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Negative corona discharge from a water droplet under the pulsating DC field
Journal of Electrostatics 71 (2013) 499e503
Contents lists available at SciVerse ScienceDirect
Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat
Negative corona discharge from a water droplet under the pulsating DC field Yoshio Higashiyama*, Shun Saito Yamagata University, 4-3-16, Jonan, Yonezawa, Yamagata 992-8510, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 September 2012 Received in revised form 9 January 2013 Accepted 9 January 2013 Available online 23 January 2013
Corona discharge from a fine water droplet always involves deformation of the droplet shape or Taylorcone formation, emission of fine water jets or disruption of droplet. Therefore, corona discharge from a water droplet always manifests complicated aspects. In addition, disruption of Taylor cone simultaneously affects not only discharge current but also motion of water droplet. To confirm corona discharge phenomena from a water droplet protruded from a tip of a metal capillary tube with a diameter of 1 mm, negative corona discharge was investigated by using a water droplet located at a tip of grounded rod electrode facing a ring electrode with positive dc voltage superimposed by ac one. Since the droplet has inherent resonant vibrating frequency defined by the size or volume, the volume of water droplet was adjusted at 20 nL where the corresponding resonant frequency was 500 Hz. The period of the event of successive corona discharge is exactly consistent with resonant frequency defined by the size of the water droplet. As a result, corona pulse trains with a definite duration appeared intermittently corresponding to its resonant vibration. When dc voltage superimposed by ac voltage with resonant frequency of 500 Hz was applied to the water droplet, corona pulse trains appeared at the period corresponding to the frequency. The maximum value of corona current reasonably increased with the applied voltage. Even when the frequency of ac field superimposed on dc field was varied from the resonant frequency, corona pulse trains occur corresponding to not only the superimposed field frequency but also resonant frequency. Ó 2013 Elsevier B.V. All rights reserved.
Keywords: Negative corona discharge Water droplet Taylor cone Resonant vibration Resonant frequency
1. Introduction A water droplet under strong electric field not only forms a Taylor cone but also sprays fine drops [1e4]. Since corona discharge from a water droplet with ejection of a number of fine drops involves vibration of the droplet, the waveform of corona discharge has unique feature [5e8]. Under dc field a water droplet forms a Taylor cone and corona discharge occurs at the instant of emission of water jets and continues to occur for the following period to restore the original droplet shape. After the cone returns to the original round shape, corona discharge deceased. As a result, the tip of water droplet vibrates periodically with a particular time interval. The periodic vibration of water droplet yields a series of corona pulse trains [8]. The occurrence frequency of corona pulse trains strongly depends on the water volume. The inherent vibrating frequency of an isolated droplet depends on the size of droplet [9e11]. Therefore, vibrating motion a tip of a Taylor cone
* Corresponding author. Tel./fax: þ81 238 26 3261. E-mail address: [email protected] (Y. Higashiyama). 0304-3886/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.elstat.2013.01.005
might be deeply related to resonant frequency of the droplet with a given volume or govern an occurrence frequency of corona discharge. However, the relationship between such resonant vibration and corona discharge has not been understood deeply. Corona discharge from a water droplet driven by pulsating field including resonant frequency would give some hints to understand the relationship. The purpose of this paper is to figure out the corona discharge from a tip of a water droplet under pulsating dc field superimposed by ac field with resonant frequency and to confirm the effect of resonant vibration on corona discharge. 2. Experimental A pair of a rod electrode having a capillary and ring electrode was used for measuring the characteristics of corona discharge from a water droplet as shown in Fig. 1. The rod electrode has a length of 10 mm and radius of 0.7 mm and has three capillary tubes inside. Radius curvature of the tip of the electrode is around 0.35 mm. The ring electrode has an inner diameter of 8 mm and a thickness of 0.5 mm. The distance between both electrodes was
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Y. Higashiyama, S. Saito / Journal of Electrostatics 71 (2013) 499e503
3. Results and discussion 3.1. Corona discharge under dc field
Fig. 1. Experimental apparatus for measuring corona discharge current from a droplet formed at a tip of capillary electrode.
set at 3.5 mm. A given volume of water droplet was formed at the tip of the rod electrode through the capillary tube where water was fed by a syringe pump. Positive dc voltage superimposed with ac voltage was applied to the ring electrode and the waveform of corona discharge current was obtained. The volume of the droplet depends on the flow rate and the elapsed time from start of the syringe pump. To keep a volume of water droplet constant, the droplet formed at the tip of the rod electrode was confirmed with a microscope. Fig. 2 shows the relationship between the height of the droplet and the droplet volume. Provided that the height from the surface of the rod electrode was kept constant, the volume was set at desired value. In this experiment, the droplet volume was in most cases adjusted at 23 nL to set the frequency of superimposed ac voltage of 500 Hz. The temperature of sample water was kept 25 C in all experiments by controlling a constant chamber temperature to make sure of surface tension or viscosity of the sample water. By applying the positive pulsating voltage to the ring electrode, the waveform of corona current flowing through a register of 10 kU was measured with a digital oscilloscope (Tektronix TDSB, 1 GHz 5 GS/s). The motion of a water droplet was recorded by a highspeed video camera (Photron, FASTCAM-Ultima II) with a speed of 9000 frames/s.
Fig. 2. Relationship between the height of a water droplet and its volume.
Fig. 3 shows a typical current waveform of negative corona discharge occurring at a sharpened water droplet when dc positive voltage was applied to the ring electrode. Corona pulse trains appeared periodically. Occurrence of periodic corona discharge means that a droplet repeats formation of a sharp cone and the returning to a round shape at regular period. The disruption of a Taylor cone appears as occurrence of the first largest pulse in a series of pulse trains. After the tip of a Taylor cone breaks into a number of fine charged jets, the cone returns to the round shape at the lower position accompanying with corona discharge. Thus, small successive corona pulses follow an initial large pulse corresponding to the motion of the tip of water droplet. Occurrence of corona pulse trains with a regular period indicates that corona discharge from a droplet occurs synchronized with change of the droplet shape or with a resonant vibration of the water droplet. A single series of corona pulse trains in the pulse groups is enlarged in Fig. 3(b). After the first pulse, the height of corona pulse increased gradually and the pulse ceased at a relatively higher pulse. Time variation in shape of a droplet during regular motion or resonant vibration is shown in Fig. 4. The upward and downward motion of the tip of a droplet is consistent with occurrence of the corona pulse trains. Fig. 5 shows the frequency of vibration or inverse value of the interval of corona pulse group in corona discharge occurring from
Fig. 3. Typical current waveform of negative corona discharge from a water droplet under a dc field. (a) Corona pulse group (b) pulse trains.
Y. Higashiyama, S. Saito / Journal of Electrostatics 71 (2013) 499e503
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Fig. 4. Resonant vibration of a 52 nL water droplet located at the tip of a rod electrode under a dc electric field. (a) 0 ms (b) 0.44 ms (c) 0.88 ms (d) 1.10 ms (e) 1.32 ms (f) 1.76 ms.
a water droplet with a given volume under dc field. Even in a dc field, corona discharge occurred at a regular period. The interval of the pulse group is increased with the volume. This means the occurrence frequency of formation of a Taylor cone and disruption strongly relates to the droplet volume and the occurrence of corona discharge was governed by droplet volume. 3.2. Corona discharge from a water under pulsating field
Fig. 5. Resonant frequency of a water droplet under dc electric field.
Fig. 6. Corona pulse group for pulsating voltage superimposed by ac voltage with 500 Hz (a) 1 kVp-p (b) 3 kVp-p.
Fig. 6 shows the corona pulse under pulsating voltage composing of 5.55 kV dc and ac voltage with 500 Hz. When the peak value of pulsating voltage with applied to the ring electrode was increased, the corona pulse was increased. The frequency of the vibration or corona discharge is consistent with applied pulsating field of 500 Hz. Applied voltage showed sudden decrease at inception of corona discharge due to drop of the voltage. The relationship between the peak current and amplitude of the superimposed ac voltage as well as duration of corona pulse group is shown in Fig. 7. The peak value of the first pulse is increased with the amplitude of pulsating voltage. Although the magnitude of successive corona pulse might strongly affect the decrease of applied voltage, the magnitude of the first pulse must manifest the effect of the applied voltage. On the other hand, the duration of corona discharge trains is almost constant, regardless of the magnitude of sinusoidal voltage. This is uncertain whether the drop of the applied voltage might affect the duration time. Fig. 8 shows the effect of a bias dc voltage on the discharging aspect. The superimposed ac voltage with 500 Hz was set at the peak to peak value of 2.5 kV. For the corona onset voltage of 4.75 kV, peak current and duration time is relatively small. As applied voltage was increased, the peak current and duration time were increased. When the applied voltage was enough high, the discrete pulse group never appeared and corona pulse occurred
Fig. 7. Maximum peak current during pulse trains and discharge duration time in a pulse trains for a 23 nL droplet under a 500 Hz pulsating dc field.
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Fig. 8. Corona discharge from a water droplet under a 500 Hz pulsating voltage with various bias voltage. (a) 4.75 kV (b) 5.55 kV (c) 6.15 kV (d) 6.35 kV.
continuously corresponding to the time variation of applied voltage. It should be noted that time of the peak of current and voltage is not consistent. This means that the tip of the water droplet varied slightly with smaller deviation of the tip than that in resonant vibration. Furthermore, the motion of the droplet was delayed by the applied voltage. The dependence of the peak current and duration time on offset voltage is shown in Fig. 9. Both values increase with the offset voltage. When higher voltage was applied to the electrode, droplet never shows vibration and never forms a Taylor cone. As a result, there are no large peak and discrete pulse groups. Fig. 10 shows the corona discharge under pulsating voltage with a frequency deferent from a resonant frequency. In case of 200 Hz as shown in Fig. 10(a), pulsating voltage was superimposed, corona discharge occurred at regular period by 5 ms. The first large pulse and followed corona pulse trains exactly appeared at the regular
Fig. 9. Magnitude of the first corona pulse and duration time in a pulse series to offset dc voltage of a pulsating voltage.
Fig. 10. Corona discharge from a water droplet under a pulsating voltage with deviated from resonant frequency. (a) 200 Hz (b) 600 Hz.
Y. Higashiyama, S. Saito / Journal of Electrostatics 71 (2013) 499e503
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driven by a pulsating voltage vibrated in the highest position at the resonant frequency. 4. Conclusion Corona discharge from a water droplet was investigated using the pulsating dc field superimposed by ac voltage with resonant frequency. When a given volume of water droplet is kept constant, water drop shows resonant vibration, regardless of frequency of superimposed ac field. This means that water drop forms Taylor cone in a regular period or its motion is governed by resonant vibration. At the higher applied voltage or higher electric field, a water droplet never forms a Taylor cone and keeps an elongated shape. It is necessary to find out the condition to keep elongated shape and without forming Taylor cone at the higher electric field. Fig. 11. Magnitude of the first corona pulse and duration time in a pulse series to frequency of ac voltage in a pulsating voltage.
References
period synchronized with the frequency of applied voltage. However, additive corona pulse was occurred at 2 ms after the first large pulse. This indicates the water droplet vibrates at 500 Hz of own resonant vibrating frequency and must form a cone, smaller or larger. Thus, corona discharge could cause at the minimum of the voltage waveform. On the other hand, in case of 600 Hz field, the corona discharge never occurred at the peak of the applied voltage and seemed to occur randomly. These phenomena are also governed by resonant vibration of the droplet. Although the corona discharge surely occurred at the higher electric field, the period of corona pulse group was around 2 ms. This shows the droplet still in the resonant motion and corona discharge occurred in consistent with resonant vibration. Fig. 11 shows the dependence of the peak current and duration time on frequency. The peak current is highest at the resonant frequency. Even at the same height of applied voltage, droplet
[1] J. Zeleny, Instability of electrified liquid surfaces, Phys. Rev. 10 (1) (1917) 1e6. [2] G. Taylor, Disintegration of water drops in an electric field, Proc. Roy. Soc. Lond. A280 (1964) 383e397. [3] M. Cloupeau, B. Prunet-foch, Electrostatic spraying of liquids in cone-jet mode, J. Electrostatics 22 (1989) 135e159. [4] G.M.H. Meesters, et al., Generation of micron-sized droplets from the Taylor cone, J. Aerosol. Sci. 23 (1) (1992) 37e49. [5] L.B. Loeb, Electrical Coronas, University of California Press, Berkeley, 1965, p. 249. [6] Y. Satoh, Y. Tsunoda, K. Arai, Corona pulses from a water drop on a cylindrical conductor surface, J. IEEJ 81 (877) (1961) 1606e1615 (in Japanese). [7] M. Akazaki, Corona phenomena from water drops on smooth conductors under high direct voltage, IEEE Trans. Power Appar. Syst. PAS 84 (1965) 1e8. [8] T. Sugimoto, K. Asano, Y. Higashiyama, Negative corona discharge at a tip of a water cone deformed under dc field, J. Electrostatics 53 (2001) 25e38. [9] T. Yamada, T. Sugimoto, Y. Higashiyama, M. Takeishi, T. Aoki, Resonance phenomena of a single water droplet located on a hydrophobic sheet under ac electric field, IEEE Trans. Ind. Appl. 39 (1) (2003) 59e65. [10] S.B. Sample, B. Raghupathy, C.D. Hendrics, Quiescent distortion and resonant oscillation of a liquid drop in an electric field, Int. J. Eng. Sci. 8 (1970) 97e109. [11] M. Strani, Sabata, Free vibration of a drop in partial contact with a solid support, J. Fluid Mech. 141 (1984) 233e247.
Contents lists available at SciVerse ScienceDirect
Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat
Negative corona discharge from a water droplet under the pulsating DC field Yoshio Higashiyama*, Shun Saito Yamagata University, 4-3-16, Jonan, Yonezawa, Yamagata 992-8510, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 September 2012 Received in revised form 9 January 2013 Accepted 9 January 2013 Available online 23 January 2013
Corona discharge from a fine water droplet always involves deformation of the droplet shape or Taylorcone formation, emission of fine water jets or disruption of droplet. Therefore, corona discharge from a water droplet always manifests complicated aspects. In addition, disruption of Taylor cone simultaneously affects not only discharge current but also motion of water droplet. To confirm corona discharge phenomena from a water droplet protruded from a tip of a metal capillary tube with a diameter of 1 mm, negative corona discharge was investigated by using a water droplet located at a tip of grounded rod electrode facing a ring electrode with positive dc voltage superimposed by ac one. Since the droplet has inherent resonant vibrating frequency defined by the size or volume, the volume of water droplet was adjusted at 20 nL where the corresponding resonant frequency was 500 Hz. The period of the event of successive corona discharge is exactly consistent with resonant frequency defined by the size of the water droplet. As a result, corona pulse trains with a definite duration appeared intermittently corresponding to its resonant vibration. When dc voltage superimposed by ac voltage with resonant frequency of 500 Hz was applied to the water droplet, corona pulse trains appeared at the period corresponding to the frequency. The maximum value of corona current reasonably increased with the applied voltage. Even when the frequency of ac field superimposed on dc field was varied from the resonant frequency, corona pulse trains occur corresponding to not only the superimposed field frequency but also resonant frequency. Ó 2013 Elsevier B.V. All rights reserved.
Keywords: Negative corona discharge Water droplet Taylor cone Resonant vibration Resonant frequency
1. Introduction A water droplet under strong electric field not only forms a Taylor cone but also sprays fine drops [1e4]. Since corona discharge from a water droplet with ejection of a number of fine drops involves vibration of the droplet, the waveform of corona discharge has unique feature [5e8]. Under dc field a water droplet forms a Taylor cone and corona discharge occurs at the instant of emission of water jets and continues to occur for the following period to restore the original droplet shape. After the cone returns to the original round shape, corona discharge deceased. As a result, the tip of water droplet vibrates periodically with a particular time interval. The periodic vibration of water droplet yields a series of corona pulse trains [8]. The occurrence frequency of corona pulse trains strongly depends on the water volume. The inherent vibrating frequency of an isolated droplet depends on the size of droplet [9e11]. Therefore, vibrating motion a tip of a Taylor cone
* Corresponding author. Tel./fax: þ81 238 26 3261. E-mail address: [email protected] (Y. Higashiyama). 0304-3886/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.elstat.2013.01.005
might be deeply related to resonant frequency of the droplet with a given volume or govern an occurrence frequency of corona discharge. However, the relationship between such resonant vibration and corona discharge has not been understood deeply. Corona discharge from a water droplet driven by pulsating field including resonant frequency would give some hints to understand the relationship. The purpose of this paper is to figure out the corona discharge from a tip of a water droplet under pulsating dc field superimposed by ac field with resonant frequency and to confirm the effect of resonant vibration on corona discharge. 2. Experimental A pair of a rod electrode having a capillary and ring electrode was used for measuring the characteristics of corona discharge from a water droplet as shown in Fig. 1. The rod electrode has a length of 10 mm and radius of 0.7 mm and has three capillary tubes inside. Radius curvature of the tip of the electrode is around 0.35 mm. The ring electrode has an inner diameter of 8 mm and a thickness of 0.5 mm. The distance between both electrodes was
500
Y. Higashiyama, S. Saito / Journal of Electrostatics 71 (2013) 499e503
3. Results and discussion 3.1. Corona discharge under dc field
Fig. 1. Experimental apparatus for measuring corona discharge current from a droplet formed at a tip of capillary electrode.
set at 3.5 mm. A given volume of water droplet was formed at the tip of the rod electrode through the capillary tube where water was fed by a syringe pump. Positive dc voltage superimposed with ac voltage was applied to the ring electrode and the waveform of corona discharge current was obtained. The volume of the droplet depends on the flow rate and the elapsed time from start of the syringe pump. To keep a volume of water droplet constant, the droplet formed at the tip of the rod electrode was confirmed with a microscope. Fig. 2 shows the relationship between the height of the droplet and the droplet volume. Provided that the height from the surface of the rod electrode was kept constant, the volume was set at desired value. In this experiment, the droplet volume was in most cases adjusted at 23 nL to set the frequency of superimposed ac voltage of 500 Hz. The temperature of sample water was kept 25 C in all experiments by controlling a constant chamber temperature to make sure of surface tension or viscosity of the sample water. By applying the positive pulsating voltage to the ring electrode, the waveform of corona current flowing through a register of 10 kU was measured with a digital oscilloscope (Tektronix TDSB, 1 GHz 5 GS/s). The motion of a water droplet was recorded by a highspeed video camera (Photron, FASTCAM-Ultima II) with a speed of 9000 frames/s.
Fig. 2. Relationship between the height of a water droplet and its volume.
Fig. 3 shows a typical current waveform of negative corona discharge occurring at a sharpened water droplet when dc positive voltage was applied to the ring electrode. Corona pulse trains appeared periodically. Occurrence of periodic corona discharge means that a droplet repeats formation of a sharp cone and the returning to a round shape at regular period. The disruption of a Taylor cone appears as occurrence of the first largest pulse in a series of pulse trains. After the tip of a Taylor cone breaks into a number of fine charged jets, the cone returns to the round shape at the lower position accompanying with corona discharge. Thus, small successive corona pulses follow an initial large pulse corresponding to the motion of the tip of water droplet. Occurrence of corona pulse trains with a regular period indicates that corona discharge from a droplet occurs synchronized with change of the droplet shape or with a resonant vibration of the water droplet. A single series of corona pulse trains in the pulse groups is enlarged in Fig. 3(b). After the first pulse, the height of corona pulse increased gradually and the pulse ceased at a relatively higher pulse. Time variation in shape of a droplet during regular motion or resonant vibration is shown in Fig. 4. The upward and downward motion of the tip of a droplet is consistent with occurrence of the corona pulse trains. Fig. 5 shows the frequency of vibration or inverse value of the interval of corona pulse group in corona discharge occurring from
Fig. 3. Typical current waveform of negative corona discharge from a water droplet under a dc field. (a) Corona pulse group (b) pulse trains.
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Fig. 4. Resonant vibration of a 52 nL water droplet located at the tip of a rod electrode under a dc electric field. (a) 0 ms (b) 0.44 ms (c) 0.88 ms (d) 1.10 ms (e) 1.32 ms (f) 1.76 ms.
a water droplet with a given volume under dc field. Even in a dc field, corona discharge occurred at a regular period. The interval of the pulse group is increased with the volume. This means the occurrence frequency of formation of a Taylor cone and disruption strongly relates to the droplet volume and the occurrence of corona discharge was governed by droplet volume. 3.2. Corona discharge from a water under pulsating field
Fig. 5. Resonant frequency of a water droplet under dc electric field.
Fig. 6. Corona pulse group for pulsating voltage superimposed by ac voltage with 500 Hz (a) 1 kVp-p (b) 3 kVp-p.
Fig. 6 shows the corona pulse under pulsating voltage composing of 5.55 kV dc and ac voltage with 500 Hz. When the peak value of pulsating voltage with applied to the ring electrode was increased, the corona pulse was increased. The frequency of the vibration or corona discharge is consistent with applied pulsating field of 500 Hz. Applied voltage showed sudden decrease at inception of corona discharge due to drop of the voltage. The relationship between the peak current and amplitude of the superimposed ac voltage as well as duration of corona pulse group is shown in Fig. 7. The peak value of the first pulse is increased with the amplitude of pulsating voltage. Although the magnitude of successive corona pulse might strongly affect the decrease of applied voltage, the magnitude of the first pulse must manifest the effect of the applied voltage. On the other hand, the duration of corona discharge trains is almost constant, regardless of the magnitude of sinusoidal voltage. This is uncertain whether the drop of the applied voltage might affect the duration time. Fig. 8 shows the effect of a bias dc voltage on the discharging aspect. The superimposed ac voltage with 500 Hz was set at the peak to peak value of 2.5 kV. For the corona onset voltage of 4.75 kV, peak current and duration time is relatively small. As applied voltage was increased, the peak current and duration time were increased. When the applied voltage was enough high, the discrete pulse group never appeared and corona pulse occurred
Fig. 7. Maximum peak current during pulse trains and discharge duration time in a pulse trains for a 23 nL droplet under a 500 Hz pulsating dc field.
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Fig. 8. Corona discharge from a water droplet under a 500 Hz pulsating voltage with various bias voltage. (a) 4.75 kV (b) 5.55 kV (c) 6.15 kV (d) 6.35 kV.
continuously corresponding to the time variation of applied voltage. It should be noted that time of the peak of current and voltage is not consistent. This means that the tip of the water droplet varied slightly with smaller deviation of the tip than that in resonant vibration. Furthermore, the motion of the droplet was delayed by the applied voltage. The dependence of the peak current and duration time on offset voltage is shown in Fig. 9. Both values increase with the offset voltage. When higher voltage was applied to the electrode, droplet never shows vibration and never forms a Taylor cone. As a result, there are no large peak and discrete pulse groups. Fig. 10 shows the corona discharge under pulsating voltage with a frequency deferent from a resonant frequency. In case of 200 Hz as shown in Fig. 10(a), pulsating voltage was superimposed, corona discharge occurred at regular period by 5 ms. The first large pulse and followed corona pulse trains exactly appeared at the regular
Fig. 9. Magnitude of the first corona pulse and duration time in a pulse series to offset dc voltage of a pulsating voltage.
Fig. 10. Corona discharge from a water droplet under a pulsating voltage with deviated from resonant frequency. (a) 200 Hz (b) 600 Hz.
Y. Higashiyama, S. Saito / Journal of Electrostatics 71 (2013) 499e503
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driven by a pulsating voltage vibrated in the highest position at the resonant frequency. 4. Conclusion Corona discharge from a water droplet was investigated using the pulsating dc field superimposed by ac voltage with resonant frequency. When a given volume of water droplet is kept constant, water drop shows resonant vibration, regardless of frequency of superimposed ac field. This means that water drop forms Taylor cone in a regular period or its motion is governed by resonant vibration. At the higher applied voltage or higher electric field, a water droplet never forms a Taylor cone and keeps an elongated shape. It is necessary to find out the condition to keep elongated shape and without forming Taylor cone at the higher electric field. Fig. 11. Magnitude of the first corona pulse and duration time in a pulse series to frequency of ac voltage in a pulsating voltage.
References
period synchronized with the frequency of applied voltage. However, additive corona pulse was occurred at 2 ms after the first large pulse. This indicates the water droplet vibrates at 500 Hz of own resonant vibrating frequency and must form a cone, smaller or larger. Thus, corona discharge could cause at the minimum of the voltage waveform. On the other hand, in case of 600 Hz field, the corona discharge never occurred at the peak of the applied voltage and seemed to occur randomly. These phenomena are also governed by resonant vibration of the droplet. Although the corona discharge surely occurred at the higher electric field, the period of corona pulse group was around 2 ms. This shows the droplet still in the resonant motion and corona discharge occurred in consistent with resonant vibration. Fig. 11 shows the dependence of the peak current and duration time on frequency. The peak current is highest at the resonant frequency. Even at the same height of applied voltage, droplet
[1] J. Zeleny, Instability of electrified liquid surfaces, Phys. Rev. 10 (1) (1917) 1e6. [2] G. Taylor, Disintegration of water drops in an electric field, Proc. Roy. Soc. Lond. A280 (1964) 383e397. [3] M. Cloupeau, B. Prunet-foch, Electrostatic spraying of liquids in cone-jet mode, J. Electrostatics 22 (1989) 135e159. [4] G.M.H. Meesters, et al., Generation of micron-sized droplets from the Taylor cone, J. Aerosol. Sci. 23 (1) (1992) 37e49. [5] L.B. Loeb, Electrical Coronas, University of California Press, Berkeley, 1965, p. 249. [6] Y. Satoh, Y. Tsunoda, K. Arai, Corona pulses from a water drop on a cylindrical conductor surface, J. IEEJ 81 (877) (1961) 1606e1615 (in Japanese). [7] M. Akazaki, Corona phenomena from water drops on smooth conductors under high direct voltage, IEEE Trans. Power Appar. Syst. PAS 84 (1965) 1e8. [8] T. Sugimoto, K. Asano, Y. Higashiyama, Negative corona discharge at a tip of a water cone deformed under dc field, J. Electrostatics 53 (2001) 25e38. [9] T. Yamada, T. Sugimoto, Y. Higashiyama, M. Takeishi, T. Aoki, Resonance phenomena of a single water droplet located on a hydrophobic sheet under ac electric field, IEEE Trans. Ind. Appl. 39 (1) (2003) 59e65. [10] S.B. Sample, B. Raghupathy, C.D. Hendrics, Quiescent distortion and resonant oscillation of a liquid drop in an electric field, Int. J. Eng. Sci. 8 (1970) 97e109. [11] M. Strani, Sabata, Free vibration of a drop in partial contact with a solid support, J. Fluid Mech. 141 (1984) 233e247.