In this work we study a r-species mixture of gases within the relativistic kinetic theory point of view. We use the relativistic covariant Boltzmann equation and incorporate the Schwarzschild metric. The method of solution of the Boltzmann equation is a combination of the ChapmanEnskog and Grad representations. The thermodynamic four-fluxes are expressed as functions of the thermodynamic forces so that the generalized expressions for the Navier-Stokes, Fick and Fourier laws are obtained. The constitutive equations for the diffusion and heat four-fluxes of the mixture are functions of thermal and diffusion generalized forces which depend on the acceleration and the gravitational potential gradient. While this dependence is of relativistic nature for the thermal force, this is not the case for the diffusion forces. We show also that the matrix of diffusion coefficients is symmetric, implying that the thermal-diffusion equals the diffusion-thermal effect, proving the Onsager reciprocity relations. The entropy four-flow of the mixture is also expressed in terms of the thermal and diffusion generalized forces, so that its dependence on the acceleration and gravitational potential gradient is also determined.

In this work we study the properties of a relativistic mixture of two non-reacting dilute species in thermal local equilibrium. Following the conventional ideas in kinetic theory, we use the concept of chaotic velocity.In particular, we address the nature of the density, or pressure gradient term that arises in the solution of the linearized Boltzmann equation in this context. Such effect, also present for the single component problem, has so far not been analyzed from the point of view of the Onsager resciprocity relations. In order to address this matter, we propose two alternatives for the Onsagerian matrix which comply with the corresponding reciprocity relations and also show that, as in the non-relativistic case, the chemical potential is not an adequate thermodynamic force. The implications of both representations are briefly analyzed.

The system of our interest is a dilute binary mixture, in which we consider that the species have different temperatures as an initial condition. To study their time evolution, we use the full version of the Boltzmann equation, under the hypothesis of partial local equilibrium for both species. Neither a diffusion force nor mass diffusion appears in the system. We also estimate the time in which the temperatures of the components reach the full local equilibrium. In solving the Boltzmann equation, we imposed no assumptions on the collision term.We work out its solution by using the well known Chapman-Enskog method to first order in the gradients. The time in which the temperatures relax is obtained following Landau's original idea. The result is that the relaxation time for the temperatures is much smaller than the characteristic hydrodynamical times but greater than a collisional time. The main conclusion is that there is no need to study binary mixtures with different temperatures when hydrodynamical properties are sought.

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In this paper we revisit the concept of chaotic velocity within the context of relativistic kinetic theory. Its importance as the key ingredient which allows to clearly distinguish convective and dissipative effects is discussed to some detail. Also, by addressing the case of the two component mixture, the relevance of the barycentric comoving frame is established and thus the convenience for the introduction of peculiar velocities for each species. The fact that the decomposition of molecular velocity in systematic and peculiar components does not alter the covariance of the theory is emphasized. Moreover, we show that within an equivalent decomposition into space-like and time-like tensors, based on a generalization of the relative velocity concept, the Lorentz factor for the chaotic velocity can be expressed explicitly as an invariant quantity. This idea, based on Ellis' theorem, allows to foresee a natural generalization to the general relativistic case.Comment: 12 pages, 2 figure