# Electrohydrodynamic Propeller as One of the Alternatives to Replace Conventional Propulsion Systems
## 2 Generation of a Corona Discharge and the Ionisation of Gases
Its evenness is attributable to the mechanism of the formation of the secondary avalanche electrons. With identical electrode geometries and voltages applied, its dimensions are a little smaller than those of a corresponding negative corona [22; 25; 26]. A positive corona has a significantly lower density of free electrons compared to that of a negative corona. Electron avalanches are formed near the electrode with an opposite charge and then flow towards the coronating electrode. By contrast, the positively charged ions flow from the coronating electrode to the other electrode at a significantly lower drifting velocity, as their masses are significantly higher. They are mostly nitrogen cations. The formed positive ions are repelled from the coronating electrode, as their electric charges are identical. Unlike in a negative corona, the positive corona produces a significantly lower amount of ozone--this is a feature beneficial for an experiment due to the irritative nature and the effects of the gas that impair the insulation [27]. Physical Description of EHD Propulsion Processes  
With regard to a continuous power supply during the operation, a constant value of the electric charge between the plates of the asymmetrical capacitor was applied. The law of conservation of charge indicates the following:  
\[\
abla\ \overline{J}=-\frac{\partial\rho_{q}}{\partial t_{\rm t}}\left(\rm A \cdot m^{-2}\right) \tag{2}\]  
wherein \(\
abla\) is the divergence (1); \(\overline{J}\) is the current density per square meter (\(\rm A\cdot m^{-2}\)); \(\rho_{q}\) is the electric charge density per square meter (\(\rm C\cdot m^{-2}\)); and \(t_{\rm t}\) is time (s). In the case that direct current is applied to the clips of the asymmetrical capacitor, the time gradient of the current density is zero:  
\[\frac{\partial\rho_{q}}{\partial t_{\rm t}}=0 \tag{3}\]  
As a result, the following equation applies:  
\[\
abla\ \overline{J}=0 \tag{4}\]  
The current density per square meter changes due to the effects of the drift velocity \(\mu\cdot\overline{E}\) of the charged particles, the effects of the velocity of the medium flowing through the asymmetrical capacitor \(\rho_{Q}\cdot w_{0}\), as well as the effects of the diffusion velocity \(D\cdot\
abla\rho_{Q}\) of the charged particles. Provided that cations are expelled from the ionisation zone to the ion drift zone by the coronating electrode, a current density per square meter that is present in any of the cross-sections of that zone, perpendicular to the \(\overline{E}\) vector, is as follows:  
\[\overline{J}=\mu_{\rm m}\cdot\overline{E}+\rho_{Q}\cdot\overline{w}_{0}-D \cdot\
abla\rho_{Q}\ (\rm A\cdot m^{-2}) \tag{5}\]  
wherein \(\mu_{\rm m}\) is the electrical mobility (\(\rm m^{2}\ V^{-1}\cdot s^{-1}\)); \(\rho_{Q}\) is the volume charge density (\(\rm C\cdot m^{-3}\)); \(\overline{E}\) is the electric field (\(\rm V\cdot m^{-1}\)); \(\overline{w}_{0}\) is the medium flow velocity (\(\rm m\cdot s^{-1}\)); and \(D\) is the diffusion rate of the charged particles (\(\rm m\cdot s^{-1}\)). The drift velocity of the charged particles in a homogeneous electric field is as follows:  
\[\overline{v}_{d}=\mu_{\rm m}\cdot\overline{E}\ (\rm m\cdot s^{-1}) \tag{6}\]  
If, for simplification purposes, a homogeneous electric field is taken into consideration, the following equation applies:  
\[\overline{E}=\frac{U}{d}\ (\rm V\cdot m^{-1}) \tag{7}\]  
wherein \(U\) is the difference in electrode potentials (V) and \(d\) is the inter-electrode distance (m).