# Study on the Performance of Liquid Metal Lubricated V-Groove Bearing Considering Turbulence
## 2 Viscosity Measurement of Gallium Based Liquid Metal  
Viscosity is a basic property of fluid. It is the measurement of internal friction force between fluid molecules when the fluid is displaced by external force. It indicates the fluidity of fluid, generally varying with different fluids. The smaller the viscosity, the better the fluidity. As an important index to evaluate the quality of lubricants, the viscosity reflects the internal friction force of fluid and is directly related to the performance, wear degree, and service life of the bearing [18]. In addition, in the theoretical analysis of lubrication, it is necessary to know the viscosity of the lubricant, judge its flow form according to the working conditions, and then establish the theoretical lubrication model for analysis. Therefore, in order to carry out the theoretical analysis of the bearing lubrication performance, it is very important to measure the viscosity of gallium based liquid metal.  
First, we prepared the GBLM, which in this paper was a gallium-indium-tin alloy with a mass ratio of 68.5:21.5:10. According to the configuration method described by [PERSON]'s team in [19], the high-purity metal was selected according to the mass ratio and mixed in the container, which should be cleaned with deionized water. Then, the mixed raw materials were heated to a certain temperature until the metal melted, stirred slightly and cooled to room temperature to obtain GBLM. As GBLM is very easy to oxidize in air, gallium oxide will be produced, which will affect the viscosity and surface tension [20; 21]. Therefore, impurity removal steps should be carried out. As is well known, NaOH can react with oxides to remove oxide impurities. We mixed a certain concentration of NaOH solution and the prepared GBLM alloy, both incompatible with each other proportionally; in addition, the density of the liquid metal was larger, so it will be layered after standing; then the LM after impurity removal can be obtained by taking the lower layer solution with a rubber tip dropper.  
Considering that the capillary viscometer is easy to operate and the error is small, this paper used this method to measure the viscosity of GBLM. The experimental setup (Model SYD-265E kinematic viscometer, China, SANUO) is shown in Figure 1a. Given that the actual working temperature can reach 300 \({}^{\circ}\)C, it was difficult for the test temperature to reach. Therefore, in order to obtain the working viscosity, first, the viscosity of GBLM at different temperatures was measured by changing the test temperature, and then the viscosity-temperature relationship was fitted by using the least squares method. The results are shown in Figure 1b, and the viscosity-temperature equation can be obtained as follows:  
\[\ln\
u=-0.004638\times T-0.616012 \tag{1}\]  
where \(\
u\) is the kinematic viscosity and \(T\) is the temperature in centigrade.  
With Equation (1), the viscosity of GBLM under actual working conditions can be predicted: when the actual working temperature reached 300 \({}^{\circ}\)C, the viscosity of GBLM was 0.134 mm\({}^{2}\)/s, converted into a dynamic viscosity of \(8.63\times 10^{-4}\) Pa\(\cdot\)s.  
By measuring the viscosity of GBLM, it was found that its viscosity was low under the actual working condition, and the rotating speed of the anode target in CTT was very high (up to about \(10,000\) r/min). Before the establishment of the theoretical model, the Reynolds number was calculated, which was about 2500. This exceeded the Reynolds number limit of laminar flow, which is 2000. Therefore, the turbulent model should be used in the theoretical analysis of lubrication.