Journal of Low Temperature Physics, VoL 41, Nos. 5/6 Boundary Effects in Fluid Flow. Application to Quantum Liquids H. H0jgaard Jensen and H. Smith Physics Laboratory I, H. C. r Institute, Copenhagen, Denmark P. W61fle and K. Nagai* Max-Planck Institut fiir Physik und Astrophysik, Miinchen, and Physik-Department der Technischen Universitdt Miinchen, Garching, Germany and T. Maaek Bisgaard Physics Laboratory L H. C. Orsted Institute, Copenhagen, Denmark (Received May 26, 1980) The effect of boundaries on the flow of rarefied gases is considered. For an excitation gas of arbitrary statistics and energy-momentum relationship we determine the magnitude of the slip length and the flow between parallel plates mostly by variational methods. Our approximate method avoids the need to solve integral equations numerically and yields in the stationary case better than 1% agreement with known exact results for the classical Maxwell- Boltzmann gas. Our general results are primarily applied to normal and superfluid Fermi liquids. We calculate the surface impedance of an oscillating plate and determine the frequency-dependent slip length for frequencies rang- ing from the hydrodynamic to the collisionless limit. Our results are applied to the analysis of viscosity measurements based on a torsional oscillator or a vibrating wire. The slip effects are shown to be very important for realistic experimental parameters, especially at low temperatures in the superfluid B phase of liquid 3He. 1. INTRODUCTION In ordin'ary aerodynamics, viscous flow of gases past solid bodies is treated by solving the Navier-Stokes equation with the condition that at the surface of the solid body the velocity of the gas is equal t 9 that of the body. Already in 1875 Kundt and Warburg I found experimentally that this *Permanent address: Department of Physics, Yamaguchi University, Yamaguchi, Japan. 473 0022-2291/80/1200-0473 $03.00/0 ~) 1980 Plenum Publishing Corporation