Modeling of vibrational kinetics in CO$_2$ dielectric barrier discharges

CO$_2$ reduction to CO is considered to improve the prospects of CO$_2$ recycling which in turn could mitigate the greenhouse effect and serve as energy storage. Non equilibrium plasmas were used in the past to achieve high energy efficiencies in dissociating CO$_2$. Non equilibrium distribution in asymmetric stretch modes of CO$_2$, driven by vibrational up-pumping (VV process), has been suggested as key for achieving such high energy efficiencies. In this work, a time-dependent, one dimensional fluid model taking into account balance equations for the densities of all relevant species and electron mean energy is used to investigate the kinetics of VV process in a pure CO$_2$ dielectric barrier discharge. A Treanor like distribution has been observed in CO$_2$ asymmetric modes and the rates of dissociation have been obtained from these distributions. The rates thus obtained have proved to be significantly lower than the rates of other dissociating processes such as electron impact dissociation. The effect of power in-coupling, duration of plasma and pressure on the vibrational distributions and CO production rate is also studied.