Fermi liquid viscosity in a finite geometry

Forced flow of a Fermi liquid is studied for a cell geometry consisting of two planes with a separation on the order of the mean free path. An approximate transport equation is used to derive an integral equation for the velocity profile, which is solved numerically. Results for the total flux through the cell, which determines the dissipation, are given as a function of the Knudsen number κ (ratio of cell thickness to mean free path.) Effects of specular reflection at the boundaries are considered. It is found that the dissipation has a minimum at κ ≈ 1/2, and behaves linearly for κ ≳ 3. Implications for present experimentation are discussed.