Knudsen flow and the thermomechanical effect in a Fermi liquid

We show that conventional kinetic theory, based on Fermi liquid theory, disagrees with the recent measurements by Greenwood of the thermomechanical effect in normal liquid {sup 3}He. The theory predicts that, in the Knudsen or long-free-path regime, dP/dT across a porous plug should be 1/3 of the entropy per unit volume {rho}s. Experimentally, the ratio decreases from {approximately}4 to {approximately}1 between 2 mK and 20 mK. The theoretical result does not depend on whether the quasiparticles exchange energy with the walls or whether the scattering is partly specular. We consider possible reasons for the discrepancy between theory and experiment. One alternative approach, which treats the {sup 3}He in the porous plug as a mesoscopic system, gives the same result as conventional kinetic theory. The relation between the thermomechanical effect in {sup 3}He and thermoelectricity in metals is also discussed.