Viscosity of liquid and gaseous helium-3 from 3 mK to 500 K

Measurements on the viscosity property of fluid helium-3 in literature were surveyed. Experimental data are found adequate in the liquid phase, while almost no data are available in the gas phase except some at pressures not higher than 0.1 MPa. A quantum version of the principle of corresponding states is used to predict the viscosity of gaseous helium-3. An equation is proposed for the viscosity of 3He along the gas–liquid equilibrium line at temperatures from 0.003 K (∼superfluid transition temperature) to 3.3157 K (the critical temperature). The estimated uncertainty of the equation compared to the high-precision experimental data is within ±0.7%. Empirical equations were developed both for the normal liquid and compressed gas regions with an uncertainty of ±1.5%. These equations are consistent to each other and supposed to be the unique ones by far for the viscosity of 3He in such a wide range. Comparison between the predictions and measurements is implemented. The thermophysical behavior of the viscosity of 3He is discussed.

► Empirical equations have been developed for the viscosity of 3He from 3 mK to 500 K.
► Below 1 K, viscosity is dominated by Fermi quantum effect and follows η ∝ T−2.
► Between 1 K and 3 K, both (∂η/∂p)T and (∂η/∂T)p switche from negative to positive.
► Isobars cross each other at almost the same temperature value (∼1 K).
► Comprehensive viscosity data are available for 3He applications.