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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 hy...
Comment: 9 pages, 3 figures. Submitted for publication. References added
Comment: 11 pages, 2 figures. Accepted for publication in J. Phys. A
Comment: 8 pages, no figures. Submitted to Physica A
Comment: 13 pages, TeX, no figures, to appear in Mol. Phys
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