Exact solution of the Gross–Krook kinetic model for a multicomponent gas in steady Couette flow

The Gross–Krook (GK) kinetic model of the Boltzmann equation for a multicomponent mixture is exactly solved in a steady state with velocity and temperature gradients (Couette flow). The hydrodynamic fields, heat and momentum fluxes, and the velocity distribution functions are determined explicitly in terms of the shear rate and the thermal gradient. The description applies for conditions arbitrarily far from equilibrium and is not restricted to specific values of the mechanical parameters of the mixture. This work completes a previous study (Physica A 289 (2001) 37) based on a formal series representation of the velocity distribution function.