Nonlinear Couette flow in a low density granular gas

A model kinetic equation is solved exactly for a special stationary state d escribing nonlinear Couette flow in a low density system of inelastic spher es. The hydrodynamic fields, heat and momentum fluxes, and the phase space distribution function are deter-mined explicitly. The results apply for con ditions such that viscous heating dominates collisional cooling, including large gradients far from the reference homogeneous cooling state. Explicit expressions for the generalized transport coefficients (e.g., viscosity and thermal conductivity) are obtained as nonlinear functions of the coefficie nt of normal restitution and the shear rate. These exact results for the mo del kinetic equation are also shown to be good approximations to the corres ponding state for the Boltzmann equation via comparison with direct Monte C arlo simulation for the latter.