Title: Gas near a wall: a shortened mean free path, reduced viscosity, and the manifestation of a turbulent Knudsen layer in the Navier-Stokes solution of a shear flow,
Abstract: For the gas near a solid planar wall, we propose a scaling formula for the
mean free path of a molecule as a function of the distance from the wall, under
the assumption of a uniform distribution of the incident directions of the
molecular free flight. We subsequently impose the same scaling onto the
viscosity of the gas near the wall, and compute the Navier-Stokes solution of
the velocity of a shear flow parallel to the wall. This solution exhibits the
Knudsen velocity boundary layer in agreement with the corresponding Direct
Simulation Monte Carlo computations for argon and nitrogen. We also find that
the proposed mean free path and viscosity scaling sets the second derivative of
the velocity to infinity at the wall boundary of the flow domain, which
suggests that the gas flow is formally turbulent within the Knudsen boundary
layer near the wall.