Common Approximations that Can Invalidate Calculations of the Flow of Superfluid Helium

Abstract

Calculations of the flow of He II are difficult because of its two-fluid nature and unusual boundary conditions. Investigators made many assumptions and approximations, over the years, to simplify the calculations and make them tractable. We find in scanning the literature that in a large number of situations approximations have been used beyond their range of validity. In some cases, this has resulted in substantially incorrect predictions. We have made a list of commonly used approximations and analyzed the range of validity of each. Examples of approximations are: assuming a critical velocity for the onset of turbulence in the superfluid when no critical velocity exists; attempting to specify the problem with less than four boundary conditions; neglect of the pressure gradient in evaluating the gradient of the chemical potential; neglect of property variations in one-dimensional flow; assuming the normal component flows like a Navier-Stokes fluid; attributing a dependence of the Gorter-Mellink coefficient to the structure of the material; using formulas for heat flow that apply only to counterflow situations when there is not mass flow; and assuming the normal fluid is clamped in porous flows. We made a comparison of calculations with and without the assumptions where possible.