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Articles by Thierry E. Magin in JoVE
Other articles by Thierry E. Magin on PubMed
Transport Properties of Partially Ionized and Unmagnetized Plasmas Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics. Oct, 2004 | Pubmed ID: 15600535 This work is a comprehensive and theoretical study of transport phenomena in partially ionized and unmagnetized plasmas by means of kinetic theory. The pros and cons of different models encountered in the literature are presented. A dimensional analysis of the Boltzmann equation deals with the disparity of mass between electrons and heavy particles and yields the epochal relaxation concept. First, electrons and heavy particles exhibit distinct kinetic time scales and may have different translational temperatures. The hydrodynamic velocity is assumed to be identical for both types of species. Second, at the hydrodynamic time scale the energy exchanged between electrons and heavy particles tends to equalize both temperatures. Global and species macroscopic fluid conservation equations are given. New constrained integral equations are derived from a modified Chapman-Enskog perturbative method. Adequate bracket integrals are introduced to treat thermal nonequilibrium. A symmetric mathematical formalism is preferred for physical and numerical standpoints. A Laguerre-Sonine polynomial expansion allows for systems of transport to be derived. Momentum, mass, and energy fluxes are associated to shear viscosity, diffusion coefficients, thermal diffusion coefficients, and thermal conductivities. A Goldstein expansion of the perturbation function provides explicit expressions of the thermal diffusion ratios and measurable thermal conductivities. Thermal diffusion terms already found in the Russian literature ensure the exact mass conservation. A generalized Stefan-Maxwell equation is derived following the method of Kolesnikov and Tirskiy. The bracket integral reduction in terms of transport collision integrals is presented in Appendix for the thermal nonequilibrium case. A simple Eucken correction is proposed to deal with the internal degrees of freedom of atoms and polyatomic molecules, neglecting inelastic collisions. The authors believe that the final expressions are readily usable for practical applications in fluid dynamics.
Rovibrational Internal Energy Transfer and Dissociation of N2(1Σg+)-N(4S(u)) System in Hypersonic Flows The Journal of Chemical Physics. Jan, 2013 | Pubmed ID: 23387589 A rovibrational collisional model is developed to study energy transfer and dissociation of N(2)((1)Σ(g)(+)) molecules interacting with N((4)S(u)) atoms in an ideal isochoric and isothermal chemical reactor. The system examined is a mixture of molecular nitrogen and a small amount of atomic nitrogen. This mixture, initially at room temperature, is heated by several thousands of degrees Kelvin, driving the system toward a strong non-equilibrium condition. The evolution of the population densities of each individual rovibrational level is explicitly determined via the numerical solution of the master equation for temperatures ranging from 5000 to 50,000 K. The reaction rate coefficients are taken from an ab initio database developed at NASA Ames Research Center. The macroscopic relaxation times, energy transfer rates, and dissociation rate coefficients are extracted from the solution of the master equation. The computed rotational-translational (RT) and vibrational-translational (VT) relaxation times are different at low heat bath temperatures (e.g., RT is about two orders of magnitude faster than VT at T = 5000 K), but they converge to a common limiting value at high temperature. This is contrary to the conventional interpretation of thermal relaxation in which translational and rotational relaxation timescales are assumed comparable with vibrational relaxation being considerable slower. Thus, this assumption is questionable under high temperature non-equilibrium conditions. The exchange reaction plays a very significant role in determining the dynamics of the population densities. The macroscopic energy transfer and dissociation rates are found to be slower when exchange processes are neglected. A macroscopic dissociation rate coefficient based on the quasi-stationary distribution, exhibits excellent agreement with experimental data of Appleton et al. [J. Chem. Phys. 48, 599-608 (1968)]. However, at higher temperatures, only about 50% of dissociation is found to take place under quasi-stationary state conditions. This suggest the necessity of explicitly including some rovibrational levels, when solving a global kinetic rate equation.