In the framework of irreversible thermodynamics, the characteristics of the Rayleigh flow problem of a rarified electron gas extracted from neutral atoms is examined and proved to obey the entropic behavior for gas systems. A model kinetic equation of the BGK (Bhatnager–Gross–Krook) type is solved, using the method of moments with a two-sided distribution function. Various macroscopic properties of the electron gas, such as the mean velocity, the shear stress, and the viscosity coefficient, together with the induced electric and magnetic fields, are investigated with respect to both distance and time. The distinction between the perturbed velocity distribution functions and the equilibrium velocity distribution function at different time values is illustrated. We restrict our study to the domain of irreversible thermodynamics processes with small deviation from the equilibrium state to estimate the entropy, entropy production, entropy flux, thermodynamic force, and kinetic coefficient and verify the celebrated Boltzmann H-theorem for non-equilibrium thermodynamic properties of the system. The ratios between the different contributions of the internal energy changes, based upon the total derivatives of the extensive parameters, are predicted via Gibbs’ equation for both diamagnetic and paramagnetic plasmas. The results are applied to a typical model of laboratory argon plasma.

In the present study, the kinetic and the irreversible thermodynamic properties of a binary gas mixture, under the influence of a thermal radiation field, are presented from the molecular viewpoint. In a frame comoving with the fluid, the Bhatnagar–Gross–Krook model of the kinetic equation is analytically applied, using the Liu–Lees model. We apply the moment method to follow the behavior of the macroscopic properties of the binary gas mixture, such as the temperature and the concentration. The distinction and comparisons between the perturbed and equilibrium distribution functions are illustrated for each gas mixture component. From the viewpoint of the linear theory of irreversible thermodynamics we obtain the entropy, entropy flux, entropy production, thermodynamic forces, and kinetic coefficients. We verify the second law of thermodynamics and celebrated Onsager’s reciprocity relation for the system. The ratios between the different contributions of the internal energy changes, based upon the total derivatives of the extensive parameters, are estimated via Gibbs’ formula. The results are applied to the argon–neon binary gas mixture, for various values of both the molar fraction parameters and radiation field intensity. Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed.

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In an irreversible thermodynamics framework, Stokes' second problem was examined for unsteady oscillating flow. The objective was to apply that for a plasma near an illimitable oscillating rigid plane plate under the influence of an unsteady nonlinear applied magnetic field. The Bhatnagar-Gross-Krook (BGK) pattern of the Boltzmann kinetic equation supplemented by Maxwell's equations was investigated. The method of moments was applied with a two-sided distribution function. The exact traveling wave solution was obtained for a system consisting of four non-homogeneous partial differential equations. The velocity, shear stress, viscosity coefficient, generated electric field, applied nonlinear magnetic field, polarization, gyro-radius, and gyro-frequency were calculated. Furthermore, the distinction between the equilibrium velocity distribution function and the perturbed distribution functions was theoretically clarified at distinct time values. The advantage of the Boltzmann equation permitted us to consider irreversible non-equilibrium thermodynamics principles. For that purpose, the calculated distribution functions should be used in the formulae of entropy, entropy flux, thermodynamic forces, and kinetic coefficient. From the analysis of the results, it is found that Boltzmann's H-theorem, thermodynamics laws, and Le Chatelier's principle were consistent with our model for the whole system. The distinct contributions of the forces exerted on the system modified its internal energies; they were expressed via the Gibbs formula. The results demonstrated that the proposed model is capable of describing the behavior of plasma helium gas in the upper atmosphere ionic belts. Based on the analytical calculations, 3D-Graphics illustrating the physical quantities were drawn to predict their conduct, and the results are deeply discussed. INDEX TERMS Plasma materials processing, nuclear and plasma sciences, electrons, atmospheric-pressure plasmas, plasma applications, plasma transport processes, kinetic theory, electrokinetics, fluid dynamics, gases, electromagnetic fields.

The extension of our previous paper [Can. J. Phys., 88 (2010), 501-511] has been made for an inhomogeneous charged rarefied gas mixture (two components plasma) instead of a single electron gas. In the present work, the kinetic and the irreversible thermodynamic properties of the plasma are presented from the molecular point of view. Our study is based on the solution of the BGK (Bhatnager-Gross-Krook) model of the Boltzmann kinetic equation together with the Maxwell's equations for both positive ions and electrons in the vicinity of a moving rigid plane. The fundamental aim of this investigation is to illustrate the mutual effects caused by collisions on the distribution functions. The distinction and comparisons between the perturbed and the equilibrium velocity distribution functions are illustrated for both electrons and ions. The ratios between the different contributions of the internal energy changes are predicted via the Gibbs's equation for both diamagnetic and paramagnetic plasmas. The results are applied to a typical model of laboratory Argon plasma.