In this work, we study by numerical simulation the effect of electric charges on the dispersion of particles transported by a turbulent flow. The Navier-Stokes equations are solved by Direct Numerical Simulations (spectral approach) coupled with a Lagrangian solver in order to calculate the trajectories of each particle. A stochastic forcing scheme allows to obtain statistically homogeneous, isotropic and stationary turbulent flows. In the thesis, an original method to take into account electrostatic forces has been developed and validated on elementary configurations. In this method, the short-range interactions are estimated via a sum of the inter-particle interactions inside a cut-off distance and the long-range ones via a sum of interactions of particles with groups of particles which, at a distance greater than the cut-off distance, are considered as pseudo-particles. The convergence, the precision and the computational cost of the method have been studied in detail for its implementation for tri-periodic domains. The ensemble of these developments has been carried out in a parallel code which allows to perform simulations on a supercomputer of gas-particle flows containing up to 2×105 particles. Firstly, the analysis of dry granular flows allowed to define a characteristic time scale of the effect of electric charges and to link it to the physical properties of the particles, in particular their diameter and agitation. The mechanism of transformation of the electric potential energy into particle kinetic energy is analyzed according to this time scale. Secondly, simulations of homogeneous isotropic turbulence transporting like-charged particles were carried out by varying their diameter (dynamic Stokes number) and their charge (electrostatic Stokes number). The simulations show that, for a given dynamic Stokes, the increase in particle charge leads to a decrease in their agitation since the electrostatic (repulsive) forces are conservative. The detailed analysis shows that, in fact, the electrostatic forces lead to a destruction of the fluid-particle velocity correlation which, according to the Tchen-Hinze theory, drives particle agitation. Besides agitation, the spatial distribution of particles is also considerably modified by electrostatic forces. In fact, the charges decrease the short-range values of the particle pair distribution function, which means that the phenomenon of preferential concentration of the particles is attenuated. In the limit of strong charges, it is even completely eliminated since electrostatic forces tend to uniformize the spatial distribution of the particles. This is because each particle tends to form an exclusion zone around it due to the strong repulsion at short distance. The relative velocity distribution functions of particle pairs are also affected by the presence of charges. Finally, the effect of the particle volume fraction is examined, where it is shown that its increase leads to a higher electric potential energy density stored the cloud of charged particles which leads to an increase of particle agitation
