Far from equilibrium velocity distribution of a dilute gas

The one-particle distribution function of a dilute gas under uniform shear flow is investigated by means of the Bhatnagar-Gross-Krook (BGK) model kinetic equation. For repulsive interaction potentials of the form V(r) − r−1 a hydrodynamic regime, characterized by a normal solution of the BGK equation, is identified in the proper limit, for arbitrary shear rates. This normal solution diverges at zero velocity, except for sufficiently small shear rates in the case of Maxwell molecules (l = 4). Besides, it becomes highly distorted as compared to local equilibrium.