Critical velocity of superfluid helium flow in fine pore filters

Abstract

Membrane filters with porosities of more than 70% have been proven to be useful for the fabrication of thermomechanical pumps (fountain effect pumps) with mass fluxes up to 1.7 g s −1 cm −2 at ≈0.25 bar∗ head of pressure. Different pumps made of 14 mm thick stacks of commercially available Sartorius cellulose nitrate membranes with filtration grades of 200, 50 and 10 nm have been investigated at various temperatures between 1.6 K at the inlet and 2.1 K at the outlet. By analysis of pressure and temperature measurements it is shown that the chemical potential difference between inlet and outlet is zero up to critical flow rates very close to the peak flow and that it increases steeply when the critical flow is exceeded. Investigations are undertaken to find out how this critical flow rate depends on the filtration grade and on the operational parameters. These investigations show that the warm end temperature is the most sensitive parameter. The results are compared with a theoretical model based on the assumption that the onset of dissipation is connected to the decay of vortex rings within the pores at the warm end. This model yields good agreement for the temperature dependence of the critical flow velocity of the superfluid component, and the quantitative predictions are reasonable with respect to the uncertainty in the geometrical parameters of the pores.