrogen, the spectrum of which lies largely in the green to violet region. At and near complete breakdown, the spectra of the streamers contains the bands representing the nitrogen and oxygen lines, similar to the case of a spark produced from a pointed metal electrode. In the case of splashes into sodium chloride solution, the corona threshold ECwas found to be insignificantly
lower (1.5 x IO5 V m- ‘) than the tap water case for the same drop size. The voltage from the power supply was set to within an accuracy of 5%. The observed luminosity of the yellow colour at the threshold was found to be more intense due to the presence of sodium chloride and about I .7 times more charge was transferred than with tap water. At high fields the streamers are highly luminous, having a bright violet colour surrounded by a bright yellow colour. Their lateral spread and length is greater than in the previous case for the same values of field. The characte~stics of the br~kdown streamers are found to be different in the present case. Instead of a single conducting channel of blue colour contained by breakdown streamers they contain more than one conducting channel originating from the single channel and branching towards the upper plate. The value of breakdown field strength is found to be lower (3.3 x 10’ V rn- ‘) than in the tap water case (3.5 x 10’ V rn-- ‘) for the same gap length. It was found that for a particular drop size, the value of Er was the same for electrode gaps of both 10 and 12 cm, indicating that the field was sufficiently uniform. The measured charge transferred during corona discharge may have had a small cont~bution from the droplets reaching the upper plate after the splashing event. At a particular gap length, the breakdown field strength varied inversely with the drop radius and was reduced for a smaller gap, possibly due to the fact that as the gap decreases, more droplets reach the upper plate and help initiate breakdown. The values of breakdown field strength for different drop sizes at different gaps are given in Table 2. Because of the physical variability of the jet, the amount of charge transferred for a particular drop size took a wide range of values. The results of charge measurement experiments in which 100 drops of each of the sizes used were dropped into tap water are shown in Fig. 3. For clarity, the standard deviations are not shown, however, they were typically around 30%. For the case of splashing water drops onto a solution of sodium chloride, it was found that more Table 2. Table of I& (breakdown field strength) for different drop sizes at different gaps Drop radius (mm) I.46 I.66 1.75 1.85 2.05
Eb (breakdown strength) IO5V m-
12cmgap
_-.. 10 cm gap
4.00 3.80 3.66 3.58 3.50
3.70 3.50 3.40 3.30 3.25
’
_-
552
M. KHALEEQ-UR-RAHMAN and C. P. R. SAUNDERS
1.0
QPC
0 I.5
2.0
2.5
3.0 E KV/cm
Fig. 3. Corona charge transfer against electric field for a range of drop sizes splashing into tap water, except for one set of results with sodium chloride.
charge was transferred during corona events, as shown for the 2.05 mm radius drop in Fig. 3. The use of sodium chloride as the target liquid also reduced the breakdown field strength ; the values of Eb for the 12 cm and 10 cm gap were 3.33 x lo5 V m-’ and 2.9 x 10’ V m- ‘, respectively.
6. DISCUSSION
For the field-free case, Table 1 indicates that the drop size influences the shape and height of the splash jet. ENGEL(1966, 1967) developed a theory for the size of the cavity formed by a splashing drop. He found that the size is a function of T/p, where T is the surface tension and p is the density of the fluid. HARL~W and SHANNON(1967) found that for drop splashes at sufficiently high velocity the crater is deep and its sides rapidly collapse, trapping much of the original drop material well below the surface. So, the resulting jet will contain mainly the target liquid, having little of the original drop material ; thus, the properties of the target liquid are important. However, Engel’s simple crater size dependence on T/p is inadequate to account for the increased jet height with sodium chloride; the surface tension is certainly greater leading to a larger cavity and higher jet, but p increases as well, and for 0.6 M sodium chloride solution the two effects just about cancel. Nevertheless, there is an effect on the jet characteristics due to the liquid properties for which an adequate theory is lacking. The terminal velocity impacts in these experi-
ments were sufficiently energetic for the collapsing primary jet to produce a secondary jet, which rose to about a third the height of the primary jet. The characteristics of the jets produced by the splashing of water drops of different sizes are considerably changed in the presence of an electric field. Principally, the jet height increases with field. For a fixed drop size, an increase in the electric field causes an increase in the attractive force on the induced charges in the jet, which, in turn, causes the jet to rise more in the field. A simple calculation of this force shows that it is sufficient to increase the jet height. However, for a constant field, the larger drop radii experience a smaller jet height increase than do the smaller drops. The factors responsible for this may include the increase in the width of the jet with increase in the drop radius, which causes a reduction in the resultant upward force on the rising jet. As the jet starts rising in the presence of an electric field, the field configuration around the jet also changes, causing an increase in the electrical stress, leading to increased electrically induced hydrodynamic instability, at a maximum when the jet is at its maximum position. The increased number of spray jets produced from the rising jet can also be attributed to this electrically induced hydrodynamic instability. These spray jets finally break up into minute droplets, which may act as charge carriers of atmospheric importance as they may contribute towards the charge transfer between the ocean and atmosphere. Because the charge measu~ng circuit used in the present study is too insensitive to measure these small charges, no estimate can be made regarding the total charge conveyed to the atmosphere. It is generally accepted that separation of charges during the splashing of water drops occurs due to the rupture of an electrical double layer (IRIBARNE,1972) and the charge separation increases with increasing applied electric field. LEV~N( 197 1) has also suggested a similar process which may occur near the ground due to the splashing of water drops during heavy rain and strong wind shears, resulting in the suspension of small water droplets to a height of 2@30 m ; if they carry negative charge, a reversal of electric field may occur near the ground. For the same field value, more charge is transferred during the splashing of water drops on sodium chloride solution of sea salt concentration than in the tap water case ; this increase in the charge transfer may be attributed to the increased conductivity of the target liquid. BLANCHARD (1963), while studying the induction charging of drops produced from bursting bubbles, found that for a given drop size the induction charge increases with conductivity. LEWNand HOBBS(1971) also found a simi-
Corona from splashing water drops
lar effect due to conductivity during a study of the splashing of water drops on solid and wetted surfaces. The splashing of rain drops on the oceans, particularly in the presence of moderate electric fields, will be an effective charge transfer mechanism between the ocean and the atmosphere.
553 +
3.00 0 SEA WATER i
+ TAP WATER
/
Corona threshold and associated charge transfer
The values of corona threshold E, for drops of different sizes reveal that it varies inversely with the drop radius (r) and hence the drop impact velocity (v). GRIFFITHS et al. (1973) have suggested that E, may be inversely related to the momentum (p) of the impacting drop. They suggested a relationship between E, andp, for drops falling at terminal velocity V,,
V, can roughly be expressed, referring to (1971) quoted values, as being proportional therefore
MASON’S
to r’j2,
E, cc r- ‘I2 + c.
Plots of E, vs. l/r712, presented by GRIFFITHS et al. (1973) and from the present work, are compared in Fig. 4. The upper straight line A represents the data presented by GRIFFITHS et al. (1973) and a best fit is given by E, = 1.9rm712+ 1.78,
where E, is in kV cm- ’ and r is in mm. The lower line B represents a linear fit to the present data given by E, = 1.2r-‘12+ 1.52.
A comparison between the present results and those of GRIFFITHS et al. (1973), as shown in Fig. 4, clearly reflects a difference in corona thresholds. The lower corona thresholds found in the present work can be attributed to the different methods and improved techniques employed for the detection of the corona threshold and the associated charge transfer. These include the use of a sensitive photomultiplier and a sensitive charge detection circuit. Also, the splashing vessel was twice as deep as that used previously and this may have avoided problems of interference from the bottom of the tank. Also, the liquid was refreshed before each set of measurements. The values of mean charge transferred by corona for E > E, for each of the drop sizes investigated are shown in Fig. 3. These plots indicate that charge transfer depends on the excess field E above the corona threshold E,, in agree-
1;lS @2
o-3
0.4
I 03
I 0.6
I 0.7
Fig. 4. Corona thresholds against a function of drop radius for (A) GRIFFITHS et al. (1973) and (B) present data.
ment with GRIFFITHS et al. (1973). As the electric field increases above E, the chargefield relationships become linear, with the slopes approaching the same value when the drop radius reaches 2.05 mm. The effect of the conductivity of the target liquid has also been found to be of importance, both in corona discharges from the jet tips and in the associated charge transfer. Figure 3 also shows the charge transfer for values of E for a 2.05 mm radius drop falling into sodium chloride solution of sea salt concentration. This clearly indicates that greater charge is transferred for the same field compared with the tap water case, due to the increased conductivity of the salt solution.
Sea surface current density during rain GRIFFITHS et al. (1973) presented an estimate of the current density produced by corona from splashing rain drops for representative values of rainfall rate and surface electric field. They obtained an expression for the total current density, after making certain approximations and assumptions,
M. KHALEEQ-UR-RAHMAN and C. P. R. SAUNDERS
554
,j=
s
‘?qPV,n
r,
dr,
where q is the quantity of charge transferred in PC, P is the probability of a discharge, V, is the terminal velocity in m s ’ and n 6r is the number of drops m- 3 in the size range r to r+ 6r. q is obtained from Fig. 3, which shows that the value of q in PC is approximately given by the value of (E-E,) in kV m- ’ for the case of the drop of radius 2.05 mm. This approximation is adequate for the estimate of corona current. The probability of a discharge is found to be 0.1 at the critical point, increasing to 1.0 as the value of (E-E,) is increased to about 0.2 kV cm- ‘. This is not found to change significantly for different values of r, and P is given by P = 4.5(E-E,+O.l).
The terminal velocity in m s- ’ is given numerically by 6 r’12, with r in mm. n dr is determined from a typical raindrop size distribution given by MARSHALL and PALMER (1948). ND = No eeAD, where D is the drop diameter, N,6D is the number of drops of diameter between D and D +6D in unit volume and N, is the value of N, for D = 0. It is found that N, = 0.08 cm-4 for any intensity of rainfall and that A = 4lR-’ 2’ cm-‘, where R is the rainfall rate in mm h-‘. The expression for the value of i, expressed in PA rn- 2, becomes Dz emD dD
j = 2.16 x 10” s Dt
r2 r”*(E-EC)
X
S[‘I
(E-E,.+0.022)
1 dr
where the first integral is the total number of drops that areactiveperm3andD, andD,are thediametersinccntimetres corresponding to the drop radii r, and r2, respectively. Drop radius r, corresponds to the size of the smallest active drop for a field E at the water surface and r2 is the largest drop size in a thunder shower, which is taken as 3.0 mm, for which EC = 1.55 kV cm-‘, as found by Griffiths et al. In the second integral, the fields are expressed in kV err-’ and radii in mm. If we take R = 50 mm h-’ then, if the electric field at the water surface were to attain a value of 2 kV cn- ‘, r, in the present case becomes 1.3 mm from Fig. 4. The value ofj will be 145 PA m-*, which is a very high current density that could only be produced as a transient, because the space charge released would reduce the surface electric field and cut off further
charge release. However, this value ofj is large compared to the value (5 PA m- ‘) obtained by GRWFITHS et al. (1973), due to the lower corona thresholds found in this work for drops of smaller sizes, which suggests that the smallest drop size active at 2 kV cm-’ is 1.3 mm instead of 1.95 mm as obtained by GRIFFITHS et al. (1973). So, the present work leads to an increased range of drop sizes and a larger concentration of raindrop capable of producing corona at 2 kV cm- ‘. Experimental results mentioned in the previous sections clearly indicate that when the surface electric field increases above the corona threshold, corona discharges from splashing drop jet tips become an effective charge transfer mechanism, which may then have an effect on the electric state of a thundercloud. This process will be confined to regions beneath the precipitation regions of thunderclouds and will occur for only a short time period. As a result of corona discharges, the surface electric field may be reduced to a value below the corona threshold and these results show that this will happen more readily due to the activity of smaller drops. In regions other than the above, the surface electric field may attain higher values than over land, due to the relative difficulty in obtaining corona over oceans. TOLAND and VONNEGUT (1977) found values of 100 kV mm ’ over water. This, in turn, will result in a reduced supply of positive charge to the updraughts. Thus, according to the convective theory proposed by VONNEGUT (1955), a strong cloud dipole may develop which leads towards a greater fraction of lightning strokes from cloud to sea than in a thunderstorm over an uneven land surface that gives corona more easily. So, oceanic thunderstorms may have a different nature to those over land. Although the present study is made in the absence of any type of waves on the water surface, it is felt that the presence of waves may affect the nature of the splash and also the conditions under which corona is initiated. Similarly, bubble bursting may produce significant quantities of space charge over the oceanic surface from the breaking up of jets (BLANCHARD, 1963), both in the absence and presence of an electric field; this also requires study regarding the conditions under which corona is initiated. Experimental results of these phenomena and their possible influences on the charge transfer between oceans and the atmosphere will be presented in a subsequent paper.
Acknowledgements-One of us, Dr 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.
Corona
from splashing
water drops
555
REFERENCES BLANCHARD D. C. DAW~~NG. A. ENGEL0. G. ENGEL0. G. GRIFFITHSR. F., PHELPSC. T. and VONNEGUT B. HARLOWH. and SHANNON J. P. IRIBARNEJ. V. LEVINZ. LEVINZ. and HOBBSP. V. L~EB L. B.
1963 1969 1966 1967 1973 1967 1972 1971 1971 1965
MARSHALLJ. S. and PALMERW. McK. MASONB. J. PHELPSC. T., GRIFFITHSR. F. and VONNEGUTB. TAYLORG. TOLANDR. B. and VONNEGUT B. VONNEGUT B.
1948 1971 1973 1964 1977 1955
WORTHINGTON A. M
1908
Prog. Oceanogr. 1,71. J. geophys. Res. 74,6859. J. ap$. phys. 37, 1798. J. aovl. ohvs. 38. 3935. J. a‘tktoi. &. Phys. 35, 1967. J. appl. Phys. 38,3855. J. Rech. atrnos. 1972, 265. J. atmos. sci. 28, 543. Phil. trans. R. Sot., A 269, 555. Electrical Corona, their Basic Physical Mechanism. University of California Press, Berkeley, California. J. Met. 5, 165. The Physics of Clouds II. Clarendon Press, Oxford. J. appl. Phys. 44, 3082. Proc. R. Sot. A 280,383. J. geophys. Res. 82,438. Proceedings of the International Conference of Atmospheric Electricity p. 169. A Study of Splashes. Longmans Green and Co., New York.
~21-9169/8~ $3.00+ ‘00 1988 Pergamon Press plc
Corona from splashing water drops M. K~L~Q-~-RA~AN Department of Physics, University of Engineering and Technology, Lahore-3 1Pakistan and C. P. R. SAUNDERS
Department of Pure and Applied Physics, UMIST, PO Box 88, Sackville Street, Manchester M60 lQD, U.K. (Received in firm/form
15Derember 1987)
Abstract-The splashing of water drops of raindrop sizes on to a water or sea-water surface has been studied ; the nature of the splash is surface dependent and, with drops at terminal velocity, a secondary splash jet is noted. In the presence of an electric field, the jet tip provides space charge by means of a corona discharge. The critical field strength for corona is found to be considerably below that reported in earlier studies and this leads to greater effectiveness of smail drops in providing space charge beneath oceanic thunderstorms.
1. INTRODUCTION The splashing of raindrops upon the ocean surface beneath thunderclouds will cause the release ofcorona charge from the tips of the jets thrown up by the splash. Such jets were initially studied by WORTHINGTON (1908), while GRIFFITHS et al. (1973) and PHELPSet al. (1973) investigated the corona produced by splashing drops. Above a critical electric field value, a splashing drop produces a Worthington jet which has a sufficiently enhanced field, due to the high curvature at the jet tip, to produce corona. Under a typical thunderstorm, the charge released will be positive and may become involved in further electri~~ation of the thundersto~ (VONNEGUT,19.55). In general, however, the production of corona over the ocean surface is more difficult than over land (where a large number of sharp points are available to initiate corona). Thus, it is important to know the conditions under which corona may be initiated over the ocean in order to determine the available current density. Experiments were performed in the laboratory to investigate the splashing of raindrop sized water drops falling at terminal velocity onto a water or salt water surface in the presence and absence of a vertical electric field. The luminous phenomena associated with the splash in an electric field were observed by eye and with a sensitive photomultiplier, in order to determine the critical field strength required to initiate corona discharge. The experiments follow those of GRIFFITHS et al. (1973) and are felt to be worth reporting because 545
of the lower values of critical fields found here, which will have implications for thundercloud processes. 2. APPARATUS The experimental set up shown in Fig. 1 is similar to that used by PHELPSet al. (1973). It comprised a metal enclosure (a hide), a drop production mechanism, a liquid surface, an electric field region in which splashing took place, a splash and corona observation and detection system and a charge transfer detector. The metal enclosure consisted of a steel drum of 0.91 m diameter and 1.83 m height inside which observations of drop splashing were made. The inside of the drum was painted black to improve contrast for observation and photography. A wire mesh on thin conducting foil was placed both on the floor and at the top of the drum to provide a complete, earthed, electrostatic shield. Inside the enclosure, the target liquid was held in an insulated container of depth 26 cm and diameter 30 cm and the liquid was connected to the positive terminal of a high voltage power supply placed outside the enclosure. A copper disc of 22 cm diameter, having a hole in the centre, formed the other electrode and was connected to storage oscilloscope through a charge detection circuit, which were both placed outside the enclosure. Water drops in the radius range 1.462.05 mm fell from hypodermic needles of various diameter through the centre of a vertical earthed metal tube. After falling 2.5 m through the hole in the centre of the upper electrode, they impacted the liquid surface at a
.. ::;t: P
546
M. K~ALEEQ-UR-OMAN
-.‘:
water tank
hypodermic needle
observer’s hide cameros and photomultiplier
---
I
+ screened cage Fig. 1. Experimental set-up for studying corona from splashing water drops.
velocity within a few per cent of their terminal velocity, which was around 7 m s- I. A video camera operating at 25 frames sP ‘, together with a recorder and monitor, were used to view and record the splash events. Higher resolution with a higher framing rate was obtained with a high speed camera running between 100 and 11,000 frames s- ‘. Backlighting through a ground glass screen provided suitable illumination. A sensitive photomultiplier, placed inside the hide, was used to confirm the occurrence of luminous activity associated with the corona discharges from splashing water drops. A lens focused the splash region onto the photomultiplier tube, and the output was fed into an oscilloscope placed outside the hide. Any charge transfer occurring in the electric tield region was detected with a charge amplifier connected between the upper electrode and a storage oscilloscope. The use of a virtual earth configuration meant that the output voltage was simply proportional to the charge induced on the upper electrode. 3. SPLASHING-IN
THE ARSENCE
ELECTRIC
OF AN
FiELD
When a 2.05 mm radius drop impacts on a tap water surface, a crater is formed whose depth increases with
and C. P. R. SAUNDERS
increase in drop size. Five milliseconds after impact, a crown is formed, having thin, almost vertical walls. Then a number of spray jets, which break up into small droplets, are ejected from the upper rim of the crown. When the crown is fully developed, its walls become thicker and higher; the height depends upon the size of the impacting drop, being greater for greater drop sizes. Smaller spray droplets are sometimes captured by the upper electrode plate, which is at 12 cm above the water surface, while the larger drops return towards the water surface Forty-five milliseconds after impact, the crown completely collapses and a cavity is formed whose depth is greater for larger drop sizes. As the cavity starts to collapse, the liquid which was forced outward returns to form a central jet, which starts rising at 65 ms to reach a height of over 3 cm at I15 ms. Then the jet starts collapsing, during which it may pinch off to form one or more large droplets, or remain intact before collapsing completely. A graph of jet height against time was not symmetrical, with the time taken for the jet to collapse being longer than the rise time by 25 ms, indicating that fluid continues to flow up the jet after it has reached its maximum height. The development of a secondary jet is then observed. As the main jet completely collapses, a cavity is formed at 205 ms and, about 30 ms later, another jet starts rising, which rises to about a centimetre at 265 ms. The development of the secondary jet has been observed only in the case of large drops and has not been reported before for drops of the sizes studied here, possibly because in previous studies the water tank was not so deep. It was observed that jets produced by a series of drops, all of the same size, were not alike in respect of height and shape at their maximum position. So, there is a natural variability in the measurements, which could be attributed to drop oscillations and the spiral motion of the falling drops due to drag effects, which may cause the impact on the water surface to be at some angle. The time taken by the whole splashing event also depends upon the drop size, taking longer in the case of large drops. The characteristics of the jets are summrised in Table 1. Sometimes, in the case of large drops, instead of a jet, a bubble was formed, which remained for a long time at the point of impact on the surface. If the next drop hit the bubble, the resulting surface disturbance led to the release of very small droplets into the air. Experiments were also performed to study the splashing of water drops of 2.05 mm in radius onto a solution of sodium chloride of concentration 0.6 mole I- ‘, which corresponds to the salinity of sea water. The sequence ofjet formation in this case is essentially the same as described in the previous section, but
Corona from splashing water drops
547
Table 1. Characteristics of the jets for different drop sizes Radius of drop (mm)
1.46 1.66 1.75 1.85 2.05
Height of jet (cm)
No. of small spray jets from crown
No. of small spray jets when jet is at maximum position
Time for whole splashing event (s)
Diameter of the jet at its widest point (mm)
3.0+0.15 3.1 kO.1 3.3kO.l 3.4kO.l 3.45kO.15
5 I I 8 9
34 56 56 6 6
0.28 0.40 0.44 0.48 0.56
5.00 6.00 7.00 7.05 8.00
there are slight variations in the physical characteristics of the jet, such as the rise and collapse times and the height, diameter and shape of the main jet. The number of spray jets drawn out from the upper rim of the crown is less than for tap water. The main jet in this case develops as a column of liquid having nearly the same diameter along its length. The jet reaches its maximum height 155 ms after the impact, which is 40 ms later than for pure water. Forty per cent of the splashes go to the maximum height of 3.7 cm and 10% to a height of 3.1 cm. The diameters of the jets lie in the range 5.5f0.5 mm, depending on the jet height, being smaller for higher jets and vice versa; this is considerably narrower than for tap water. The sequence of the collapsing jet is similar to that described in the previous section. However, the total time taken by the splashing events is about 50 ms longer than for tap water. The development of a secondary jet also takes place in the present case; it collapses back to form a cone with a drop at the apex which then separates from the collapsing secondary jet. The splashing of water drops on the salt solution also results in the production of very small spray droplets which move upward and are hardly visible. Their presence is confirmed by observing the upper plate; the small droplets carry salt which can be seen as a deposit on the plate after evaporation. The production of these very small droplets due to the splashing of water drops on the sea surface may be of atmospheric importance in providing a source of small salt particles which will be carried aloft. The observations and results mentioned above reveal that the nature of the target liquid has influenced the various characteristics of the splashing events. thus, it can be inferred that the physical parameters of the target liquid, such as surface tension and density, may affect the nature of the splash. 4. SPLASHING-IN
THE PRESENCE
ELECTRIC
OF AN
FIELD
In this section, the effects of an electric field on the characteristics of the jet due to the splashing of water
drops onto tap water and sodium chloride solution are described. In order to ascertain whether the field is uniform in the 12 cm gap, with no edge effect distortions reaching the splash sites, a subsidiary experiment was performed with a 6 cm gap which would have produced a more uniform field. It was found that there was no difference in the characteristics of the jet in the presence of the same field values for both the gaps, which suggests that the field was sufficiently uniform in the 12 cm gap. When a drop splashes onto tap water in the presence of an electric field, the sequence of the jet formation is mainly the same as described earlier. However, the presence of an electric field causes some changes in the physical chracteristics of the jets, as noted by GRIFFITHS et al. (1973). High speed photographs of the splashing of water drops of 2.05 mm radius in the presence of an electric field of 2.5 x lo5 V mm ’ were analysed. It was observed that some time after the onset of a jet, its upper end becomes pointed when reaching its maximum position. The presence of an electric field also causes the jet to rise higher, with a corresponding decrease in the width of the jet. The number of filaments drawn out from the developing jet also increases with increase of field intensity. These filaments are found to disintegrate into numerous small droplets, some of which are levitated by the field for a short while before falling back to the water surface. Measurements regarding the time taken by different splashing events revealed that there is an increase produced by the field to a value of 155 ms for the jet to reach its maximum height, compared with 115 ms in the absence of an electric field. Similarly, the shape of the collapsing jet is slightly different ; the jet remains pointed for a long time during its collapse and simultaneously it becomes thinner with decreasing height, whereas, in the absence of an electric field, it collapses as a whole without losing thickness. When the jet is near to complete collapse it starts disintegrating into a number of small droplets, some of which are levitated by the field. The splashing events finish 245 ms after the drop impact.
548
M. KHALEEQ-UR-RAHMAN and C. P. R. SAUNDERS
It was also observed during the frame by frame observations of high speed film that the jet splits up into two or three parts when it is near to its maximum height. The upper portion is pulled by the electric field and becomes pointed while the other parts show similar behaviour. The portions are rejoined when the collapse starts. The maximum jet height was noted for a range of values of electric field for all the drop sizes investigated. The effect for all drop sizes was similar, with the jet height increasing from around 3 cm at zero field to about 5 cm at a field of 3.5 x 10’ V mm ‘. The increase of jet height with field was linear, indicating an increasing upward force on the jet with field. The splashing of water drops of radius 2.05 mm on to sodium chloride solution of 0.6 mole I-’ concentration in the presence of an electric field of 2.5 x 10’ V rn- ’ is described in this section. Figure 2 shows a time sequence of a splash event from the high speed camera. The presence of an electric field causes the resulting jet to have distinctive characteristics. The jet starts rising 85 ms after the drop impact, and it becomes pointed only 15 ms later. The jet starts rising 20 ms later and becomes pointed 40 ms earlier than the jet in the tap water case. The jet is at its maximum height 180 ms after the drop impact and achieves a height of 4.7 cm in the field, whereas in the absence of a field it reaches only 3.7 cm. The jet shape is quite distinctive, being long and thin as compared with the jet shape described in the tap water case, and it does not disintegrate into parts. There are fewer filaments drawn out from the developing jet. The main jet starts collapsing in a similar fashion to the field-free case. It remains pointed for a longer time, about 80 ms after the initiation of the collapse, whereas with tap water it remained pointed for only 65 ms. The collapsing jet also does not disintegrate into drops before complete collapse, as it does in the case of tap water. It collapses completely 295 ms after the drop impact. As mentioned earlier, the above observations indicate that the nature of the target liquid, such as surface tension and density, possibly affect the nature of the splash. The results now suggest that the conductivity of the liquid also plays a significant role in the splashing phenomena occurring in the presence of an electric field.
5. CORONA AND ASSOCIATED CHARGE TRANSFER
Observations and results presented in this section are related to the electrically induced hydrodynamic instability at the tip of a jet, which results in corona and charge transfer. Such a hydrodynamic instability
is independent
of polarity
1969 ; F’HELPSet al., 1973)
(TAYLOR, 1964 ; DAWSON,
; the present study is made
with the water at a positive potential. Normally, a run of 100 drops was made for each set of observations. Both tap water and a prepared solution of sodium chloride were used. Visual observations of corona were made inside a well darkened hide after waiting for more than 1 h, so that the eyes became dark-adapted. The drops were allowed to fall continuously while the electric field was steadily increased. The experimental sequence is as follows. Initially, there are no signals on the oscilliscopes linked to the photomultiplier and the charge measuring circuit. Application of an electric field results in a very small signal on the oscilloscope from the charge measuring circuit, but no signal from the photomultiplier, indicating that some very small charged droplets due to the mechanics of the splash are levitated by the field to such an extent that they are captured by the upper plate. When the field is further raised, a stage is reached at which the photomultiplier, along with the charge measuring circuit, detects small signals, evidence that charge transfer and some type of luminous phenomena of very weak intensity are occurring which are not visible to the dark-adapted eye. At this moment, charge in the range of lo- 9 C is being transferred. The electric field at which this occurs is almost the same for all drop sizes used at about 10’ V mm ‘. As the field is raised beyond this point, a critical stage is reached at which both the photomultiplier and charge measuring circuit detect large signals. A very feeble, yellow luminosity, which can just be seen with well dark-adapted eyes, is observed around the point where the jet is estimated to be at its maximum height, and is accompanied by a low intensity audible hiss. These manifestations reveal the onset of a corona discharge from the tip of the disrupting jet. However, at this field strength, corona occurs for only some of the splashing events. The field strength for which 10% of the splashes produce corona is called the critical field strength (E,.), or the threshold field strength for a splashing drop of radius r, and it increases as the drop radius decreases. When the field is increased by about 0.2 x IO5 V mm’ above EC (typically 1.6 x 10’ V mm’ for tap water), nearly every splashing event results in corona discharge. These discharges are of positive streamers with characteristic branched filamentary structure (like a paint brush) with a yellow coloured stem and a purple coloured flare; they are accompanied by relatively large amounts of charge transfer. However, for drops of a given size the luminosity varies, and the corresponding amounts of charge transferred also vary, being greater in the case of a
Corona from splashing water drops
Fig. 2. High speed photoaaphs of drops of radius 2.05 mm splashing into sodium chloride solution in an electric field of 2.5 kV cm-‘ ‘. Time sequence : (a) 85 ms jet onset ; (b) I00 ms pointed jet rising ; (c) 115ms developing jet ; (d) I80 ms jet at maximum height, 47 cm ; (e) 240 ms pointed jet collapsing; (f) 290 ms jet just before complete collapse.
549
551
Corona from splashing water drops
highly luminous discharge. These observations can be attributed to the range of jet heights for the same drop size, as already described. So, these corona discharges can be classified as strong, medium and weak, depending upon their associated luminosities and corresponding charge transfer. At and around 0.34x 10’ V m-’ above E,, the resulting corona streamers are highly luminous and can easily be seen with the naked eye in a darkened room. Their lateral spread and length also increase with increase in field intensity. At higher field strengths a glow is also observed near the upper plate, which may be a corona discharge from the drop surface as it approaches the upper plate. Further increase of the field strength results in the production of very strong streamers from the tip of the jet, which cover nearly all the gap. These are highly luminous, being violet colour in the outer regions and blue in the central regions, with a relatively large amount of charge being transferred. These are very similar to the pre-breakdown streamers which are observed in metal point to plane gaps. A further increase in the field results in the production of more intense streamers, being predominantly blue in colour with a very bright conducting channel. At this stage, some splashes resulted in a complete breakdown of the gap, producing a spark ; these may be regarded as breakdown streamers. The field strength at which 10% of the splashes due to drops of radius r resulted in complete breakdown is designated as the breakdown field strength Eb for a particular gap length, and has a value around 3.5 x 10’ V rn- ‘. Measurements reveal that for a particular drop size it varies with the gap length, and for a particular gap length it varies inversely with the drop radius. Visual observations made during the different stages of corona discharge from the tip of a jet have established that these are of the same nature as those produced from pointed metal electrodes, as described by L~EB (1965). The yellow luminosity observed by eye at the threshold is also observed during pulsed streamer discharge from a pointed electrode, and is indicative of the presence of the first positive bands system of nitrogen. It also implies a low field condition at the tip. The observed violet and blue colours at higher fields represent the presence of the second positive bands of nitrogen, the spectrum of which lies largely in the green to violet region. At and near complete breakdown, the spectra of the streamers contains the bands representing the nitrogen and oxygen lines, similar to the case of a spark produced from a pointed metal electrode. In the case of splashes into sodium chloride solution, the corona threshold ECwas found to be insignificantly
lower (1.5 x IO5 V m- ‘) than the tap water case for the same drop size. The voltage from the power supply was set to within an accuracy of 5%. The observed luminosity of the yellow colour at the threshold was found to be more intense due to the presence of sodium chloride and about I .7 times more charge was transferred than with tap water. At high fields the streamers are highly luminous, having a bright violet colour surrounded by a bright yellow colour. Their lateral spread and length is greater than in the previous case for the same values of field. The characte~stics of the br~kdown streamers are found to be different in the present case. Instead of a single conducting channel of blue colour contained by breakdown streamers they contain more than one conducting channel originating from the single channel and branching towards the upper plate. The value of breakdown field strength is found to be lower (3.3 x 10’ V rn- ‘) than in the tap water case (3.5 x 10’ V rn-- ‘) for the same gap length. It was found that for a particular drop size, the value of Er was the same for electrode gaps of both 10 and 12 cm, indicating that the field was sufficiently uniform. The measured charge transferred during corona discharge may have had a small cont~bution from the droplets reaching the upper plate after the splashing event. At a particular gap length, the breakdown field strength varied inversely with the drop radius and was reduced for a smaller gap, possibly due to the fact that as the gap decreases, more droplets reach the upper plate and help initiate breakdown. The values of breakdown field strength for different drop sizes at different gaps are given in Table 2. Because of the physical variability of the jet, the amount of charge transferred for a particular drop size took a wide range of values. The results of charge measurement experiments in which 100 drops of each of the sizes used were dropped into tap water are shown in Fig. 3. For clarity, the standard deviations are not shown, however, they were typically around 30%. For the case of splashing water drops onto a solution of sodium chloride, it was found that more Table 2. Table of I& (breakdown field strength) for different drop sizes at different gaps Drop radius (mm) I.46 I.66 1.75 1.85 2.05
Eb (breakdown strength) IO5V m-
12cmgap
_-.. 10 cm gap
4.00 3.80 3.66 3.58 3.50
3.70 3.50 3.40 3.30 3.25
’
_-
552
M. KHALEEQ-UR-RAHMAN and C. P. R. SAUNDERS
1.0
QPC
0 I.5
2.0
2.5
3.0 E KV/cm
Fig. 3. Corona charge transfer against electric field for a range of drop sizes splashing into tap water, except for one set of results with sodium chloride.
charge was transferred during corona events, as shown for the 2.05 mm radius drop in Fig. 3. The use of sodium chloride as the target liquid also reduced the breakdown field strength ; the values of Eb for the 12 cm and 10 cm gap were 3.33 x lo5 V m-’ and 2.9 x 10’ V m- ‘, respectively.
6. DISCUSSION
For the field-free case, Table 1 indicates that the drop size influences the shape and height of the splash jet. ENGEL(1966, 1967) developed a theory for the size of the cavity formed by a splashing drop. He found that the size is a function of T/p, where T is the surface tension and p is the density of the fluid. HARL~W and SHANNON(1967) found that for drop splashes at sufficiently high velocity the crater is deep and its sides rapidly collapse, trapping much of the original drop material well below the surface. So, the resulting jet will contain mainly the target liquid, having little of the original drop material ; thus, the properties of the target liquid are important. However, Engel’s simple crater size dependence on T/p is inadequate to account for the increased jet height with sodium chloride; the surface tension is certainly greater leading to a larger cavity and higher jet, but p increases as well, and for 0.6 M sodium chloride solution the two effects just about cancel. Nevertheless, there is an effect on the jet characteristics due to the liquid properties for which an adequate theory is lacking. The terminal velocity impacts in these experi-
ments were sufficiently energetic for the collapsing primary jet to produce a secondary jet, which rose to about a third the height of the primary jet. The characteristics of the jets produced by the splashing of water drops of different sizes are considerably changed in the presence of an electric field. Principally, the jet height increases with field. For a fixed drop size, an increase in the electric field causes an increase in the attractive force on the induced charges in the jet, which, in turn, causes the jet to rise more in the field. A simple calculation of this force shows that it is sufficient to increase the jet height. However, for a constant field, the larger drop radii experience a smaller jet height increase than do the smaller drops. The factors responsible for this may include the increase in the width of the jet with increase in the drop radius, which causes a reduction in the resultant upward force on the rising jet. As the jet starts rising in the presence of an electric field, the field configuration around the jet also changes, causing an increase in the electrical stress, leading to increased electrically induced hydrodynamic instability, at a maximum when the jet is at its maximum position. The increased number of spray jets produced from the rising jet can also be attributed to this electrically induced hydrodynamic instability. These spray jets finally break up into minute droplets, which may act as charge carriers of atmospheric importance as they may contribute towards the charge transfer between the ocean and atmosphere. Because the charge measu~ng circuit used in the present study is too insensitive to measure these small charges, no estimate can be made regarding the total charge conveyed to the atmosphere. It is generally accepted that separation of charges during the splashing of water drops occurs due to the rupture of an electrical double layer (IRIBARNE,1972) and the charge separation increases with increasing applied electric field. LEV~N( 197 1) has also suggested a similar process which may occur near the ground due to the splashing of water drops during heavy rain and strong wind shears, resulting in the suspension of small water droplets to a height of 2@30 m ; if they carry negative charge, a reversal of electric field may occur near the ground. For the same field value, more charge is transferred during the splashing of water drops on sodium chloride solution of sea salt concentration than in the tap water case ; this increase in the charge transfer may be attributed to the increased conductivity of the target liquid. BLANCHARD (1963), while studying the induction charging of drops produced from bursting bubbles, found that for a given drop size the induction charge increases with conductivity. LEWNand HOBBS(1971) also found a simi-
Corona from splashing water drops
lar effect due to conductivity during a study of the splashing of water drops on solid and wetted surfaces. The splashing of rain drops on the oceans, particularly in the presence of moderate electric fields, will be an effective charge transfer mechanism between the ocean and the atmosphere.
553 +
3.00 0 SEA WATER i
+ TAP WATER
/
Corona threshold and associated charge transfer
The values of corona threshold E, for drops of different sizes reveal that it varies inversely with the drop radius (r) and hence the drop impact velocity (v). GRIFFITHS et al. (1973) have suggested that E, may be inversely related to the momentum (p) of the impacting drop. They suggested a relationship between E, andp, for drops falling at terminal velocity V,,
V, can roughly be expressed, referring to (1971) quoted values, as being proportional therefore
MASON’S
to r’j2,
E, cc r- ‘I2 + c.
Plots of E, vs. l/r712, presented by GRIFFITHS et al. (1973) and from the present work, are compared in Fig. 4. The upper straight line A represents the data presented by GRIFFITHS et al. (1973) and a best fit is given by E, = 1.9rm712+ 1.78,
where E, is in kV cm- ’ and r is in mm. The lower line B represents a linear fit to the present data given by E, = 1.2r-‘12+ 1.52.
A comparison between the present results and those of GRIFFITHS et al. (1973), as shown in Fig. 4, clearly reflects a difference in corona thresholds. The lower corona thresholds found in the present work can be attributed to the different methods and improved techniques employed for the detection of the corona threshold and the associated charge transfer. These include the use of a sensitive photomultiplier and a sensitive charge detection circuit. Also, the splashing vessel was twice as deep as that used previously and this may have avoided problems of interference from the bottom of the tank. Also, the liquid was refreshed before each set of measurements. The values of mean charge transferred by corona for E > E, for each of the drop sizes investigated are shown in Fig. 3. These plots indicate that charge transfer depends on the excess field E above the corona threshold E,, in agree-
1;lS @2
o-3
0.4
I 03
I 0.6
I 0.7
Fig. 4. Corona thresholds against a function of drop radius for (A) GRIFFITHS et al. (1973) and (B) present data.
ment with GRIFFITHS et al. (1973). As the electric field increases above E, the chargefield relationships become linear, with the slopes approaching the same value when the drop radius reaches 2.05 mm. The effect of the conductivity of the target liquid has also been found to be of importance, both in corona discharges from the jet tips and in the associated charge transfer. Figure 3 also shows the charge transfer for values of E for a 2.05 mm radius drop falling into sodium chloride solution of sea salt concentration. This clearly indicates that greater charge is transferred for the same field compared with the tap water case, due to the increased conductivity of the salt solution.
Sea surface current density during rain GRIFFITHS et al. (1973) presented an estimate of the current density produced by corona from splashing rain drops for representative values of rainfall rate and surface electric field. They obtained an expression for the total current density, after making certain approximations and assumptions,
M. KHALEEQ-UR-RAHMAN and C. P. R. SAUNDERS
554
,j=
s
‘?qPV,n
r,
dr,
where q is the quantity of charge transferred in PC, P is the probability of a discharge, V, is the terminal velocity in m s ’ and n 6r is the number of drops m- 3 in the size range r to r+ 6r. q is obtained from Fig. 3, which shows that the value of q in PC is approximately given by the value of (E-E,) in kV m- ’ for the case of the drop of radius 2.05 mm. This approximation is adequate for the estimate of corona current. The probability of a discharge is found to be 0.1 at the critical point, increasing to 1.0 as the value of (E-E,) is increased to about 0.2 kV cm- ‘. This is not found to change significantly for different values of r, and P is given by P = 4.5(E-E,+O.l).
The terminal velocity in m s- ’ is given numerically by 6 r’12, with r in mm. n dr is determined from a typical raindrop size distribution given by MARSHALL and PALMER (1948). ND = No eeAD, where D is the drop diameter, N,6D is the number of drops of diameter between D and D +6D in unit volume and N, is the value of N, for D = 0. It is found that N, = 0.08 cm-4 for any intensity of rainfall and that A = 4lR-’ 2’ cm-‘, where R is the rainfall rate in mm h-‘. The expression for the value of i, expressed in PA rn- 2, becomes Dz emD dD
j = 2.16 x 10” s Dt
r2 r”*(E-EC)
X
S[‘I
(E-E,.+0.022)
1 dr
where the first integral is the total number of drops that areactiveperm3andD, andD,are thediametersinccntimetres corresponding to the drop radii r, and r2, respectively. Drop radius r, corresponds to the size of the smallest active drop for a field E at the water surface and r2 is the largest drop size in a thunder shower, which is taken as 3.0 mm, for which EC = 1.55 kV cm-‘, as found by Griffiths et al. In the second integral, the fields are expressed in kV err-’ and radii in mm. If we take R = 50 mm h-’ then, if the electric field at the water surface were to attain a value of 2 kV cn- ‘, r, in the present case becomes 1.3 mm from Fig. 4. The value ofj will be 145 PA m-*, which is a very high current density that could only be produced as a transient, because the space charge released would reduce the surface electric field and cut off further
charge release. However, this value ofj is large compared to the value (5 PA m- ‘) obtained by GRWFITHS et al. (1973), due to the lower corona thresholds found in this work for drops of smaller sizes, which suggests that the smallest drop size active at 2 kV cm-’ is 1.3 mm instead of 1.95 mm as obtained by GRIFFITHS et al. (1973). So, the present work leads to an increased range of drop sizes and a larger concentration of raindrop capable of producing corona at 2 kV cm- ‘. Experimental results mentioned in the previous sections clearly indicate that when the surface electric field increases above the corona threshold, corona discharges from splashing drop jet tips become an effective charge transfer mechanism, which may then have an effect on the electric state of a thundercloud. This process will be confined to regions beneath the precipitation regions of thunderclouds and will occur for only a short time period. As a result of corona discharges, the surface electric field may be reduced to a value below the corona threshold and these results show that this will happen more readily due to the activity of smaller drops. In regions other than the above, the surface electric field may attain higher values than over land, due to the relative difficulty in obtaining corona over oceans. TOLAND and VONNEGUT (1977) found values of 100 kV mm ’ over water. This, in turn, will result in a reduced supply of positive charge to the updraughts. Thus, according to the convective theory proposed by VONNEGUT (1955), a strong cloud dipole may develop which leads towards a greater fraction of lightning strokes from cloud to sea than in a thunderstorm over an uneven land surface that gives corona more easily. So, oceanic thunderstorms may have a different nature to those over land. Although the present study is made in the absence of any type of waves on the water surface, it is felt that the presence of waves may affect the nature of the splash and also the conditions under which corona is initiated. Similarly, bubble bursting may produce significant quantities of space charge over the oceanic surface from the breaking up of jets (BLANCHARD, 1963), both in the absence and presence of an electric field; this also requires study regarding the conditions under which corona is initiated. Experimental results of these phenomena and their possible influences on the charge transfer between oceans and the atmosphere will be presented in a subsequent paper.
Acknowledgements-One of us, Dr 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.
Corona
from splashing
water drops
555
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1908
Prog. Oceanogr. 1,71. J. geophys. Res. 74,6859. J. ap$. phys. 37, 1798. J. aovl. ohvs. 38. 3935. J. a‘tktoi. &. Phys. 35, 1967. J. appl. Phys. 38,3855. J. Rech. atrnos. 1972, 265. J. atmos. sci. 28, 543. Phil. trans. R. Sot., A 269, 555. Electrical Corona, their Basic Physical Mechanism. University of California Press, Berkeley, California. J. Met. 5, 165. The Physics of Clouds II. Clarendon Press, Oxford. J. appl. Phys. 44, 3082. Proc. R. Sot. A 280,383. J. geophys. Res. 82,438. Proceedings of the International Conference of Atmospheric Electricity p. 169. A Study of Splashes. Longmans Green and Co., New York.