Primary and secondary tip coronae from splashing water drops in electric fields

Atmospheric Research 109-110 (2012) 14–24

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Primary and secondary tip coronae from splashing water drops in electric fields P.B. Kinsey c/o The University of Manchester, School of Earth, Atmospheric and Environmental Sciences, Williamson Building, Oxford Road, Manchester, Lancashire M13 9PL, United Kingdom

a r t i c l e

i n f o

Article history: Received 20 May 2011 Received in revised form 31 January 2012 Accepted 3 February 2012 Keywords: Coronae Electrification: thunderstorms Hurricanes

a b s t r a c t An enquiry has been carried out into millimetre size water drops falling through vertical electric fields, at terminal and near terminal velocities, and impacting a water surface. A laboratory method was devised to electronically observe the splashing event, together with the onset, duration and magnitude of all ensuing coronae. The production of a secondary jet tip and the discovery of a previously unknown corona were originally recorded by Kinsey (1986) and are here described in detail. Emanating from the secondary jet tip, the corona is synonymous with the release and electrification of an airborne water drop and its nC range of charge transfer (being field/momentum dependant) offer low level luminosity to the dark adapted eye (mentioned by ur Rahman and Saunders, 1988). For terminal and near terminal velocity drops, the resulting water jets follow under-damped sinusoidal oscillation and, in fields above a critical value (Ec), their primary tips often support more than one corona, thus yielding charge to the aerosol and space charge below oceanic thunderstorms. Secondary tip, or jet drop, corona data show the phenomenon to occur in fields of 100 V cm− 1 and maybe even lower. The role of such drops, in oceanic thunderstorm electrification, being subject to drop size, ambient field, updraft and wind shear speeds. Oscilloscopic and photographic evidence is presented in support of the discovered corona and oscillographs, photographs and data are taken from P. B. Kinsey Ph.D. thesis (1986). © 2012 Elsevier B.V. All rights reserved.

1. Introduction Franklin's (1749) exploits, into thunderstorm and lightning electrification, stimulated many imaginations and generated a wealth of research into processes of charge transfer between the Earth's surface and the atmosphere. Roughly two centuries on, the thoughts of Elster and Geitel (1913), Mason (1953), the "convective theory" of Vonnegut (1953, 1955), Reynolds et al. (1957), Latham and Mason's (1961) “precipitation theory” and Mason (1972, 1953) have been superseded. The two processes which are presently accepted as the major candidates of thunderstorm charge development are described by Saunders (2008) and concluded to be the relative diffusion growth rates in ice/ice collisions and the inductive charging of otherwise uncharged particles, which may be transferred dur-

E-mail address: [email protected]. 0169-8095/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.atmosres.2012.02.005

ing collisions. Electric field values for intracloud (IC) and cloud to ground (CG) lightning being well reported by Uman and Krider (1982). Since the oceans account for some 70.8% of the Earth's surface (Trent and Gathman, 1972) all assessments of a global electric budget must include maritime storms. While the literature favours those of continental origin with multi, natural, land based, charge transfer points (Jhawar and Chalmers, 1965, 1967), (Chalmers, 1964), (Chalmers, 1966a, 1966b), (Stromberg, 1971a, 1971b), their oceanic counterparts, albeit less frequently, also yield appreciable amounts of lightning (Christian and Latham, 1998). Therefore knowledge of charge production at a water/sea surface is important to calculations of current density and an assessment of the significance to cloud electrification. The aim of this research was to investigate the electrical activity of water drops and bubbles respectively impacting and bursting on/at a water surface, in strong electric fields,

P.B. Kinsey / Atmospheric Research 109-110 (2012) 14–24

and to review their possible roles in oceanic thunderstorm development and biogenesis. Water jets formed by impacting drops are called Worthington jets, due to Worthington (1908) presenting ample data on their nature and those of bursting bubbles Blanchard jets, due to Blanchard's (1961, 1963) sturdy enquiries into their role within the oceanic environment. Original data on Worthington primary jet tip coronae is described by Phelps et al. (1973) and Griffiths et al. (1973). Earlier work on stability/instability, interaction, disruption and charge limit of water masses/drops include Rayleigh (1879, 1882), Macky (1931), Hendricks and Schneider (1963), Doyle et al. (1964), Taylor (1964), Matthews (1967), Abbas and Latham (1967) and Ausman and Brook (1967). Work on corona induced disruption of water surfaces, drops and points are reported by Zeleny (1915), English (1948), Dawson (1969, 1970), Barreto (1969), Richards and Dawson (1971, 1973) and Latham (1975). Other data include electrification of rain, jet drop and aerosol by Simpson (1909), Blanchard (1954, 1955, 1958, 1961, 1963), Blanchard and Woodcock (1957) and Muhleisen (1962). It has not gone unnoticed that the mechanism, or nature, of the discovered jet drop corona may prove important in Latham's (1975) postulation of biogenesis and this, together with the present work on bubbles, will be discussed in a separate paper. 2. Experimental method 2.1. Experimental arrangement and hardware The structure (Fig. 1) fundamentally resembles that of Phelps et al. (1973) and Griffiths et al. (1973). Comprising a vertical, earthed, extendable plastic dropping tube, it's upper and lower ends respectively hosting a micro manipulator assembly and a horizontal 3 mm thick brass plate. The plate, acting as upper electrode, was of 22.5 cm in diameter, with a

Fig. 1. Schematic of experimental configuration.

15

2.3 cm in diameter central hole and was affixed to the base of the tube via a sliding collar. This collar regulation allowed for gap size selection, of 0 to 10 cm, between the plate and water surface. To reduce spurious electrical interference effects, the plane parallel pair was housed within an earthed steel drum of 2 m. height and 1 m. diameter. The drum interior was painted matt black, to aid in photography, and an access doorway cut into same. A light-tight observation hide was built around the doorway and all electrical equipment, except for a light bulb, kept external to the drum and internally connected through rubberized holes. The drum's base and top were covered with an earth bonded laminate of wire mesh and thin conducting foil, thus providing an electrostatic shield or Faraday cage. 2.1.1. Water drop production and alignment Five syringe needles of varying tip radii (mm) were vertically mounted into a triaxial micro manipulator and adjoined to a water reservoir via a locking device, rubber tube and needle valve. Thus enabling choice of production rate, drop size and drop trajectory. 2.1.2. Water jet production Drops were allowed to impact an electrically stressed water surface from a height of variable elevation. The water was held in a robust rubber container to a depth of 23.5 cm; its surface providing the lower electrode of a plane parallel pair. Upon impact the opposing force causes the under damped oscillation of a water column or Worthington jet. 2.1.3. Instrumentation and calibration For a positive water surface the top electrode was earthed and vice versa for negative. The vertical field between the electrodes was provided by a Brandenberg power supply, giving voltage selection in the range 0 to 30 kV and choice of polarity. The EHT supply was first of all calibrated against an electrostatic voltmeter and a correction chart created. A suitably buffered Cole Palmer chart recorder was also calibrated and initially served data acquisition. Its input signal was supplied by a fabricated charge measuring device (1 second integrator) with four ranges of operation (fsd's of 100 pC, 10 nC, 100 nC and 1 μC) and connecting the electrode pair. Likewise a Tektronix 555/21A/22A oscilloscope was calibrated via a standard pulse/signal generator and alternately connected across the plane parallel pair: its original use being to monitor the pulse created by impact drop entry into the electric field. The chart recorder and oscilloscope ranges proved to have less than a ±1% error margin. In applying the EHT, up to steady state, the oscilloscope experienced a + 0.12 V shift in reference level. Deployment of a stroboscope allowed the water column activity to be observed wholly or in part and both a cine and still camera were used to record the events. The still camera was clipped to the oscilloscope with a detachable bracket and the cine camera rigidly fixed inside the hide with its field of view focused on the impact area. 2.1.4. Experimental practice The process involved selecting a drop size, production rate, electrode separation (gap size) and fall height (relative

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P.B. Kinsey / Atmospheric Research 109-110 (2012) 14–24

to the drops attaining terminal or near terminal velocity). The micro device was used to align the drops, ensuring they passed cleanly through the central hole of the upper electrode. A pre selected period of dark adaptation then followed, prior to starting the experimentation. The mode of operation allowed a total of 25 or 50 drops, termed a run, to impact the water surface. Each run related to one of various electric field strengths (ER). Once coronae appeared the electric field value was recorded as the minimum, or onset, field (EM) for that drop's size and momentum (p). Since there was never just one discharge event per run, this minimum field was recorded as the critical field (Ec), which ultimately proved to be around 10% of the run. The word “event” denotes the period of Worthington jet motion; from drop impact to cessation of oscillations. 2.1.5. Initial Observational data Initial scrutiny established droplet impact with the water surface caused the contact area to perform under damped sinusoidal oscillation. After impact a cavity forms (Worthington, 1908; Engel, 1966, 1967), trailed by several rise and fall, under damped, water column oscillations. The falling drops tended to spiral, more so at 6.5 m fall height, and coupled with molecular drag, inherent oscillations and static charging of the dropping tube, not all drops hit the water in the same manner or spot. Hence, a minimum drop production rate was set at 1.5 min to ensure a ripple free water surface between impacts. Heightened by the dark adaptation period, the visual sense frequently stimulated the imagination into thinking more than one discharge was occurring during an event. The diameters of the rising water jets looked to be the same as that of the impacting drop, an observation previously noted by Latham (1975). 2.1.6. Data quality; original method Stroboscopic surveillance of the splash event highlighted myriads of tiny drops being swiftly levitated from the water surface, by the electric field, and collecting on the upper electrode. This occurrence was especially rampant during jet tip disruption and corona emission. Such charged drops proved to be additional to measured values, due to the integration time of the charge measuring device. While the effect radically decreased with reducing field strength, it was most prevalent at the enquiry's initial point of interest. Thus it became increasingly clear, a more accurate method of monitoring and measuring electro mechanical and corona activity within the gap would be invaluable and the system was reviewed. 2.1.7. System review and analysis Since the upper and lower electrodes basically form a parallel plate condenser, movement of either will generate an emf within the system. The mathematical expression for a sinusoidal emf is shown in Eq. (1), and the first term exponential (e − t/RC) suggested a possible method for electronically observing the splashing event. −t=RC

Iðt Þ ¼ c: e


 2 1=2 þ ωVo ⋅C= 1 þ ðωRCÞ ⋅sinðωt–δÞ

where δ = − (1/ωRC).

ð1Þ

In Eq. (1), the first term decays stably as t increases and the last term indicates the steady state current, which is sinusoidal. With t denoting the event time and RC the time constant of the circuit, making RC the same order of magnitude as the event (~180 ms) any change, or system generated emf, will emulate or replicate the force, or motion, causing the change. Consequently a system analysis was executed, taking account of electrode pair dimensions, plate separation, average jet height, tip geometry and oscilloscope input capacitance. This gave capacitive values of 3.5 pF, 0.0027 pF and 20 pF respectively. Since the oscilloscope input resistance was 1 MΩ, it was necessary to introduce a control, or network capacitor (CN), of 100 nF value. Such that the total capacitance: CT ≈CW þ CJ þ CO þ CN ≈100 nF:

ð2Þ

With an oscilloscope input resistance of 1 × 10 6 Ω, the time constant (ROCT) becomes 100 ms. 3. Devised method of electronic detection observation and measurement 3.1. Waveform analysis The outcome of using the devised method and CN is shown in Fig. 2a, b, where a 1.76 mm radius water drop falling 2.5 m (near terminal velocity) has impacted a water surface in a field of 1.9 kV cm − 1. The water surface is positively charged and the upper electrode is grounded. 3.1.1. Drop motion pre impact Reviewing Fig. 2, using the oscilloscope time base (20 ms per graduation) and moving from left to right, the rising trace (~35 ms into frame) signals the drop's entry into the electric field. Its direction establishes that motions in the “in field” direction are seen as positive going (toward frame top) and in the “out of field” direction are seen as negative going (toward frame base). 3.1.2. Point of impact baseline shift and cavity The initial positive going pulse undergoes inflection as the drop impacts the water surface (~ 40 ms into frame), and instantly notable is the baseline shift; thought to arise from a large perturbation of the space charge amidst the electrodes. Following impact (~ 40 to 70 ms) the surface layers are forced upward and outward toward the ground plane and as penetration deepens, forming a cavity, the lower layers eject more vertically (noted by Worthington, 1908 and Engel, 1966, 1967). The charged splash layer motions look to restore the space charge region, because the oscilloscope trace then oscillates about the original baseline voltage. 3.1.3. Primary tip: Worthington water jet and corona With the cavity formed (~120 ms) the water jet begins rising, the trace going negative toward and below the baseline. On nearing maximum height (~ 215 ms) a necking process begins, which terminates in the production of a jet drop and secondary jet tip. Fig. 2(a, b) also shows that during the cycle, the jet's primary tip has supported a pre corona pulse (~170 ms) and two primary point corona; one before and one after

P.B. Kinsey / Atmospheric Research 109-110 (2012) 14–24

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production (~275 ms, for 1.76 mm radius drops in fields of 1.9 kV cm − 1). Basic reasoning suggested a corona between the secondary jet tip and the newly formed jet drop would charge the drop in such a way as to simulate motion of a charged body toward the ground plane; since it would remain electrically adjoined by the discharge (Fig. 3b).

3.1.5. Oscilloscopic waveforms and selected images of filmed events In trying to resolve the jet drop anomaly, the splash event was filmed in entirety (cine), from pre impact to cessation of jet oscillation and each frame sequenced against a photograph of its corresponding oscilloscopic waveform. Sample images are here shown and Fig. 3(a, b) displays the result of studying the anomaly. Phelps et al. (1973) noted the drop production, but seemingly failed to observe, and/or record, both the corona and the secondary tip shape.

Fig. 2. [Oscilloscope: Time Base = 100 ms.cm− 1, Voltage Scale = 1.0 V.cm− 1]. a) Impact drop entry into electric field. b) Drop impact on water surface; trace undergoes inflection. c) Splash water; surface layers. d) Splash water; cavity layers. e) Restoration of space charge. f) Cavity shaped by impacting drop. g) Water jet rising from the cavity. h) Pre corona pulse, followed by a primary point corona, prior to jet reaching maximum height. i) Beginning of the necking procedure. j) Primary point corona, during the necking procedure. k) Discovered jet drop corona following jet drop release.

reaching maximum height (~175 ms, ~ 250 ms respectively). In addition the corona pulse heights are noted to be off screen and a method of voltage level calculation is described in Section 3.1.6. 3.1.4. Secondary tip: Worthington water jet and corona The negative pulse (~ 280 ms) was initially perplexing. The direction of propagation signifies a negative corona, but its fuzzy broad form is like the positive discharge shown by Griffiths et al. (1973). However two further factors made the anomaly's resolution primarily important: i) The discharge continued to exist in fields (Ef) b 0.5 kV cm− 1 for all drop sizes (mm). Where Ef denotes fundamental fields. ii) For like sized drops, the sequential location of the discharge was much the same, around the time of jet drop

Fig. 3. Both images are the result of a 1.76 mm radius drop impacting a water surface in a field of 1.7 kV cm− 1.a) Displays a newly released jet drop and the underlying secondary jet tip, which looks to host a needle like radius of curvature.b) Displays a newly released jet drop, and the discovered jet drop corona charge transfer.

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P.B. Kinsey / Atmospheric Research 109-110 (2012) 14–24

3.1.6. Method of corona measurement The corona data are taken directly from (photographed) oscilloscope images. A reticle was adapted and served, along with the oscilloscope voltage scale and a travelling microscope, in measuring each pulse. Charge values were then obtained via the fundamental expression: Q ¼ V⋅C:

−t=RC

(Limited data, drop radii of 1.76 and 1.34 mm) Oscilloscope data ± 1%. Field E kV cm− 1

ð3Þ

Where Q is the charge, V the voltage and C the capacitance (equal to CN). With “off screen” pulse heights, the voltages were calculated using the standard relation: V ¼ V0 e

Table 2 Exploratory exercise; a review of possible average current density nAm− 2 generated by oceanic activity, in various electric fields.

:

ð4Þ

Where t is the pulse time base separation (between point of rise and decay) and RC denotes the circuit resistance and capacitance. (V0 is given the value 0.12 V; oscilloscope baseline shift on application of EHT.) During initial trials all corona seemed to fall into one of several regimes, each ably described by the time base separation of the decaying pulse. But amidst the enquiry proper it became clear that most regular coronae, meeting the Ec criterion, were weak and strong in nature and their decay time periods are here listed as being 5 to 20 ms and 20 to 80 ms respectively. 3.1.7. Oscilloscopic observed data Increases in E above Ec caused coronae to be initiated earlier in the event, such that rising jet tips disrupted at various heights below their maximum. This occurred for each drop size (mm) used. For drops of 1.34 and 1.46 mm radius, in an electric field of 2.1 kV cm− 1, corona were initiated from jets that were just emerging from the cavity, whereas drops of 1.76 and 1.88 mm radius required fields around 2.6 kV cm− 1 to produce corona at the same location in the event. This may be due to jet tip geometries in respect of cone angles and instability; as reported by Taylor (1964), Abbas and Latham (1967), Barreto (1969) and Dawson (1969, 1970). There also looks to be an optimum drop size of 1.88 mm radius, regardless of fall height; which can be seen in Tables 1 and 2, and Fig. 4(a, b).

0.1 0.5 1.0 1.9 2.0 2.2

Average jet drop charge nC

Current density (J) nAm− 2

Charge integrator

Oscilloscope

Oscilloscope data ≥ 0.5 kV cm− 1

0.44 0.84 1.8 2.9 3.6 4.3

– 0.82 1.7 2.6 3.2 3.6

39.2 72.9 151.3 231.4 284.8 320.4

Note: charge Integrator data included for comparison only. Values compromised (Sections 2.1.6 and 3.1.8).

errors were introduced by the grain size and image blur (bg) of both celluloid films (cine and still). With the still camera, attention was also given to print paper and a high quality (fine grain) used. Moreover, to reduce blurring, numerous trials were performed contrasting the camera shutter speed with oscilloscope beam intensity; yielding optimum values. Grain/blur estimates were made for each data set, and found to be in the range of 0.1% ≤ bg ≤ 0.2%. The spread in value may be due to instrumentation drift, or film process disparities. Coupling this with the oscilloscope ±1.0% voltage discrepancy, the method lay within experimental error. With the cine camera, and prior to testing, a metric gauge was temporarily held vertical in the view field (drop impact zone) and filmed. Thereby enabling quantitative analysis of the water surface and jet actions. Similarly grain/blur estimates were attained with regard to depth of field and film lighting. Since there was no definitive way of measuring the amount of charge transferred by levitated drops (per event) in the initial monitoring method (Section 2.1.6), the devised method was deemed the more accurate and used throughout the enquiry. The chart recorder and charge integrator being reserved for occasional data comparison and periods of oscilloscopic range limitation. 4. Results and discussion 4.1. Primary tip corona

3.1.8. Data quality: devised method The strategy in developing this method of corona detection and measurement is vindicated, to a large extent, by the outcome. Apart from the oscilloscope ±1.0% error margin, further

Just two fall heights were used in this study. First, a 2.5 m elevation for data comparison with the literature (Phelps et al., 1973; Griffiths et al., 1973) and second a 6.5 m height, to

Table 1 Recorded coronae onset field values for Worthington jet tips ± relative error. Onset field (Ec) values: Worthington primary and secondary jet tip corona kV cm− 1 Drop radii (mm)

1.34

1.46

1.59

Primary tip Weak corona Strong corona Weak corona Strong corona

(Critical electric field, Ec kV cm− 1) 2.10 (± 0.0048) 2.00 (± 0.0050) 2.30 (± 0.0043) 2.15 (± 0.0116) 2.20 (± 0.0045) 2.10 (± 0.0048) 2.35 (± 0.0043) 2.30 (± 0.0043)

Secondary tip Jet drop corona

(Oscilloscope “lower limit”, Ec ≥ 0.50 kV cm− 1) 0.50 (± 0.020) 0.50 (± 0.020) 0.50 (± 0.020)

1.90 2.00 2.00 2.10

1.76

(± 0.0053) (± 0.0050) (± 0.0050) (± 0.0048)

1.70 1.75 1.80 1.90

1.88

(± 0.0143) (± 0.0143) (± 0.0056) (± 0.0053)

0.50 (± 0.020)

1.55 1.70 1.70 1.80

2.30

(±0.0161) (±0.0147) (±0.0143) (±0.0056)

0.50 (±0.020)

1.60 1.75 1.70 1.80

Fall height (m)

(± 0.0156) (± 0.0143) (± 0.0143) (± 0.0056)

0.50 (± 0.020)

6.5 6.5 2.5 2.5

2.5

P.B. Kinsey / Atmospheric Research 109-110 (2012) 14–24

quantifiably review the field momentum (E,p) co reliance for coronae. The study data is shown in Table 1 and the impact speeds in relation to fall height and drop size were calculated from Wang and Pruppacher (1977). The enquiry was extended to include a validation analysis of the features encircling the devised method of detection and thus no weight was given to critical field (Ec) values for which 20% of the events produced corona (as in the literature); though it proved to be around 10% per run, regardless of drop size or discharge strength. Equally little attention was paid to noting whether a distinctly audible hiss occurred with each discharge. 4.1.1. Comparison (primary tip corona) with literature Fig. 4a and b, respectively contrasts the present data against that of Griffiths et al. (1973) and Phelps et al. (1973). Graphing the present 2.5 m data with the literature (Fig. 4a), shows weak and strong Ec values which, while lower, are close aligned to those reported. The data spread may be due to choice of criteria; the literature needs 20% of the jets to yield (audible) corona, whereas the present data list Ec values at which coronae, with pre defined time base periods, first appear. In matching the 6.5 m data with the 2.5 m literature data, Fig. 4b clearly displays the corona onset field dependence on drop momentum (Ec,p) for weak and strong electrical activity. With both types of corona, there looks to be an optimum impact drop size (~1.88 mm); regarding the onset field (mentioned in Section 3.1.7). The literature also draws on the Marshall and Palmer (1948) drop size distribution, although Mason (1971) has shown this to underestimate numbers of very small and very large drops when applied to rain showers. From the present data, the field strength (Ec) for corona onset can be seen to be inversely related to the drop's size and impact velocity. Additionally, the literature shows Ec to be inversely proportional to impact drop momentum (p). Such that:

EC α

1 þ c: r 3 ⋅V t

In Mason's (1971) quoted values, Vt is roughly proportional to r1/2 and can be expressed as being equal to 6r1/2. Thus: EC α

1 þ c: r 7=2

The line of best fit to the literature data (Griffiths et al., 1973) yields: EC ¼ 1:9=r

7=2

þ 1:78:

ð5Þ

Fig. 4. a) Charting the 2.5 m drop fall height data of the present enquiry against that of Griffiths et al. (1973), shows the EC data for weak and strong discharges to be lower in value. There is, however, some measure of alignment with the literature data. b) Contrasting the present 6.5 m drop fall height data with the 2.5 m drop fall height data of Griffiths et al. (1973), clearly exhibits the onset field (EC) dependence on impact drop momentum (p). The present enquiry’s 2.5 m drop fall height data are here omitted, for increased clarification. In addition, there looks to be an optimum impact drop size, of around 1.88 mm radius, with respect to the lowest onset field (EC) values for both types of corona, regardless of impact momentum.

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P.B. Kinsey / Atmospheric Research 109-110 (2012) 14–24

For the present data, the line of best fit for weak and strong corona, at both fall heights, are: 6:5m :

2:5m :

Weak EC ¼ 1:75=r 7=2 þ 1:50 Strong EC ¼ 1:75=r 7=2 þ 1:65 Weak EC ¼ 1:83=r 7=2 þ 1:60 Strong EC ¼ 1:83=r 7=2 þ 1:70

ð5:a; bÞ

ð5:c; dÞ

4.1.2. Primary tip charge transfer and its possible contribution to electrical activity in oceanic thunderstorms The charge transfer data shown in Fig. 5a was obtained for impact drops of radius 2.3 mm. The onset fields (Ec) for weak and strong corona are 1.7 kV cm − 1 and 1.8 kV cm − 1 respectively. The literature also presents an estimate for the total current density generated by splashing drops during oceanic thunderstorms. Whilst the relationship's derivation is based on several assumptions and approximations, it nevertheless provides a basis for quantitative analysis. Such that the total current is given by: r2

j ¼ ∫ p:q:vt :nδr:

ð6Þ

r1

Where p is the probability of a discharge, q the quantity of charge transfer per event in μC, vt the terminal velocity in ms − 1 and nδr the number of drops per m 3 in the range r to r + δr. 4.1.2.1. Charge — (q). The value of q is obtained from Fig. 5a, and a approximation seems reasonable for drops in the mm size range (as in the literature), since the spread in the data shows that q does not have a specific value for any given field above Ec. Considering only the data for strong corona: with q in μC, and the applied field in kV cm − 1, q can be seen to be roughly equal to 0.75 [E − Ec]. 4.1.2.2. Probability — (p). On reaching the corona critical field (Ec), around 10% of drops produced a discharge. Thus at onset the probability of obtaining a primary tip discharge was 0.1. This value increased to 1 as the field was raised around 0.4 kV cm − 1 above the threshold level. Giving: p ¼ ½2:25:ðE−Ec Þ þ 0:1≡p ¼ 2:25:½ðE–Ec Þ þ 0:044’:

ð7Þ

4.1.2.3. Terminal velocity – (v). The terminal velocity (vt), in ms − 1, can be expressed as 6r 1/2, for r in mm, especially for large drops (Griffiths et al., 1973).

Fig. 5. a) The data is that for drops of 2.3 mm radius impacting a water surface at various field strengths. The critical fields for weak and strong corona are 1.7 and 1.8 kV cm− 1 respectively. b) The charge transfer values (nC) mainly relate to oscilloscope recorded jet drop coronae, in various electric fields, for drops of radii 1.76 mm and 1.34 mm. Note; data for fields below 0.5 kV cm− 1 were recorded with the charge integrator device.

4.1.2.4. Number of drops — (n). The number of drops in the range, nδr, is given by Marshall and Palmer (1948) expression for a raindrop size distribution. Such that: ND = N0 e− ΔD , where D is the drop diameter, NDδD is the number of drops per unit volume in the range D and D + δD, R is the precipitation rate in mm hr− 1, Δ is equal to 41R− 0.21 cm− 1, and NO is taken as 0.08 cm− 4 for any intensity of rainfall. The Marshall and Palmer (1948) integral depicts the number of active drops per m 3 and D1 and D2 are the diameters (in centimetres) corresponding to r1 and r2 (in millimetres). The largest drop in a thundershower is taken to have a radius (r2) of 3 mm. A value for r1 is obtained by putting E = Ec in Eq. (5.c,d) (present data; r1 = 1.68 mm). Therefore the complete relationship for the value of J, expressed in μA m − 2, is given by: 6

D2

ΔD

J ¼ 0:81  10 ∫ e D1

r2 n o 1=2 dD ∫ r ½E−Ec ½ðE−Ec Þ þ 0:44 dr: ð8Þ r1

P.B. Kinsey / Atmospheric Research 109-110 (2012) 14–24

4.1.3. Primary tip sample calculations of surface current per m 2 4.1.3.1. Calculation 1. In the present enquiry it was noted that falling water drops of 3 mm radius often broke up on surface impact, but for a direct comparison with the literature a value of r2 equal to 3 mm is here used together with the corresponding (extrapolated) value of 1.7 kV cm − 1 for Ec (Fig. 4a). Thus, taking R to be 50 mm hr − 1, the electric field at the water surface to be 2 kVcm − 1, r2 and r1 equal to 3 mm and 1.68 mm radius respectively, and the extrapolated value of Ec to be 1.7 kVcm − 1, then the resulting magnitude of J is roughly 21 μA m − 2, which is much too large and may only be produced as a transient pulse. 4.1.3.2. Calculation 2. Alternatively, using the present maximum drop size of 2.3 mm radius for r2, with r1 equal to 1..68 mm radius, the listed value of Ec (relative to a 2.3 mm radius drop) to be 1.8 kVcm− 1 (Table 1. and Fig. 4a) and substituting them into equation 8, computes a value for the surface current (J) equal to ~4 μA m− 2, which is in very good agreement with the 5 μA m − 2 reported by Griffiths et al. (1973), but this is also too large and may only occur as a transient. 4.1.3.3. Comment. Whichever value is considered (21 or 4 μA m − 2), both are vastly different to the 145 μAm− 2 reported by ur Rahman and Saunders (1988).

21

4.2.1. Secondary tip charge transfer and its possible contribution to electrical activity in oceanic thunderstorms Additional to the prior listed errors, are those of the Marshall and Palmer (1948) expression for drop size distribution (Section 4.1.1). The immediate limited data are for mid range raindrop sizes of 1.76 and 1.34 mm radius and here serve to indicate possible quantities of available charge. With a review of this type, small drop sizes are primarily important, since updraft speeds and potential gradients are essential to levitating any charged water drops into the cloud's mixing layers. In trying to introduce a modicum of quantitative analysis, a plot of charge transfer (Qt) versus electric field (Ef) for the two water drops is shown in Fig. 5b. Data for the field value of 100 V cm− 1 was obtained via the charge integrator and chart recorder, due to oscilloscope, low end, scale limitation and are here included for fullness. For electric fields ≥500 V cm− 1, all data are taken from oscilloscope images. Subsequently, Eqs. (6) and (8) were again utilized. 4.2.1.1. Charge. Due to limited oscilloscope data a value for q is gained from Fig. 5b and taken to be the average of the two data points per electric field strength (Ef). Thus in this review q takes on a specific value for each field strength. 4.2.1.2. Probability p. Extensive data does not exist for all impact drop sizes used in the enquiry, but data for jet drop production does. Each impact drop size was found to exhibit the jet drop corona phenomenon, down to electric fields of 500 V cm − 1 and possibly lower. In this exploratory study the probability of its occurrence is 1.

4.2. Secondary tip corona With the present enquiry several difficulties were encountered in providing an exact value for the charge transferred at the point of jet drop production. These are listed as follows: i) The jet drop corona's true magnitude is veiled by the drop itself, and it looks hazy, unlike the fast rising, positive, pulses of the primary jet tips. Electrostatic theory dictates majority charge migration to the jet drop's elongated upper hemisphere (the growing charge possibly aiding the conical distortion noted by Taylor, 1964), but not all the charge will locate in this way. In remaining electrically connected via the discharge, it is the drop's rapidly increasing charge density that simulates the brief, speedy, motion of a charged body within the system. ii) Because both camera films were celluloid, rather than digital memory card, minor errors were introduced, but these have been shown to be very small (Section 3.1.8). Numeric values for charge quantities transferred during secondary tip corona were obtained by measuring the pulse heights of respective photographs and, for the 100 V cm − 1 field, use of the charge integrator circuit. Care was taken in the measurement, but values are prone to error for reasons listed. However, the data offers a modicum of quantitative analysis. For the oscilloscope photographs, data is likely to be undervalued for reason (ii) above; and in using the charge integrator values may be compromised by the inclusion of charge from tiny drops drawn to, and collecting on, the system's upper electrode.

4.2.1.3. Terminal velocity v. From Mason's (1971) quoted values, the terminal velocity vt in ms − 1 can be expressed as 6r 1/2 for r in mm, and this relationship was again used 4.2.1.4. Number of drops n. The Marshall and Palmer (1948) expression for raindrop size distributions is considered valid in this case, since the largest and smallest drops have respective radii of 1.76 and 1.34 mm. Thus Eq. (8) becomes:

J¼

8 < :

6

D2

−ΔD

0:48  10 ∫ e D1

r2

1=2

dD ∫ r r1

9 =

⋅dr;  Q Average

Where J is expressed in nA m − 2. 4.2.2. Secondary tip sample calculation of Surface current per m 2 Taking R to be 50 mm hr− 1, the electric field at the water surface to range from100 V cm− 1 to 2.2 kV cm− 1, r2 and r1 equal to 1.76 and 1.34 mm radius respectively, the corresponding magnitudes for J are (approximately) as shown in Table 2. In order to have any environmental meaning, Table 2 data rely on two further assumptions: i) The electric field strengths at the water surface are attainable. ii) Upon becoming airborne all newly charged jet drops in the size range can be elevated into the cloud, via updrafts and potential gradients.

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P.B. Kinsey / Atmospheric Research 109-110 (2012) 14–24

5. Possible environmental implications, discussion and summary 5.1. Possible implications Extensive discourse on the charging of the atmosphere and marine aerosol has been offered by many workers, in particular Blanchard and Woodcock (1957) and Blanchard (1961), and calculations of current density accruing from the top jet drops of bursting bubbles formed by oceanic “white capping”, are reported. Furthermore, Vonnegut (1974a, 1974b) states; the electric field 0.5 m above an ocean surface can be twice the value over a wave crest as over a trough and Toland and Vonnegut (1977) have reported electric field values of 1.3 kV cm − 1 above a lake. In this study the naturally occurring jet drop corona has been shown to occur in fields down to 100 V cm − 1 (and possibly lower). Because drops from bursting bubbles are produced far more speedily than spray or Worthington jet drops, the latter two will almost certainly carry a higher charge. They may also contribute to the atmospheric electrification, providing the drop sizes are able to be elevated by wind shear, updraft and potential gradients. It is interesting to note that Black et al. (2007) presentation of the CBLAST data highlights the importance of sea spray drops in hurricane conditions moving from CAT1 to CAT5. While the significance may be their salt content, such drops will nevertheless be charged to some level below the Rayleigh limit (qRa), in accordance with the developing electric field gradient. The Rayleigh limit (1882), is here briefly defined as the maximum charge on a hydrometeor prior to disruption and depicted by qRa. 5.2. Discussion and summary 5.2.1. General The processes by which maritime clouds become electrified are commonly accepted to be different from continental ones. Should charge transfer from splashing drops and bursting bubbles make a significant contribution, then those of continental origin may also benefit, to a lesser degree, by way of lakes, rivers and tarns. Whether water drops, graupel, hail pellets, or mixture, their impacting a sea, or water, surface creates Worthington jets and drops, and crashing waves produce spray and spray drops. Otherwise bubble jet drops are formed by the encapsulation and entrainment of air, by wave motion. Due to differences in drop release speeds, drop longevity within the path length for corona propagation and sustainability is far greater for Worthington jet drops and Spray drops, than Blanchard jet drops. Crucial effects include, rain showers, wave motion, wind speeds/shear, water conductivity, updraft speeds and ambient electric fields. Because the present data are the result of a laboratory enquiry, as opposed to an environmental one, these influences need to be considered. 5.2.2. Space charge Adkins (1959) stated that charged droplets, produced by drops impacting hard surfaces, create a space charge which exponentially reduces the surface electric field with a time constant of 2.5 min for a heavy rainfall rate. Griffiths et al. (1973)

report a similar find for water surfaces, with a time constant of 1 min and report that the corona process can only take place for a short time and can only be initiated by rapid field changes. The present study shows droplet entry into the space charge region causes a huge perturbation, which recovers, over some 40 ms, due to upward moving layers of charged surface water. Environmentally, during rain showers, this effect will see space charge regions as being in a continual state of fluctuation. 5.2.3. Worthington jet: primary tip corona It is verified that multiple corona can propagate from the rise and fall of a Worthington jet's primary tip, as it performs under-damped sinusoidal oscillation. In Fig. 2(a, b), two such coronae are seen to have occurred around 70 ms apart. While the second is noticeably less intense, it is uncertain whether this is due to space charge suppression or corona avalanche during the necking process. It is then followed by a jet drop corona roughly 20 ms later. The present results, for Worthington primary point corona, give some support (Section 4.1.3) to the data of Phelps et al. (1973) and Griffiths et al. (1973), although there are matters for debate. In reviewing the aspect of water conductivity, ur Rahman and Saunders (1988) provide data for water mixed with sodium chloride (NaCl), to a sea salt concentration (0.6 mole l − 1). Using the same fall height (2.5 m) and similar drop size range to that of the literature (Griffiths et al., 1973) and the present enquiry, they report lower corona onset field (Ec) values. A line of best fit to their data is reportedly described by Ec = 1.2/r 7/2 + 1.52, as opposed to 1.9/r 7/2 + 1.78 for Griffiths et al. (1973) data, and 1.83/r 7/2 + 1.70 for the (strong) data of this enquiry. They also compute a sea surface current density of 145 μAm − 2 during rain showers. Despite increased conductivity this value seems quite high, in contrast to the 5 μAm − 2 reported by Griffiths et al. (1973) and the 21 μAm − 2 and 4 μAm − 2 calculated from extrapolated and present data (Section 4.1.3). On the same topic, Boussaton et al. (2005) investigated the influence of water conductivity on micro-discharges from raindrops, in onset streamer pulse mode, in strong electric fields and conclude it the discharge characteristic control parameter: “The higher the conductivity, the higher the pulse frequency and the lower the peak current intensity”. With respect to the corona onset field, they deem their results inconclusive, since measurements were made at atmospheric pressure and, citing Dawson (1969), state corona emission is clearly favoured by a decrease in pressure. The fact of their investigation utilizing a horizontal electric field, rather than a vertical one, may be of no great significance, since the experimental data of Blyth et al. (1998), using a vertical electric field, supported the earlier findings of Griffiths and Latham (1974) for a horizontal electric field, with regard to drop-graupel collision discharge. 5.2.4. Worthington jet: secondary tip corona The discovery of a prior unknown corona is reported and shown to initiate consequent to and coincident with, the production and airborne release of a naturally occurring jet drop. Nearing maximum height, about the top fifth of the water jet begins to thin, in a neck like manner. The necking continues, due to the outer layers receding while core layers are still

P.B. Kinsey / Atmospheric Research 109-110 (2012) 14–24

rising. As the neck breaks, the spawned drop's base fleetingly flares and flattens, whereas the underlying jet tip retains a hyperfine point of needle like radius. At this instant, the geometry resembles that of a “point to plane” gap (Fig. 3a) and a corona ensues (Fig. 3b). The necking procedure is detailed by many, not least of all Iribarne and Mason (1967), and is present in most water disruptive processes, like the breakup of large and small free falling drops, bubble bursting and splashing. Necking is probably inherent to all liquid drop production regardless of nature. With water, the mechanism appears prevalent to splash drops, jet drops, crown drops, spray drops and drip drops. Blanchard and Woodcock (1957), in citing research by Boyce (1951), state the experiment suggested that “relatively few salt particles were produced by the mere mechanical ‘tearing’ of the water in a breaking wave but that a significantly greater number could be produced a few seconds later when the bubbles resulting from the wave action had burst at the sea surface”. In essence, relating to the tearing or shearing of the electric double layer. Iribarne and Klemes (1974) show shear current to be a function of the necking process and report its taking place during the neck's final collapse. Since the collapse is synonymous with jet drop release, there appears to be two modes of current flow (two geometries) within the same natural event. Corona normally occurs between two asymmetric electrodes, one flat and one pointed (Loeb, 1965), as in jet drop release. The extent of the discharge is also dependant on the drop's release velocity, since this governs its dwell time in the corona propagation path length, for respective field gradients (Section 5.2.1). Taking wind and air flow into account: Bazelyan et al. (2009), citing earlier work by Chalmers (1967) and D'Alessandro (2009), amongst others, describe the wind's role in clearing space charge from coronating points; thereby vastly increasing the corona current. While the work is aimed at lightning, lightning rods and other earthed objects, it has relevance to this study insofar as the wind could prove counter-productive. Increased corona current may occur, but the addition of wind speed to the drop's release velocity would adversely affect its dwell time in the corona propagation path length. Given the present enquiry, whether the balance of two such effects would favourably increase drop charging, has yet to be determined. This setting is also relevant to updraft speeds and the elevation of charged water drops and particles into clouds. In this regard, Black and Hallett (1998) report wind speeds b4.5 ms − 1 will fail to carry water drops >1 mm in diameter aloft, whereas vertical winds >8–10 ms − 1 will carry all water drops aloft; possibly reaching levels much colder than 0 °C. Tinsley et al. (2006), propose the elevation of charged droplets and particles in the vicinity of a cloud may be indirectly involved in affecting the climate. They also convey the interaction between cloud droplets and aerosol particles, each with their own, leads to increased rates for coagulation and precipitation, due to electrically induced scavenging. In this same vein earlier treatise, by Pruppacher and Klett (1997), provide extensive analysis on collection and collision efficiencies, along with calculations for the scavenging of aerosol particles by cloud droplets. Regarding the long lasting argument between Simpson (1903) and Wilson (1903), their discord and rivalry being notably researched, and reported,

23

by Williams (2009): The discovered corona may have offered support to Wilson's reasoning and possibly a novel twist, in respect of charge being carried into the cloud by water drops. Jet drop corona are here not thought to be just a sudden occurrence, but more an extension, the next step in the natural phenomenon associated with electric double layer shear and the airborne release of water drops. From charging in zero or near zero fields, via electric double layer shear, to surging jet drop corona with magnitudes allied to ambient potential gradients. 6. Additional work 6.1. Oscilloscope The limitation on the oscilloscope range (fields ≥ 500 V m − 1) was extremely unfortunate and disappointing. Knowledge of the jet drop corona magnitudes in very low fields (approaching zero) is thought to be important. Modern day equipment should not find this to be a problem. 6.2. Possible method for the accurate measurement of charge on jet drop With present day electronics, and fast, light sensitive, switching times, it might be possible to fashion circuitry to collect drops following charge transfer. The equipment, similar in principal to the Bainbridge Mass Spectrometer, would utilize a horizontal magnetic field aligned above the water surface at right angles to the electric field. The onset and cessation of the low level luminosity, emitted by the discharge, could be used to arm and trigger the active and inactive states of both fields simultaneously. Since drops would tend to move in circular orbit, charge sensitive collection bins could be strategically positioned. Funding source (sponsor) The author wishes to thank the UMIST Department of Physics for funding the Ph.D. programme of research. Acknowledgements The author most definitely wishes to thank John Latham, for useful discussions and support during the course of study. He also wishes to thank Elsevier Editors, Reviewers and Support Staff, for their assistance and consideration. References Abbas, M.A., Latham, J., 1967. The instability of evaporating charged drops. J. Fluid Mech. 30, 663–670. Adkins, C.J., 1959. The small-ion concentration and space charge near the ground. Q.J.R. Met. Soc. 85, 237–252. Ausman, E.L., Brook, M., 1967. Distortion and disintegration of water drops in strong electric fields. J. Geophys. Res. 72, 6131–6135. Barreto, E., 1969. Electrical discharges from and between clouds of charged aerosols. J. Geophys. Res. 74, 6911–6925. Bazelyan, E.M., et al., 2009. Corona processes and lightning attachment: the effect of wind during thunderstorms. Atmos. Res. 94, 436–447. Black, R.A., Hallett, J., 1998. Electrification of the hurricane. J. Atmos. Sci. 56, 2004–2028. Black, P.G., et al., 2007. Air–sea exchange in hurricanes. Bull. Amer. Meteor. Soc. 88, 357–374.

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