Oscillatory shear-driven gas flows in the transition and free-molecular-flow regimes

We investigate oscillatory shear-driven gas flows in the transition and free-molecular-flow regimes. Analytical results valid through slip flow and the early transition regime are obtained using a recently proposed, rigorous second-order slip model with no adjustable coefficients. Analytical solution of the collisionless Boltzmann equation provides a description of the high Knudsen number limit Kn 1 including the bounded shear layers present in the limit of high oscillation frequency. These layers are analogous to the Stokes layers observed in the Kn 1 limit, but contrary to the latter, they exhibit a nonconstant wave speed as demonstrated by Park, Bahukudumbi, and Beskok in Phys. Fluids. 16, 317 2004 . All theoretical results are validated by direct Monte Carlo simulations. We find that the second-order slip results are in good agreement with direct simulation Monte Carlo DSMC solutions up to Kn 0.4; in some cases these results continue to provide useful approximations to quantities of engineering interest, such as the shear stress, well beyond Kn 0.5. The collisionless theory provides, in general, a good description of DSMC results for Kn 10, while in the high frequency limit the agreement is very good for Knundsen numbers as low as Kn 5. © 2005 American Institute of Physics. DOI: 10.1063/1.1874193