Gas Near a Wall: Shortened Mean Free Path, Reduced Viscosity, and the Manifestation of the Knudsen Layer in the NavierStokes 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 NavierStokes solution of the velocity of a shear flow parallel to the wall. Under the simplifying assumption of constant temperature of the gas, the velocity profile becomes an explicit nonlinear function of the distance from the wall and exhibits a Knudsen boundary layer near the wall. To verify the validity of the obtained formula, we perform the Direct Simulation Monte Carlo computations for the shear flow of argon and nitrogen at normal density and temperature. We find excellent agreement between our velocity approximation and the computed DSMC velocity profiles both within the Knudsen boundary layer and away from it.
 Publication:

Journal of NonLinear Science
 Pub Date:
 June 2018
 DOI:
 10.1007/s0033201794297
 arXiv:
 arXiv:1701.02276
 Bibcode:
 2018JNS....28..833A
 Keywords:

 Physics  Fluid Dynamics
 EPrint:
 12 pages, 3 figures