## 3 Results and Discussion  
### Quantitative Assessment of Lubricity  
The corrected wear scar diameter \(WS_{1.4}\) at 60 \({}^{\circ}\)C for the tested samples is shown in Figure 4. The \(WS_{1.4}\) values for LO/DO mixtures in the concentration range studied were in the range of 163-212 \(\upmu\)m for fresh oil mixtures and 79-217 \(\upmu\)m for used oil mixtures. In both situations, the wear scar value decreased within the range \(C\) to 2% m/m, showing that the lubricating properties of the mixtures improve as the concentration of DO in the mixture increases. Thus, the lubricity of the mixture improves as the level of dilution with DO C increases. Figure 4: Variation in the corrected diameter of the wear scar \(WS_{1.4}\) at 60 \({}^{\circ}\)C for the tested LO and diesel mixtures as a function of the DO concentration in the mixture. Generally, the effect of LO/DO mixture on the lubricity of the mixture is complex and does not exhibit a consistent pattern of change (lubricity alternates between improvement and deterioration with increasing DO content in the LO mixture), as demonstrated in previous publications [53]. In contrast, in the present experiment for the concentration range of 2-20% m/m, the nature of changes in \(WS_{1,4}\) values increased in general. The lubricity of used oil mixtures is improved compared to fresh oil because used oil contains oil aging products such as resins and organic acids, which improve the adhesion of oils to lubricated surfaces [57]. The relationship \(WS_{1,4}=f(C)\) for FLO mixed with DO can be represented by a linear function of the following form:  
\[WS_{1,4}=1.4439\ C+183.390, \tag{5}\]  
This function is depicted in Figure 4 with a blue dotted line. The mean value of the measured \(WS_{1,4}\) was 193.86 \(\upmu\)m. The standard deviation for model (5) was 12.86 \(\upmu\)m, and its root-mean-square error (RMSE) was 14.81 \(\upmu\)m. The coefficient of determination for model (5) was \(R^{2}>0.91\), indicating a very good model fit. For mixtures of ULO with DO, the relationship \(WS_{1,4}=f(C)\) takes the following form:  
\[WS_{1,4}=5.3679\ C+99.929, \tag{6}\]  
This function is shown in Figure 4 with an orange dotted line. The mean value of the measured \(WS_{1,4}\) was 140.57 \(\upmu\)m. The standard deviation for model (6) was 42.98 \(\upmu\)m, and its RMSE was 22.79 \(\upmu\)m. The coefficient of determination of model (6) was \(R^{2}>0.73\), which indicates a good fit of the model. The graph of Figure 5 shows the average sliding friction coefficient \(\mu\) of the specimen recorded during the ball wear test in the HFFR apparatus for the tested LO/DO mixtures. The values obtained exhibited some dispersion, with local fluctuations increasing and decreasing within the measured range, while the mixtures showed an overall increasing trend across the entire range studied. The values \(\mu\) for LO and diesel mixtures in the studied concentration range fell within the range of 0.123-0.133 \(\upmu\)m for the fresh oil mixtures and 121-132 \(\upmu\)m for the used oil mixtures. The relationship \(\mu=f(C)\) for both fresh and ULO mixtures can be represented as a linear function with a positive slope coefficient of the curve (showing an increasing  
Figure 5: Sliding friction coefficient \(\mu\) during the HFFR test for the tested mixtures of LO and DO varies with the concentration of DO in the mixture. trend). Mixtures of FLO and mixtures of ULO can be described by similar functions since the values of these coefficients are similar for both lubricating oils. For mixtures of FLO with DO, the relationship \(\mu=\text{f}(C)\) can be modeled with the following function:  
\[\mu=0.0004\ C+0.1233, \tag{7}\]  
This function is shown in Figure 5 with a blue dotted line. The mean value of the measured \(\mu\) was 0.126. The standard deviation for model (7) was 0.003, and its RMSE was 0.002. The coefficient of determination of model (7) was \(R^{2}>0.66\), so the model fit was satisfactory.