Regulation strategy and analysis of the ultra-low temperature heat and mass transfer capacity of 3He-4He mixture in the mixing chamber of dilution refrigerator

Abstract

As an important method for achieving millikelvin temperatures, dilution refrigerators (DRs) have been widely utilized in the fields of low-temperature superconductivity, low-temperature measurement, and space exploration. The mixing chamber (MC) uses a 3He-4He mixture as the refrigerant and serves as the cold end of the DR. However, the current research lacks a detailed study of the effect of the structure of porous media on the MC cooling capacity. In this study, the heat and mass transfer model in the MC is established using the finite element method. The model is based on the improved two-fluid model to evaluate its cooling capacity and propose regulation strategies. The reliability of the model is verified through experiments. When the load power stabilizes at 10 μW, the steady-state temperature is 59.6 mK, and the Kapitza thermal resistance significantly affects the cooling process of the MC. Three strategies for regulating Kapitza thermal resistance are provided. First, the optimal porosity of the sintering cylinder for the porous medium is ε = 0.5. Second, the extreme point of the sintering cylinder is at a height of h = 1.75 cm, and the cooling capacity is at its minimum at this location. Third, the steady-state temperature initially increases and then decreases with an increase in the cylinder radius. This study is of great significance as it reveals the influence of a porous medium heat exchanger on the heat and mass transfer process of mixtures at ultra-low temperatures, guiding the design of DR.