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 .