# Electrohydrodynamic gas flow in a positive corona discharge

Éric Moreau, Pierre Audier, Thomas Orrière, Nicolas Bénard

► To cite this version:

Éric Moreau, Pierre Audier, Thomas Orrière, Nicolas Bénard. Electrohydrodynamic gas flow in a positive corona discharge. Journal of Applied Physics, 2019, 125 (13), pp.133303. 10.1063/1.5056240. hal-02129303

HAL Id: hal-02129303

https://hal.science/hal-02129303v1

Submitted on 16 May 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Electrohydrodynamic gas flow in a positive corona discharge

Eric MOREAU*, Pierre AUDIER, Thomas ORRIERE, Nicolas BENARD

University of Poitiers, Pprime institute, CNRS, ISAE-ENSMA

Téléport 2, BP 30179, 86962 Futuroscope, France

* corresponding author : eric.moreau@univ-poitiers.fr
**Abstract**

When a sufficient high voltage is applied between a point and a plate in atmospheric air, a corona discharge is ignited and an electrohydrodynamic force can be produced, resulting in an ionic wind of a few meters per second flowing from the point toward the plate. In this study, we aimed at characterizing the ionic wind EHD flow produced by DC positive a point-to-plate corona discharges. This is realized with the help of a high-speed particle image velocimetry system and Schlieren visualizations. The obtained measurements allowed us to characterize precisely the ionic wind versus time, as well as its dynamics when the discharge is switched on. Hence, for the first time, we highlighted the key role of the breakdown streamers in the ionic wind hydrodynamics. We discovered that, in presence of breakdown streamers, the positive corona discharge produces a pulsed ionic wind whose frequency corresponds to the frequency of the current pulses. To explain this EHD result, we investigated and showed that each single current pulse is composed of several streamers or several branches of one streamer, this phenomenon being at the origin of a space charge mainly composed of positive ions. Finally, we highlighted that when the steady breakdown streamer regime takes place, the time-averaged current become greater than theoretical values given by Townsend's law since it evolves nearly linearly with the high voltage.
# I. Introduction

Corona discharges have been the subject of intensive studies that started at the end of the 19th century¹,². Since then, throughout the 20th century, much progress has been realized, leading to a better understanding of the extremely complex phenomena related to these discharges³⁻¹⁷. A corona discharge is usually generated in air at or near atmospheric pressure when a high voltage is applied to a sharp edge, a point or a small diameter wire electrode. Due to the strong electric field close to this active electrode, the gas is ionized and a plasma is created. On the one hand, in most engineering applications, the capability of corona discharges can be used to modify the gas chemistry, for ozone production¹⁸,¹⁹, reduction of gaseous pollutants²⁰,²¹, surface treatment²² or assisted-combustion²³,²⁴ to name a few examples. On the other hand, it can be used for its electrohydrodynamic (EHD) properties, either for manipulating the trajectory of particles in electrostatic precipitators²⁵⁻²⁷, either to induce a thrust or an air flow²⁸⁻³². For about twenty years, this last EHD phenomenon has been the subject of a lot of research because of its numerous applications, mainly for airflow control by plasma actuators³³⁻³⁵. Indeed, the ions produced by the corona discharge drift from the active electrode toward the other one, exchange momentum with the air neutral molecules by collisions, resulting in an EHD jet flow usually called electric or ionic wind. The EHD mechanisms involved in corona discharges have been intensively studied²,¹⁶,²⁸,³⁰,³¹,³⁶. However, only the time-averaged steady state of the phenomenon is usually described, except in a recent article in the case of a negative corona discharge composed of Trichel pulses³⁷. Understanding the underlying phenomena occurring during the transient regime of the discharge, from the corona discharge onset to its steady-state, is a fundamental step to unveil the mechanisms of ionic wind production and plasma-gas interactions.

Hence, in the present study, we propose to deeply investigate the temporal behavior of the ionic wind and to link it with its electrical, optical and mechanical properties. For that purpose, we developed an original multi-metrology experimental bench including electrical characterization, intensified imaging, Schlieren photography and time-resolved particle image velocimetry (PIV).

# II. Experimental Setup

The corona discharge is ignited in applying a positive DC high voltage to a needle, pointing to a plate electrode connected to the ground. Both electrodes are made of stainless-steel and are separated by a 25 mm gap (Fig. 1), such as in Moreau et al.³⁸. The needle electrode is 60 mm-long, 1 mm in diameter and ended with a tip having a curvature radius of about 100 µm. The plate electrode has a disk shape, with a diameter of 80 mm and rounded edges. Both electrodes are set on an insulating stand. The high voltage is generated by a 3000V/V amplifier
(Trek 30kV/40mA), amplifying a positive DC voltage provided by a signal generator (Lecroy WaveStation 3082) with a slew rate of about 500V.µs⁻¹. The voltage V between the two electrodes is measured with a high voltage probe (North StarPVM-1, 500MHz). The discharge current waveform is computed using a Lecroy voltage probe (PP018, 500MHz, 10pF) measuring the voltage across a 1kΩ resistor set between the plate electrode and earth. All the signals are recorded with a digital oscilloscope (Lecroy HDO6054, 500MHz, 2.5GS.s⁻¹). All the experiments are realized at atmospheric pressure in few successive days. Temperature, pressure and humidity are quite constant during this period (T = 22 ± 2°C, P = 1020 ± 2hPa, RH = 50 ± 15%).

Images of the discharge are recorded by a fast gateable iCCD camera (Princeton, Pi-max4 Gen2) with a resolution of 1024×1024 pixels² and equipped with a 60mm objective. The final field of view covers a region corresponding to 39 × 39mm (38 µm per pixel). The same trigger source used for Schlieren imaging is also used to synchronize the camera and the discharge. The time delay between the discharge ignition and the shutter opening of the camera is managed using the software of the camera (Princeton Light Field). In this study, the shutter of the camera is triggered to open 5ms after the high voltage rise, during 2ms, to observe the morphology of the plasma a few milliseconds after the ignition (t ∈ [5ms, 7ms]).

To gain insight into the dynamics of the discharge onset, a LaVision time-resolved PIV system is used. The whole needle-to-plate apparatus is put into a hermetic PMMA tank (30 × 80 × 40mm³). The air is seeded with dielectric oil droplets (Ondina 915) with a mean diameter of 0.3µm and a 532nm Nd:YAG laser generator (Continuum Mesa), fitted with divergent cylindrical lens, is used to provide a laser sheet to illuminate the particles. Images are acquired using a high-speed camera (Photron Fastcam SA-Z), with a resolution of 1024 × 1024 pixels² and combined with a 60mm lens. The acquisition frequency is set to 20kHz, leading to a time delay of 50µs between two consecutive images. In total, 3000 vector fields are acquired for each experiment. Velocity fields were computed in the x-y plane, passing through the needle and the middle of the plate (z = 0). Longitudinal and normal velocity components are computed using a cross-correlation algorithm with adaptive multi-passes, interrogation windows of 64 × 64 down to 16 × 16 pixels² and an overlap set to 50%.
The resulting images have a size of 30 × 30mm and the final flow field resolution is one vector every 266µm.

In addition to PIV, Schlieren imaging is used to visualize the discharge onset. The set-up consisted in a Z-type Schlieren system, with two spherical mirrors (50mm diameter and 1.016m focal length) and with a high-power LED (Luminus CBT-120) as light source. The entrance slit is adjusted to 1mm, and the knife-edge is positioned to get a 80% light cutoff. Images are acquired using a camera (JAI CV-M2) with a 1600 × 1200 pixels² CCD sensor, equipped with a 180mm lens and a focal length doubler. The final field of view covers a region corresponding to 36 × 27mm (22 µm per pixel). The LED, the camera and the discharge are synchronized with a
common trigger source (ARMEXEL PDG-2520), to easily change the delay between the discharge ignition on the one hand and the 1 µs long light pulse and the shutter opening of the camera on the other. In this way, snapshots are acquired at a precise time delay after the beginning of the discharge, to be compared to the PIV velocity fields.

<figure><img src="image_2.png" /><figcaption>FIG. 1. Experimental setup.</figcaption></figure>

### III. Electrical Measurements

Although the terminologies are not always the same, several authors<sup>9,11-13,15,39</sup> described the different regimes of the positive point-plane corona discharge when the applied voltage is increased. In the case of a thin active electrode, an intermittent regime composed of onset streamers starting just above the ignition voltage is firstly observed. Then a stable regime called Hermstein's glow regime<sup>12</sup> appears and finally, before spark occurs, a regime composed of breakdown streamers crossing the electrode takes place<sup>9,10</sup>. In order to clearly identify the regime of our corona discharge, we started by studying its electrical and optical characteristics. As illustrated in Fig. 2, for a voltage below a certain threshold value (14 kV in our experimental conditions), we observe a stable Hermstein's glow regime characterized by a small ionized region close to the tip of the high voltage electrode and a discharge current which is only composed of a steady component of a few µA (not visible in the first plot of Fig. 2(a) because the current scale is in mA). When the voltage reaches 14 kV, the glow discharge becomes unstable and the breakdown streamer regime starts to appear. It is characterized by the apparition of some erratic current peaks with an amplitude of a few mA added to the steady DC component and corresponding to the propagation of streamers between both electrodes<sup>14</sup>. The threshold value of 14 kV corresponds then to the transition between the glow and the streamer discharge regimes, in our experimental conditions. Increasing the
applied voltage above this threshold value leads to the formation of more and more breakdown streamers, their light emission increasing with the applied high voltage. The amplitude and the repetition rate of the current pulses increase while the time interval between two consecutive peaks becomes more uniform with a frequency around a few kilohertz. From 16 kV, we may assume that we are in the presence of a steady breakdown streamer regime. This result is not new since it has already been highlighted in one of our previous article³⁸.

If we focus on one single current pulse (Fig. 3(a)), several remarks can be done. First, the duration of the current pulses spreads over 400ns, its rising time becomes shorter when the applied voltage increases. Secondly, by taking a closer look at the shape of the current pulse for 14 kV and 16 kV, we can observe that it looks like the one observed by several authors in the past¹³,¹⁵,⁴⁰ and precisely explained in a recent paper of Eichwald et al.⁴¹ concerning primary and secondary streamers. In this last paper, the authors highlighted that the first peak of one single current pulse corresponds to the arrival of a primary streamer at the cathode, then followed by a secondary streamer. By determining Δt, the time needed for the primary streamer to cross the interelectrode gap, one can estimate the velocity of the primary streamer. If we apply this method to our corona discharge (voltage equal to 16 kV), we find Δt = 125 ns, corresponding to a streamer velocity of about 0.2×10⁶ m/s. This value is in agreement with the Eichwald's ones. Consequently, we might think that we are in the same discharge regime as Marode⁴⁰ and Eichwald et al.⁴¹. However, it is not so simple. Indeed, in our case, there are several extremums in a single current pulse, even when the current is dropping. This is especially visible at 20kV, where two main extremums are present around 50 ns and 80 ns, followed by several others during the current drop. That means that this whole current pulse is the addition of several shorter current pulses, each of them corresponding certainly to the arrival of a single streamer in a streamer branching process.

Moreover, by analyzing this current pulse, we can show that its maximum magnitude as well as the energy and the charge transferred by these successive streamers, increase linearly with the applied voltage (Fig. 3(b)).

To finalize the electrical characterization of the discharge, we decided to plot the evolution of the time-averaged discharge current as a function of the applied voltage in order to verify whether it follows the theoretical I-V Townsend's expression¹,³,⁴:

$$I = C \times V (V - V_0) \qquad (1)$$

where V is the applied DC voltage, V₀ the ionization threshold value and C a constant depending on the electrode configuration, temperature, pressure and gas composition. As we can see in Fig. 3(c), when V is smaller than or equal to 14 kV, equation (1) allows us to correctly interpolate the I-V experimental curve (with V₀ = 5 kV and C = 0.152 A.V⁻²). On the opposite, when the steady breakdown streamer regime takes place (for
V > 14 kV), the measured currents become greater than theoretical values and evolve nearly linearly with the high voltage³⁸. Several authors had already highlighted some difference between the theoretical and experimental I-V curves, this difference being usually observed for very small current values and depending on the electrode geometry⁴²,⁴³ or air humidity⁴⁴ for instance. In our case, the explanation seems to be following: the pulsed component of the current is significant because the charge they transfer is high. This current being added to the DC one, that results in a shift of the total current compared to the Townsend's equation. Besides, if we compute the time-averaged value of the pulsed current, it corresponds to the shift between the Townsend curve and the measured current.

<figure><img src="image_3.png" /><figcaption>(a)
FIG. 2. Electrical and optical characteristics of the discharge. (a) Discharge current versus time for t ∈ [5 ms, 10 ms] (5 ms after the high voltage is switched on) and (b) visualisations of the discharge, for applied voltages from 12 kV to 18 kV. The shutter of the camera is opened during 2 ms, 5 ms after the discharge ignition (t ∈ [5 ms, 7 ms]). Both electrodes appear in grey color. Scale bar, 10 mm.</figcaption></figure>

<figure><img src="image_4.png" /></figure>
<figure><img src="image_5.png" /><figcaption>FIG. 3. Analysis of the discharge current. (a) Zoom of a single current peak for different high voltage values. Each plot is the time average of 100 successive current peaks. (b) Energy, charge transferred and amplitude of one single current peak as a function of the high voltage. (c) Time-averaged discharge current versus applied voltage. The red circles (○) corresponds to experimental measurements and the dot curve plots the theoretical equation (1).</figcaption></figure>

## IV. Ionic wind measurements

After characterizing the discharge by electrical and optical measurements, we then focused on the electrohydrodynamic (EHD) gas flow induced by the discharge. For that, we conducted particle image velocimetry (PIV) measurements in quiescent atmospheric air seeded with 0.3 µm-diameter oil droplets. These measurements allowed us to highlight that the EHD flow is strongly affected by the presence of breakdown streamers. For instance, in Fig. 4 we show two examples of time-averaged velocity fields as well as velocity profiles midway between the point and the plate, for several voltage values covering both glow and streamer
regimes. We can see that the mean ionic wind velocity suddenly increases when the streamer discharge appears (Fig. 4(a)). In addition, the spatial distribution of the mean velocity, which is presented in Fig. 4(b) for both regimes, underlines some differences in terms of flow topology. For a glow discharge, the EHD force occurs only close to the tip of the high voltage electrode, showing that the EHD force takes place mainly in the ionization zone. Consequently, when one moves away from the tip, the EHD force decreases and is not able to counter viscous effects. As a result, the velocity decreases in the drift region. In presence of breakdown streamers, we highlight for the first time that a stronger and constant ionic wind is generated through a narrow channel all along the gap, connecting the two electrodes. This feature means that the positive space charge at the origin of the EHD force is not concentrated only close to the point. In this case, the EHD force occuring in the electrode gap is able to counter viscous effects, resulting in a constant velocity in the whole inter-electrode gap.

To gain an insight into the role of streamers which are strongly unsteady by nature, we decided to conduct time-
resolved PIV measurements and to synchronize them with the ignition of the discharge at t = 0. Of course we
have not been able to characterize the EHD flow occurring during one single streamer or on the duration of one
current peak because the time scales of electrical and mechanical phenomena are fully different. Indeed, the
duration of a single streamer propagation is about 100 ns while the time scale of fluid dynamics is usually in the
order of 0.1 ms. In Fig. 5(a), we have represented instantaneous velocity fields of the ionic wind at four different
times, from 1 to 10 ms after the high voltage has been switched on. We can see that a flow is created, from the
point toward the plate electrode, forming a thin jet of a few millimeters in diameter. This jet seems to be
unsteady, with structures developing at its front and, as it expands, a shear layer develops around it. A few
milliseconds later (t ≈ 6 ms), the flow reaches the plate electrode and behaves as a wall-impinging jet with two
visible vortices, rotating in opposite directions and underlining that a three-dimensional axisymmetric annular
vortex is developing against the wall.

In order to cancel any suspicion of electrostatic precipitation which could be due to the electric charge of the
seeding oil particles and to be sure that these particles follow correctly the ionic wind without any slipping, we
decided to attempt observing qualitatively the same phenomenon with a method requiring no seeding particles:
Schlieren photography, which allows the visualization of density variations⁴⁵. Indeed, we could expect being
able to see the trace of the gas heated at the needle by the electrical energy and convected by the EHD flow. In
the past, only one study had used Schlieren photography to observe the topology of an ionic wind flow⁴⁶ but the
image quality was too weak to characterize accurately the gas flow during the discharge transient regime.
However, thanks to the improvements in Schlieren techniques in recent years⁴⁵, we could be optimistic on the
capability of this method for observing the ionic wind in the absence of particles. Some of the visualizations
obtained are presented in Fig. 5(b). The first important information is that the Schlieren method allowed for a correct visualization of the ionic wind since the heat brought at the tip of the high voltage electrode by the corona discharge was sufficient to induce a density gradient. Moreover, although Schlieren imaging leads to an qualitative information, we can see that it is matching those obtained with the PIV measurements, thereby demonstrating that the motion of the particles (only when these are correctly chosen and it is the case here) is the same as the one of the ionic wind. More, it is important to emphasize that during the PIV experiments, electrostatic precipitation of oil particles on the surface of the plate electrode has never been observed.

Let us return now on the time-resolved PIV measurements because they give quantitative information that can be post-treated. A thorough observation shows that the flow velocity is not constant between both electrodes. The vector fields highlight that the flow is strongly unsteady and it seems to fluctuate like a pulsed blowing jet (indicated by the narrows in Fig. 5(a) at $t = 10$ ms for instance). We can notice that the Schlieren snapshots being fuzzy, they do not allow us to observe this fast transient phenomenon at 16 kV but it was visible at 18 kV (not shown here). To deepen this phenomenon, we extracted the streamwise velocity from instantaneous velocity fields midway between the needle and the plate and we computed the velocity power spectra density (PSD). Results are presented in Fig. 6(a) for voltages ranging from 12 kV to 18 kV. In the case of a steady breakdown streamer regime ($V > 14$ kV), the PSD of the velocity is composed of a strong fundamental peak (around 3.3 kHz for $V = 16$ kV and 4 kHz for $V = 18$ kV) as well as its first harmonic, whereas no frequency peak is visible in the case of a glow regime. This underlines that the production of the EHD flow is not only intermittent, but also periodical with a frequency increasing with the applied voltage, when the discharge regime is the streamer one. By computing the PSD of the corresponding discharge current that has been previously presented in Fig. 2(a), we can highlight an interesting feature: the frequency of the current peaks, related to the streamer propagation, is totally matching the one of the ionic wind “puffs” (Fig. 6(b)). This means that the EHD flow dynamics is fully affected by the streamer occurrence. It is important to notice that the temporal signature of the EHD flow, in the case of a streamer regime, is always present in our experimental conditions and not only during the few milliseconds after the discharge ignition.
<figure><img src="image_6.png" /><figcaption>FIG. 4. Time-averaged velocity of the ionic wind. (a) Time-averaged velocity profiles midway between the needle and the plate (x = 12.5 mm) for different high voltage values, computed from particle image velocimetry (PIV) measurements. The needle tip is located at x = 0 mm and y = 0 mm. The plate is located at y = 25 mm. (b) Time-averaged 2D velocity fields in case of a glow (12 kV) and a streamer (16 kV) discharges. Every mean velocity field is computed from 3000 instantaneous fields in order to ensure a 2 % convergence. Velocity fields are computed in the x-y plane, passing through the needle and the middle of the plate (z = 0). Velocity in m/s.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>FIG. 5. Time-resolved ionic wind after ignition of the discharge. (a) Instantaneous velocity vectors fields obtained from time-resolved PIV measurements. (b) Instantaneous Schlieren visualisations. For both experiments, the observed transient flow evolution is presented here at four instants (t = 1, 2, 4 and 10 ms) after the high voltage has started to rise (t = 0).</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>FIG. 6. Power spectra density of the ionic wind and discharge current. (a) Power spectra density of the ionic wind velocity at x = 12.5 mm and y = 0, for voltages from 12 kV to 18 kV. 3000 samples of the velocity versus time from the instantaneous PIV velocity fields have been taken into account. (b) Power spectra density of the discharge current for voltages equal to 16 kV and 18 kV. For this computation, 50 000 samples are considered with a frequency rate of 500 MHz.</figcaption></figure>

V. Discussion

By synthesizing the results obtained in this experimental study, we can propose an explanation concerning
the effect of streamers on the ionic wind dynamics, without being totally certain that it corresponds to reality
because we cannot theoretically demonstrate it.

On the one hand, one can think that there is certainly no ionic wind during the propagation of one single
streamer because this one corresponds to an ionization wave, without ion displacement. Indeed, as demonstrated
by the numerical simulations of Boeuf et al.⁴⁷ in the case of surface dielectric barrier discharges, a single
streamer can be at the origin of a strong EHD force, but its duration is so short (typically smaller than 100 ns)
that its contribution to the total body force is negligible. On the other hand, by observing a zoomed view of one
single discharge current pulse, we highlighted that one current pulse was composed of successive streamers, with
a total pulse duration reaching 400 ns. Then, these successive streamers could be at the origin of a space charge
mainly composed of positive ions located in a column all along the inter-electrode gap. This model seems to be
relevant because if we compute the charge transferred during one current peak and the one transferred between
two current peaks by the DC current, both values are in the same order of magnitude (≈ 3 nC and 9 nC at 16 kV,
respectively). Finally, the only unanswered question is whether the gas flow acceleration occurs *during* or *after* the propagation of these streamers.

## VI. Conclusion

In this paper, several new results have been presented. First, we highlighted that when the steady breakdown streamer regime takes place, the time-averaged current become greater than theoretical values given by Townsend's law and that it evolves nearly linearly with the high voltage. This is due to the pulsed current component that is added to the DC one. Secondly, we showed by time-resolved PIV measurements that in this regime, a stronger and constant EHD flow is generated through a narrow channel all along the gap, connecting the two electrodes. This feature means that the positive space charge at the origin of the EHD force is not concentrated only close to the point. Moreover, thanks to the improvements in Schlieren techniques in recent years, we have been able to observe the ionic wind topology in absence of seeding particles, demonstrating that Schlieren method allows for a correct visualization of the ionic wind produced by corona discharges.

Finally, we discovered that the EHD flow dynamics of a positive corona is fully affected by the streamer occurrence since their presence results in a pulsed ionic wind whose frequency totally matches the one of the streamers.

This last result is very interesting because it highlights the role of streamers in the EHD flow dynamics and because it opens the path to new applications. For instance, if we control the streamer frequency with the help of a pulsed high voltage added to the DC one, then we can imagine using them to produce stronger EHD flows for applications in airflow control or electro-microfluidics in gas for instance.

## Acknowledgements

This work has been funded by the French Government program INVESTISSEMENT D'AVENIR (LABEX INTERACTIFS, reference ANR-11-LABX-0017-01).

## References

1. Warburg, E. Ueber die Spitzenentladung. *Ann. Phys. Chem.* **303**, 69–83 (1899).

2. Chattock, A. P. XLIV. *On the velocity and mass of the ions in the electric wind in air*. *Philos. Mag. Ser. 5* **48**, 401–420 (1899).

3. Zeleny, J. The Discharge of Electricity from Pointed Conductors. *Phys. Rev. Ser. I* **26**, 129–154 (1907).
4. Townsend, J. S. & Edmunds, P. J. LXXXIX. *The discharge of electricity from cylinders and points*. Philos. Mag. Ser. 6 **27**, 789–801 (1914).

5. Kip, A. F. Positive-Point-to-Plane Discharge in Air at Atmospheric Pressure. *Phys. Rev.* **54**, 139–146 (1938).

6. Kip, A. F. Onset Studies of Positive Point-to-Plane Corona in Air at Atmospheric Pressure. *Phys. Rev.* **55**, 549–556 (1939).

7. Trichel, G. W. The Mechanism of the Positive Point-to-Plane Corona in Air at Atmospheric Pressure. *Phys. Rev.* **55**, 382–390 (1939).

8. Loeb, L. B. Recent Developments in Analysis of the Mechanisms of Positive and Negative Coronas in Air. *J. Appl. Phys.* **19**, 882–897 (1948).

9. English, W. N. Positive and Negative Point-to-Plane Corona in Air. *Phys. Rev.* **74**, 170–178 (1948).

10. Gaunt, H. M. & Craggs, J. D. Pre-Breakdown Discharges in D.C. Positive Point to Plane Corona. *Nature* **168**, 859–861 (1951).

11. Murphy, B. Positive-Point D.C. Corona. *Nature* **176**, 397–398 (1955).

12. Hermstein, W. Die Stromfaden-Entladung und ihr Übergang in das Glimmen. *Arch. Für Elektrotechnik* **45**, 209–224 (1960).

13. Hudson, G. G. & Loeb, L. B. Streamer Mechanism and Main Stroke in the Filamentary Spark Breakdown in Air as Revealed by Photomultipliers and Fast Oscilloscopic Techniques. *Phys. Rev.* **123**, 29–43 (1961).

14. Loeb, L. B. *Electrical coronas, their basic physical mechanisms*. (1965).

15. Sigmond, R. S. The residual streamer channel: Return strokes and secondary streamers. *J. Appl. Phys.* **56**, 1355–1370 (1984).

16. Goldman, M., Goldman, A. & Sigmond, R. S. The corona discharge, its properties and specific uses. *Pure Appl. Chem.* **57**, 1–10 (1985).

17. Ražer, I. P. *Gas discharge physics*. (Springer, 1997).

18. Ono, R. & Oda, T. Dynamics of ozone and OH radicals generated by pulsed corona discharge in humid-air flow reactor measured by laser spectroscopy. *J. Appl. Phys.* **93**, 5876–5882 (2003).

19. Lukes, P., Clupek, M., Babicky, V., Janda, V. & Sunka, P. Generation of ozone by pulsed corona discharge over water surface in hybrid gas-liquid electrical discharge reactor. *J. Phys. Appl. Phys.* **38**, 409–416 (2005).

20. Masuda, S. & Nakao, H. Control of NO/sub x/ by positive and negative pulsed corona discharges. *IEEE Trans. Ind. Appl.* **26**, 374–383 (1990).
21. Kim, H. H., Takashima, K., Katsura, S. & Mizuno, A. Low-temperature NO x reduction processes using combined systems of pulsed corona discharge and catalysts. *J. Phys. Appl. Phys.* **34**, 604–613 (2001).

22. Ryu, J., Wakida, T. & Takagishi, T. Effect of Corona Discharge on the Surface of Wool and Its Application to Printing. *Text. Res. J.* **61**, 595–601 (1991).

23. Kulacki, F. A. & Boriah, S. Catalytic combustion in a tube with electrical discharge: preliminary measurements of augmented reaction rates. *Nature* **283**, 362–364 (1980).

24. Ju, Y. & Sun, W. Plasma assisted combustion: Dynamics and chemistry. *Prog. Energy Combust. Sci.* **48**, 21–83 (2015).

25. Gilbert, L. A. & George, G. T. Electrical Resistance of Oxide Films formed on the Roll of a Corona Discharge Roll-Type Separator. *Nature* **194**, 1068–1069 (1962).

26. Dascalescu, L. et al. Charging of particulates in the corona field of roll-type electroseparators. *J. Phys. Appl. Phys.* **27**, 1242–1251 (1994).

27. Mizuno, A. Electrostatic precipitation. *IEEE Trans. Dielectr. Electr. Insul.* **7**, 615–624 (2000).

28. Robinson, M. Movement of air in the electric wind of the corona discharge. *Trans. Am. Inst. Electr. Eng. Part Commun. Electron.* **80**, 143–150 (1961).

29. Christenson, E. A. & Moller, P. S. Ion-neutral propulsion in atmospheric media. *AIAA J.* **5**, 1768–1773 (1967).

30. Yabe, A., Mori, Y. & Hijikata, K. EHD study of the corona wind between wire and plate electrodes. *AIAA J.* **16**, 340–345 (1978).

31. Mizeraczyk, J. et al. Measurements of the velocity field of the flue gas flow in an electrostatic precipitator model using PIV method. *J. Electrost.* **51–52**, 272–277 (2001).

32. Moreau, E., Benard, N., Lan-Sun-Luk, J.-D. & Chabriat, J.-P. Electrohydrodynamic force produced by a wire-to-cylinder dc corona discharge in air at atmospheric pressure. *J. Phys. Appl. Phys.* **46**, 475204 (2013).

33. Moreau, E. Airflow control by non-thermal plasma actuators. *J. Phys. Appl. Phys.* **40**, 605–636 (2007).

34. Cattafesta, L. N. & Sheplak, M. Actuators for Active Flow Control. *Annu. Rev. Fluid Mech.* **43**, 247–272 (2011).

35. Benard, N. & Moreau, E. Electrical and mechanical characteristics of surface AC dielectric barrier discharge plasma actuators applied to airflow control. *Exp. Fluids* **55**, (2014).
36. Yamamoto, T. & Velkoff, H. R. Electrohydrodynamics in an electrostatic precipitator. *J. Fluid Mech.* **108**, 1 (1981).

37. Mizeraczyk, J., Berendt, A. & Podlinski, J. Temporal and spatial evolution of EHD particle flow onset in air in a needle-to-plate negative DC corona discharge. *J. Phys. Appl. Phys.* **49**, 205203 (2016).

38. Moreau, E., Audier, P. & Benard, N. Ionic wind produced by positive and negative corona discharges in air. *J. Electrost.* **93**, 85–96 (2018).

39. Giao, T. & Jordan, J. Modes of Corona Discharges in Air. *IEEE Trans. Power Appar. Syst.* **PAS-87**, 1207–1215 (1968).

40. Marode, E. The mechanism of spark breakdown in air at atmospheric pressure between a positive point and a plane. I. Experimental: Nature of the streamer track. *J. Appl. Phys.* **46**, 2005–2015 (1975).

41. Eichwald, O. et al. Experimental analysis and modelling of positive streamer in air: towards an estimation of O and N radical production. *J. Phys. Appl. Phys.* **41**, 234002 (2008).

42. Ferreira, G. F. L., Oliveira, O. N. & Giacometti, J. A. Point-to-plane corona: Current-voltage characteristics for positive and negative polarity with evidence of an electronic component. *J. Appl. Phys.* **59**, 3045–3049 (1986).

43. Meng, X., Zhang, H. & Zhu, J. (Jesse). A general empirical formula of current–voltage characteristics for point-to-plane geometry corona discharges. *J. Phys. Appl. Phys.* **41**, 065209 (2008).

44. Nouri, H., Zouzou, N., Moreau, E., Dascalescu, L. & Zebboudj, Y. Effect of relative humidity on current–voltage characteristics of an electrostatic precipitator. *J. Electrost.* **70**, 20–24 (2012).

45. Willert, C. E., Mitchell, D. M. & Soria, J. An assessment of high-power light-emitting diodes for high frame rate schlieren imaging. *Exp. Fluids* **53**, 413–421 (2012).

46. Ohyama, R., Inoue, K. & Chang, J. S. Schlieren optical visualization for transient EHD induced flow in a stratified dielectric liquid under gas-phase ac corona discharges. *J. Phys. Appl. Phys.* **40**, 573–578 (2007).

47. Boeuf, J. P., Lagmich, Y., Unfer, T., Callegari, T. & Pitchford, L. C. Electrohydrodynamic force in dielectric barrier discharge plasma actuators. *J. Phys. Appl. Phys.* **40**, 652–662 (2007).