A supersonic thermal plasma is a useful tool used in the spraying technology  to produce high-quality coatings, especially the thermal barrier coatings for aircraft engines. Indeed, this configuration accelerates particles to higher impact velocity, leading to a higher density of the deposit and less contamination. Technologies such as spraying, cutting, welding, metallurgy, surface treatment, etc..., in order to be used in their full potential, still demand a better understanding of the behavior of such plasmas. Recent modeling work on the supersonic plasma jet [2-4] assumed LTE, and only limited number modeling studies were devoted to the study of deviation from LTE [5-9]. In this work, a mathematical model for an Ar/(He, H2, O2, N2) inductively coupled plasma torch with a supersonic nozzle is developed under chemical and thermal non-equilibrium. Under thermal non-equilibrium, the reaction rate depends upon the heavy particles temperature as well as the vibrational temperature. This poses a problem when the heavy particles temperature and the vibration temperature are not in equilibrium because it is not clear which temperature is controlling the reaction. To treat this problem, we use Park's  multi temperature approach. By using this approach, the backward and forward rate coefficients are evaluated with a so-called rate controlling temperature. The thermal non equilibrium or multi-temperature model is developed by assuming that all rotational states are fully equilibrated with the translational energies of heavy particles, at a common translational-rotational temperature Thr and the translational energies of free electrons, bound electronic and vibrational energies are fully equilibrated at a common electro-vibrational temperature Tev. Furthermore, two coupled energy equations are used, one for the calculation of the translational-rotational temperature Thr and one for the calculation of the electro-vibrational temperature Tev. Because the supersonic plasma jet dissipates significant energy in the high shear zones , the viscous dissipation is taken into account in the translational-rotational energy equation. The electro-vibrational energy equation also includes the pressure work of the electrons, the Ohmic heating power, and the exchange due to elastic collisions. Since the thermodynamic and transport properties of high-temperature gases are so important in the prediction of the plasma fields, the present model puts a lot of emphasis on their prediction. The transport properties are computed with the method of Chapman and Enskog, including the most recent sets of collision integrals available in the literature and taking into account higher-order formulas to compute the electron transport properties.
The results obtained by this model were compared with results from the one temperature chemical non equilibrium model . Using this model, the influence of the power and the pressure chamber on the chemical and thermal non equilibrium was investigated. The different diffusion formulations are used in a numerical model of demixing in a mixture and in order to validate this model, recent experimental results were compared to the model predictions.
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Available at: http://works.bepress.com/abdel_bannari/13/