A closed set of transport equations with collision terms evaluated by the 13-moment approximation is used, under well-defined assumptions, to derive a generalized Ohm's law in multicomponent nonisothermal plasmas as a function of the electric and magnetic fields and the temperature and pressure gradients. The nine coefficients defining this dependence are obtained in two successive approximations and are expressed in terms of component properties for any number N of components in the plasma, each component having its own temperature. The matrixes and determinants involved in these expressions are of order N. Results obtained for N = 4 and 5 allow the investigation of new effects that cannot be studied with the available 3-fluid expressions. It is shown that the only temperature gradient that needs to be considered in Ohm's law is that of the electrons and that all plasma properties, except those that describe or include interactions between heavy components, must be determined at the electron temperature. It is concluded that interactions between heavy particles cannot always be neglected in favor of electron-heavy particle interactions and that the results of this study may be used for a more general evaluation of all the coefficients of Ohm's law in multicomponent nonisothermal plasmas. The results are valid for any degree of ionization greater than approximately 10−7 and are presented in a form useful for many applications.

Effect of magnetic field on molecular orientation of nematic liquid crystalline polymers under simple shear flow J. Rheol. 52, 451 (2008); 10.1122/1.2837113 Transient electric birefringence of colloidal particles immersed in shear flow. I. Approximate calculations from low fields to high fields under the action of a rectangular pulse and a reversing pulse

A closed analytical model for compressible magnetohydrodynamic boundary layers is formulated by using transport equations for the turbulent fluctuations of species mass density, velocity, and temperature, and thus avoiding a priori relations between turbulent fluxes and mean flow quantities. The equations for both the mean and the fluctuating motion are simplified according to the boundary-layer approximation, and closure of the system is achieved by the introduction of “universal turbulence structure parameters” that only relate turbulent correlations among themselves. This model accounts for convection and diffusion of turbulent fluxes as well as for the effect of turbulence suppression by applied magnetic fields. It is shown that if convection, diffusion, and electromagnetic effects were omitted in the equations of fluctuating motion, the latter would reduce to algebraic forms defining the concepts of mixing length, turbulent Prandtl number, and turbulent Schmidt number in terms of turbulence structure parameters.

The coupled distributions of current density, electron temperature, and plasma composition in nonequilibrium plasma flows depend strongly on relaxation effects arising from finite reaction rates and from electron-energy convection. This dependence is studied in multielectrode magnetohydrodynamic channels in conjunction with the influence of thermal and concentration diffusion, and of thermal and velocity boundary layers. Relaxation effects are shown to control the possibility of current shorting along the conductor walls and to influence the stability of the distributions. For slow reaction rates and large gas velocities, the current and plasma-property distributions tend to become uniform in the core of the flow, but in the electrode-boundary regions nonuniformities persist both in the transverse and in the flow direction, and are strongly dependent upon the gas temperature and velocity boundary layers. Consequently, although relaxation effects allow high conductivity layers to extend over the insulator segments of the electrode walls, the possibility of Hall potential shorting through this path depends critically on the length of insulator segment between electrodes. Converging solutions, describing stable operation, have been obtained for values of the local Hall parameter β/ε as high as 6, depending on the geometry. At high values of β/ε, the current density and plasma-property distributions become time dependent, resulting in overall electrical characteristics that oscillate by large factors.

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