Since the project begin, there has two aspects of progerss. One is the study of the equation of state (EOS) for 3He-4He mixtures. Another is the building of experimental system.
For the EOS of 3He-4He mixtures, this project developed the first wide-range equation of state for 3He-4He mixtures based on the Helmholtz free energy, which is reliable for the temperature from 2.17 K to room temperature, pressure from vapor pressure to higher than 3 MPa. To obtain an accuracy calculation model, four different departure functions from KW0, 4He-Ne, 4He-Ar and Ne-Ar multi-fluid model are tested. For each of them, five parameters were optimized to find the minimum deviation from the available experimental data by using the Levenberg–Marquardt method. The results showed that the KW0 model was the best one to predict the thermophysical properties for 3He-4He mixtures. The comparison between the present model and the available experimental data shows that the present model has a good predictive performance not only on the liquid and gas ρpT relation but also on the vapor-liquid equilibrium properties of 3He-4He mixtures. For the most data of ρpT relation, saturated liquid density and speed of sound, the error of present EOS is less than 2 %. For the most data of bubble point pressure, dew point pressure, saturated vapor density and isochoric heat capacity, the error of present EOS is less than 5%, except some points near the critical region or λ point, the error of which can be higher than 8%. Although the present model gives a relatively poor prediction of the saturated heat capacity, it can be improved in the future if more accurate experimental data is available. Furthermore, by comparing with the virial EOS, it also shows that the current model has good extrapolation performance at temperatures above 20 K to room temperature. Based the present EOS, a software was developed by using MATLAB graphical user interfaces (GUI). One can use it to calculate the thermophysical properties at a given point. In addtion, the calculated tabulated database was built, which covers thermophysical properties of ρpT relation, entropy, enthalpy, heat capacity, volumetric thermal expansion, and compression factor at the pressure from saturated pressure up to 3 MPa, temperature from 2.2 K to 350 K, and 3He concentration from 0 to 1.
For the experimental system, in order to save the consumption of helium-3, a small pulse tube (D=5.5 mm) was built. The cold traps within a heater were used as the compressor. In the experiment, the cold trap was put into liquid nitrogen. By heating and removing the heating on the cold trap, a pressure wave can be generated. Meanwhile, another cold trap with some phase different heating can be used as phahe shifter. Theoretically, those two cold trap can generate a Stiling cycle. But unfortunatelly, this idea was failed because the frequency of this compressor can only be around 0.1 Hz, which is too low to generate a avilable cooling power.
In summary, the main output of this project is the first wide-range equation of state for 3He-4He mixtures. The results have been submitted to the J. Phys. Chem. Ref. Data (open access), in which a easy use database and software has been built as the Supplementary Material. It will be very useful for the design and optimization of ultra-low temperature refrigerators.
