  The interplay of bulk and boundary scattering is explored in a regime where
quantum size effects modify mesoscopic transport in a degenerate Fermi liquid
film of $^3$He on a rough surface. We discuss mass transport and the momentum
relaxation time of the film in a torsional oscillator geometry within the
framework of a quasiclassical theory that includes the experimentally
determined power spectrum of the rough surface. The theory explains the
anomalous temperature dependence of the relaxation rate observed
experimentally. We model further studies on $^3$He confined in nanofluidic
sample chambers with lithographically defined surface roughness. The improved
understanding of surface roughness scattering can be extended to the analogous
system of electrons in metals and suggests routes to improve the conductivity
of thin metallic films.
