A digital platform for the simulation of the transport of electric charges in electrohydro-dynamic phenomena (EHD) has been developed on the basis of the finite volume method. A one-year post-doc was devoted to this end. The implementation of dedicated digital schemes has been successfully carried out and it is now possible to solve EHD equations in the context of complex 2D and 3D geometries (plane-plane, plane-blade, coaxial cylinders). In the case of a high symmetry between the electrodes, the results [61,63,68,79] showed the existence of a non-linear supercritical bifurcation in the regime of finite amplitude, whereas until now the literature on EHD phenomena only mentions the existence of a subcritical bifurcation. For asymmetric electrode geometries, the structure of the flow and its effects on the transport of electrical charges in the mass were studied. Particularly in the planar blade configuration, different types of electrodes have been considered, with different injection laws which quantify the creation of electric charge on their surface.

During a one-year postdoctoral fellowship, the experience acquired with the applications of the finite volume method to EHD fluxes (dielectric liquids) was used to model the ESP configurations which contain pointed electrodes and collecting electrodes. smooth. The numerical modeling of such an ESP required the resolution of the Navier-Stokes equations coupled to the EHD equations, taking into account the Coulomb force as well as the calculation of the amount of charge exchanged during particle collisions.