The present paper shows that in the case of a micro-discharge modelling using the hydrodynamics assumption, the second order fluid model involving the complete electron momentum conservation equation must be used in order to better quantify the radical formation in a micro-discharge applied to air pollution control. The present results show large differences in the micro-discharge parameters (such as velocity and electron density) between the three tested hydrodynamics models: the classical first order model using the local electric field approximation and two second order models using the local energy approximation with or without the drift–diffusion approximation. The tests have been carried out in the case of a wire-to-plane corona reactor filled with a typical flue gas (76% N2, 12% CO2, 6% O2, 6% H2O) at atmospheric pressure and ambient temperature. The simulation of the micro-discharge dynamics is performed using a 1.5D numerical streamer model coupled with a simple chemical kinetics model involving 31 species (charged and neutral particles in their fundamental or metastable state) reacting following 29 selected chemical reactions.