Nonlinear transport in a binary mixture in the presence of gravitation

The effect of gravity on the tracer particles immersed in a dilute gas of mechanically different particles and subjected to the steady planar Couette flow is analyzed. The results are obtained from the Gross–Krook (GK) kinetic model of a binary mixture and the description applies for arbitrary values of both velocity and temperature gradients. The GK equation is solved by means of a perturbation method in powers of the field around a nonequilibrium state which retains all the hydrodynamic orders in the shear rate a and the thermal gradient ε. To first order in the gravity field, we explicitly determine the hydrodynamic profiles and the partial contributions to the momentum and heat fluxes associated with the tracer species. All these quantities are given in terms of a,ε, and the mass and size ratios. The shear-rate dependence of some of these quantities is illustrated for several values of the mass ratio showing that in general, the effect of gravity is more significant when the particles of the gas are lighter than the tracer particles.