Shear-rate dependent transport coefficients in a binary mixture of Maxwellmolecules

Mass and heat transport in a dilute binary mixture of Maxwell molecules und er steady shear flow are studied in the limit of small concentration gradie nts. The analysis is made from the Gross-Krook kinetic model of the Boltzma nn equation. This model is solved by means of a perturbation solution aroun d the steady shear flow solution [Phys. Fluids 8, 2756 (1996)], which appli es for arbitrary values of the shear rate. In the first order of the expans ion the results show that the mass and heat fluxes are proportional to the concentration gradient but, due to the anisotropy of the problem, mutual di ffusion and Dufour tensors can be identified, respectively. Both tensors ar e explicitly determined in terms of the shear rate and the parameters of th e mixture (particle masses, concentrations, and force constants). A compari son with the results derived from the exact Boltzmann equation at the level of the diffusion tensor shows a good agreement for a wide range of values of the shear rate. (C) 2000 American Institute of Physics. [S1070-6631(00)0 2102-4].