## 1 Introduction
This problem becomes even more significant when lubricating oils are diluted with DO containing biocomponents, such as fatty acid methyl esters (FAME) [11; 12]. In such a case, the LO/DO mixture may not only exhibit deteriorated lubricity properties [13] but also significantly reduce thermal and oxidative stability [14; 15], and such a mixture may intensify the corrosion processes in the engine [16]. Some previous studies indicated that as little as 2-5% [17] or 3-5% [10] of DO in LO can pose risks to the engine, which coincides with the requirements mentioned in the literature regarding the allowable change in the viscosity value and flash point of LO in an engine during operation. According to these recommendations, the kinematic viscosity of the oil used in the engine, relative to the viscosity of fresh oil, determined at the reference temperature (40 \({}^{\circ}\)C or 100 \({}^{\circ}\)C) should not change by more than \(-10\%\) to \(+10\%\), considered the warning range [18], or by more than \(-20\%\) to \(+30\%\)[1], taken as the alarm range (preventive action is then required). According to the 2008 CIMAC recommendation, the viscosity alert levels are \(-20\%\) to \(+25\%\) at 40 \({}^{\circ}\)C and \(-15\%\) to \(15\%\) at 100 \({}^{\circ}\)C, while the alarm levels are \(-25\%\) to \(+45\%\) at 40 \({}^{\circ}\)C and \(-10\%\) to \(+25\%\) at 100 \({}^{\circ}\)C [19]. According to other recommendations, the kinematic viscosity of circulating LO at 100 \({}^{\circ}\)C should not decrease by more than 3.0 mm\({}^{2}\)/s or increase by more than 3.5 mm\({}^{2}\)/s relative to the value for fresh oil [20]. The dilution of LO with DO has a complex effect on changing the lubricity of the oil itself. The reasons for this are the simultaneous change in the viscosity and density of the LO/DO mixture, the change in its volatility, and its chemical composition [21]. The relatively good lubricity of today's distillation fuels makes the resulting situation even more complex due to additives to DO that improve their ability to form a boundary layer [22]. For marine distillate fuels with a sulfur content of less than 500 mg/kg (0.050% m/m), the permissible value of lubricity described as the corrected mean scar diameter of the sample during the test, \(WS_{1.4}\), according to ISO 8217:2017 [23], must not exceed 520 \(\upmu\)m when measured at 60 \({}^{\circ}\)C with the high-frequency reciprocating rig (HFFR) apparatus. In this instance, the DO used in the experiment contained 6.4 mg/kg of sulfur, and, as per the PN-EN ISO 590+A1:2017-06 standard [24], the local RMG [25] requirements, and the ZN-ORLEN-5:2019 [26] standard, the allowable sulfur content must not exceed 10 mg/kg. These requirements are specified in ISO 12156:2018 Part 2 [27]. On the other hand, according to the mentioned standards, the allowable value of the corrected wear scar \(WS_{1.4}\) in the test sample, which is a measure of lubricity for DO, must not exceed 460 \(\upmu\)m. In contrast, ASTM D975 [28] indicates a maximum allowable value of \(WS_{1.4}\), which equates to 520 \(\upmu\)m for DO. However, the Worldwide Fuel Charter Edition 5 [29] recommends \(WS_{1.4}\leq 400\)\(\upmu\)m for DO in categories 4 and 5 (markets with advanced requirements for emission control [30]). Considering the factors mentioned above and the complex nature of changes in lubricity in LO diluted with DO, the authors conduct an experiment to determine the nature of these changes and the impact of oil aging and engine component wear on the results. To achieve this aim, comparative measurements of lubricity are made as a function of DO concentration in LO for mixtures of fresh and ULO. A study of DO concentrations in mixtures up to 20% m/m is undertaken, which basically covers any situation encountered in operating conditions where the dilution level usually does not exceed a few percent. The concentration range is also determined based on previously published research results by various researchers, aiming to maintain data reproducibility and enable their comparison.