## 3 Results and Discussion
### Quantitative Assessment of Lubricity
However, for mixtures of ULO with DO, the relationship \(\mu=\text{f}(C)\) takes the following form:  
\[\mu=0.0004\ C+0.1221, \tag{8}\]  
This function is depicted in Figure 5 using the orange dotted line. The mean value of the measured \(\mu\) was 0.125. The standard deviation for model (8) was 0.003, and its RMSE was 0.002. The coefficient of determination of model (8) was \(R^{2}>0.71\), which indicates a good fit of the model. The linear approximation of \(\mu\) trends is just a hypothesis that we made with the certain margin of error estimated above. The obtained coefficient values of \(\mu\) indicate that, as the DO content in the LO/DO mixture increases, the friction coefficient also increases. This is due to the decrease in mixture viscosity resulting from dilution with a lower viscosity component, leading to a reduction in the oil film thickness. The experiment in question did not include a detailed analysis of changes in the viscosity values of lubricating oils diluted with DO; this was presented in the articles of other researchers [58; 59; 60]. The graph of Figure 6 illustrates the percentage reduction in the thickness (resistance) of the oil film \(r\) recorded during the execution of the ball wear test in the HFFR apparatus for the tested LO/DO mixtures. The values obtained displayed some dispersion, with local increases and decreases within the measured range, while the mixtures exhibited a decreasing trend across the entire range under study. The values of \(r\) for LO and diesel mixtures in the tested concentration ranged from 100 to 85 \(\upmu\)m for the fresh oil mixtures and from 100 to 87 \(\upmu\)m for the used oil mixtures. The relationship \(r=\text{f}(C)\) for both FLO and ULO mixtures can be presented as a linear function with a negative value of the slope coefficient of the curve (a decreasing trend). Mixtures of  
Figure 6: Coefficient of reduction in the thickness of the oil film \(r\) during the execution of the HFFR test for the tested LO and DO mixtures as a function of the concentration of DO in the mixture. FLO and mixtures of ULO can be described by similar functions since the values of these coefficients are alike for both lubricating oils. For all measurement points of the tested mixtures included in the experiment, we obtained boundary friction under test conditions. This was confirmed by the \(r\) indicator, referred to in other sources as the _FILM_ parameter [31]. Its high values, determined during the HFFR tests and amounting to \(>84\), indicate that, during the lubricity measurement, there was no direct dry contact of the cooperating samples due to surfactant adsorption. The obtained values of \(r\) show that, with an increase in the content of DO in the LO/DO mixture, the thickness of the oil film decreases and the risk of film breakage increases, which relates to the decrease in the viscosity of the mixture due to dilution with the lower-viscosity component. For mixtures of FLO with DO, the relationship \(r=\text{f}(C)\) can be modeled with the following function:  
\[r=-0.5020\;C+100, \tag{9}\]  
This function is presented in Figure 6 with a blue dotted line. The mean value of the measured \(r\) was 96.86%. The standard deviation for model (9) was 4.37%, and its RMSE was 3.02%. The coefficient of determination here was \(R^{2}>0.69\), so the fit of model (9) was satisfactory. However, for mixtures of ULO with DO, the relationship \(r=\text{f}(C)\) takes the following form:  
\[r=-0.5258\;C+100, \tag{10}\]  
This is shown in Figure 6 with an orange dotted line. The mean value of the measured \(r\) was 96.14%. The standard deviation for model (10) was 4.30%, and its RMSE was 3.08%. The coefficient of determination here was \(R^{2}>0.61\), which indicates a satisfactory fit for model (10). The linear approximation of \(r\) trends is just a hypothesis that we made with the certain margin of error estimated above.