Finite-size and gravity effects on the thermal conductivity of 4He near the λ line

This paper reviews the opportunities for microgravity and Earth-based measurements of the thermal conductivity lambda(t, L) of He-4 confined in cylindrical geometries of radius L with axial heat flow at temperatures near the bulk superfluid-transition line T-lambda(P) (t is the reduced temperature T/T-lambda - 1). It provides an evaluation of existing data for L = 1 mu m near T-lambda at saturated vapor pressure (SVP), and uses these to derive a scaling function for the resistivity R(t, L) = 1/lambda(t, L). The purpose of future measurements over a wide range of L and of the pressure P 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 for R is particularly severe below T-lambda. For typical three-mm-high samples at SVP, values of L significantly larger than 8 mu m can only be investigated fully in micro-gravity. At higher pressures the gravity effect is larger. At 30 bar, three-mm samples with L greater than or similar to 4 mu m require micro-gravity for measurements below T-lambda(P). Modern thermometry has sufficient resolution to permit quantitative measurements in micro-gravity of the anticipated finite-size effect for values of L as large as 50 mu m.