TRANSPORT PROCESSES IN A MULTICOMPONENT ASSEMBLY ON THE BASIS OF RECONSIDERED GENERALIZED B-G-K COLLISION MODEL

Abstract

Bhatnagar, Gross and Krook developed a collision model for one component neutral assembly in order to overcome the inherent difficulties of the Boltzmann collision integral. This has been generalized to an N-component assembly of charged and neutral particles by Bhatnagar and Devanathan. However, for the simplicity of the model, the above mentioned authors have taken the collision cross section to be a constant. In fact the collision cross section is some unknown function of the relative velocity between the particles, as has already been pointed out by Krook and also by Koga. Koga have some expressions for the cross section, which are linear and exponential function of the square of relative velocity, and calculated the coefficients involved in the model. In this paper. choosing the same types of cross section as suggested by Koga, we have obtained the transport equations by expanding the distribution functions in generalized Hermite polynomials following Grad. It is found that variable cross section enhances the relaxations times of all physical variables and thereby decreases the electrical conductivity and diffusion coefficients. Also such variable cross section introduces very high anisotropy even in the absence of magnetic field and tbe magnitudes of the viscosity coefficients in the principal directions are decreased. The bulk viscosity of the plasma is increased apart from introducing anisotrory. Further this model introduces anisotropy in tbe heat flux tensor also. All the transport prooerties have been obtained in an earlier paper by Devanathan, Uberoi and Bhatnagar. We have obtained the modified expressions for viscosity, electrical conductivity, heat conductivity and diffusion coefficients.