**1. Introduction**

Micro-discharges are specific cold filamentary plasma that are generated at atmospheric pressure between electrodes stressed by high voltage. As cold plasma or non-thermal plasma, we suggest that the energy of electrons inside the conductive plasma is much higher than the energy of the heaviest particles (molecules and ions). In such kind of plasma, the temperature of the gas remains cold (i.e. more or less equal to the ambient temperature) unlike in the field of thermal plasmas where the gas temperature can reach some thousands of Kelvin. This high level of temperature can be measured for example in plasma torch or in lightning.

The conductive channels of micro-discharges are very thin. Their diameters are estimated around some tens of micrometers. This specificity explains their name: micro-discharge. Another of their characteristic is their very fast development. In fact, micro-discharges propagate at velocity that can attain some tens of millimetres per nanosecond i.e. some 107 cm.s-1. This very fast velocity is due to the propagation of space charge dominated streamer heads. The space charge inside the streamer head creates a very high electric field in which the electrons are accelerated like in an electron gun. These electrons interact with the gas and create mainly ions and radicals. In fact, the energy distribution of electrons inside streamer heads favours the chemical electron-molecule reactions rather than the elastic electron-molecule collisions. Therefore, micro-discharges are mainly used in order to activate chemical reactions either in the gas volume or on a surface (Penetrante & Schultheis, 1993, Urashima &Chang, 2010, Foest et al. 2005, Clement, 2001).

Several designs of plasma reactors are able to generate micro-discharges. The most convenient and the well known is probably the corona discharge reactor (Loeb, 1961&1965, Winands, 2006, Ono & Oda a, 2004, van Veldhuizen & Rutgers, 2002, Briels et al., 2006 ). Corona micro-discharges reactor has at least two asymmetric electrodes i.e. with one of them presenting a low curvature that introduces a pin effect where the geometric electric field is enhanced. The corona micro-discharges are initiated from this high geometric field area. Some samples of corona reactor geometries are shown in Fig. 1.

The transient character and the small dimensions make some micro-discharges parameters, like charged and radical densities, electron energy or electric field strength, difficult to be accessible to measurements. Therefore, the complete simulation of the discharge reactor, in complement to experimental study can lead to a better understanding of the physico-

Electro-Hydrodynamics of Micro-Discharges in Gases at Atmospheric Pressure 271

For a high voltage threshold value, some regular repetitive current pulses appear with a repetition frequency of some tens of kHz and a magnitude of some tens to hundred of mA. Each current pulse lasts some hundred of nanoseconds and corresponds to the propagation

Fig. 2. Photography of the different corona discharge regimes under positive DC voltage condition (inter-electrode distance = 7mm, pin radius = 20 µm, dry air, atmospheric pressure). a: onset streamer, DC voltage magnitude = 3.2kV, time camera shutter = 1s, b: glow discharge, DC voltage magnitude = 5kV, time camera shutter = 10ms, c: streamer micro-discharge, DC voltage magnitude = 7.2kV, time camera shutter = 10µs (Eichwald et

More detailed information on the spatio-temporal evolution of the micro-discharge can be obtained thanks to the analysis of the streak camera picture shown in Fig. 3 and the corresponding current pulse shown in Fig. 4 (Eichwald et al., 2008, Marode, 1975). In Fig. 3, the X-axis is the time axis while the Y-axis is the inter-electrode distance. The electrode location is shown in the drawing at the left side of Fig. 3. For a given time on the X-axis, the light emission of the micro-discharge filament at each position is focused along the corresponding Y-axis coordinate. When 8.2kV is applied to the pin, three main phases can be distinguished in the corona micro-discharge development. The first one corresponds to the primary streamer propagation from the anode pin towards the cathode plane. The primary streamer propagates a luminous spot (called streamer head) which leaves the first narrow luminous trail shown on the streak picture of Fig. 3. During this first phase, the current rapidly increases as shown in Fig. 4 between 50ns and 75ns. The second phase

Fig. 3. Streak camera picture of a corona micro-discharge: Inter-electrode distance = 7mm,

pin radius = 20 µm, dry air, atmospheric pressure, DC voltage magnitude = 8.2kV

of a mono-filament corona micro-discharge shown in Fig. 2c.

al., 2008).

Fig. 1. Sample of pin-to-plane and wire-to-cylinder corona discharge reactors. The light blue material corresponds to a dielectric material. Depending on applications, design and reactor efficiency, the High Voltage (HV) shape can be DC, pulsed, AC or a combination of them.

chemical activity triggered by the micro-discharge during the plasma process. All these information can be used in order to improve the reactor design and to achieve the best operating conditions (such as the reactor geometry, the flue gas resident time, the applied voltage shape and magnitude, among others) as a function of the chosen applications.

The present chapter is devoted to description of the main electro-hydrodynamics phenomena that take place in non-thermal plasma reactors at atmospheric pressure activated by corona micro-discharges. The first section describes the micro-discharges characteristics using the experimental results obtained in a mono pin-to-plane reactor stressed by either DC or pulsed high voltage. The physics of the micro-discharges development is explained and a complete hydrodynamics model is proposed based on the moments of Boltzmann equations for charged and neutral particles. Then before to conclude, the previous described model is used in order to simulate the strongly coupled chemical and hydrodynamics phenomena generated by micro-discharges in a non thermal plasma reactor.
