Boundary effects in fluid flow. Application to quantum liquids

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 ranging 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.