Finite-size and gravity effects on the thermal conductivity of4He near the λ line

This paper reviews the opportunities for microgravity and Earth-based measurements of the thermal conductivityλ(t, L) of⁴He confined in cylindrical geometries of radiusL with axial heat flow at temperatures near the bulk superfluid-transition lineT _λ (P) (t is the reduced temperatureT/T _λ −1). It provides an evaluation of existing data forL=1 μm nearT _λ at saturated vapor pressure (SVP), and uses these to derive a scaling function for the resistivityR(t, L)=1/λ(t, L). The purpose of future measurements over a wide range ofL and of the pressureP will be to test the applicability of this function. In the present paper the scaling function is used to assess quantitatively the effect of gravity on potential Earth-based measurements. It is found that the gravity effect forR is particularly severe belowT _λ . For typical three-mm-high samples at SVP, values ofL significantly larger than 8 μm can only be investigated fully in micro-gravity. At higher pressures the gravity effect is larger. At 30 bar, three-mm samples withL≳4 μm require microgravity for measurements belowT _λ (P). Modern thermometry has sufficient resolution to permit quantitative measurements in micro-gravity of the anticipated finite-size effect for values ofL as large as 50 μm.