High-Pressure Thermophysical Properties of Eight Paraffinic, Naphthenic, Polyalphaolefin and Ester Base Oils

Citation: Villamayor, A.; Guimarey, M.J.G.; Mariño, F.; Liñeira del Río, J.M.; Urquiola, F.; Urchegui, R.; Comuñas, M.J.P.; Fernández, J. High-Pressure Thermophysical Properties of Eight Paraffinic, Naphthenic, Polyalphaolefin and Ester Base Oils. Lubricants 2023,11, 55. https://doi.org/10.3390/ lubricants11020055 Received: 10 January 2023 Revised: 24 January 2023 Accepted: 28 January 2023 Published: 31 January 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). lubricants Article High-Pressure Thermophysical Properties of Eight Paraffinic, Naphthenic, Polyalphaolefin and Ester Base Oils Antía Villamayor 1,2, María J. G. Guimarey 1,3, Fátima Mariño 1, JoséM. Liñeira del Río1,4, Francisco Urquiola 5, Raquel Urchegui 5, María J. P. Comuñas 1,* and Josefa Fernández 1 1 Laboratory of Thermophysical and Tribological Properties, NaFoMat Group, Department of Applied Physics, Faculty of Physics and Institute of Materials (iMATUS), University of Santiago de Compostela, 15782 Santiago de Compostela, Spain 2Plasma Coating Technologies Unit, Tekniker, Basque Research and Technology Alliance (BRTA), c/Iñaki Goenaga 5, 20600 Eibar, Spain 3Department of Design and Engineering, Faculty of Science & Technology, Bournemouth University, Talbot Campus, Poole BH12 5BB, UK 4 INEGI, Universidade do Porto, Faculdade de Engenharia, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal 5Verkol S.A.U. Quaker Houghton, Polígono Zalain, 23 I, 31780 Bera Navarra, Spain *Correspondence: [email protected] Abstract: In this work, the thermophysical properties of four mineral (paraffinic and naphthenic) and four synthetic (polyalphaolefin and ester) base oils are measured. Knowledge of these properties is of vital importance for the correct and optimal formulation and design of lubricants, and for the development of equations of state and transport models that adequately represent their properties. Density, isothermal compressibility, thermal expansion coefficient, dynamic viscosity, pressure– viscosity coefficient, and contact angle were determined. To carry out this work, a p ρ T apparatus, a rotational viscometer, a falling body viscometer, and a contact angle analyzer were used. Highest densities were found for the polyalphaolefin and ester synthetic oils, increasing around 5% from 0.1 to 100 MPa for all the base oils. The density of the synthetic oils is less dependent on temperature changes. For the expansivity and compressibility of all the base oils, decreases with pressure of up to 35% and 45% were observed. From the contact angle measurements, it was observed that base oils with a higher viscosity grade have a worse wetting. The greatest effect of pressure on the dynamic viscosity was obtained for the naphthenic mineral oil and the lowest effect for the polyalphaolefin oil. Paraffinic and naphthenic oils present the highest universal pressure–viscosity coefficients. Keywords: high pressure; mineral oils; synthetic oils; density; isothermal compressibility; thermal expansion coefficient; contact angle; dynamic viscosity; pressure–viscosity coefficient 1. Introduction In accordance with the demands of society, modern development trends in the industry have shifted towards the use of biodegradable and low-toxicity synthetic lubricants, compared with petroleum-derived lubricants, in addition to lower emissions of organic volatile compounds [ 1 , 2 ]. Lubricants have a great impact on the energy efficiency, reliability, average life, and noise levels of industrial machinery [ 3 ]. In lubricant formulation, the selection of the base oils is of utmost importance [ 4 ]. Mineral-based oils are usually divided into paraffinic (PARA) and naphthenic (NAPH) depending on the chemical structure of the predominant component [ 5 ]. Synthetic base oils, such as polyalphaolefins (PAOs) and esters (ESTERs), are obtained by chemical synthesis, which makes it possible to achieve lubricants with very specific characteristics. Synthetic oils have another advantage over the former, i.e., they improve machine protection and maintain the stability of their properties for a longer period. Moreover, the low toxicity and excellent biodegradability of the ester base oils make them highly interesting from an environmental point of view [6]. Lubricants 2023,11, 55. https://doi.org/10.3390/lubricants11020055 https://www.mdpi.com/journal/lubricants Lubricants 2023,11, 55 2 of 24 For industrial applications, the knowledge of the lubricating properties and the thermophysical and tribological characterization of base oils of different nature (mineral, synthetic and vegetable oils) is essential. Knowledge of the density at high pressures is essential to determine the dynamic viscosity as a function of pressure and, subsequently, the pressure– viscosity coefficient and film thickness, parameters that are directly related to the proper selection of a lubricant for each application. Contact angle measurements ( θ ) are used to evaluate the tendency of the lubricants to spread on a solid surface (wetting ability), which is a key factor for many industrial processes involving two different phases and a very important factor affecting their lubrication performance [ 7 ]. The affinity of the lubricant to the surrounding surfaces is a system variable and, therefore, depends not only on the lubricant, but also on the contact surfaces. Properties such as foaming depend on the viscosity and surface tension of the lubricant [ 8 ]. Thus, it is crucial to have databases of the thermodynamic and transport properties, as well as equations of state and models that adequately represent these properties. Liquid lubricants are generally considered incompressible, even though their compressibility is an important property that varies with changes in temperature and pressure and must be taken into account in various cases, such as heavily loaded lubricated contacts or hydraulic fluid applications [ 9 ]. In hydraulic systems operating at high pressure, oils with low compressibility are required to transmit power efficiently, as low compressibility results in a fast response time, high-pressure transmission speed, and low power loss. However, a certain amount of compressibility is desirable because it dampens the pressure peaks caused by switching and thus provides a smoother operation [ 10 ]. For this reason, knowing the volumetric behavior of base oils at high pressures allows the evaluation of their degree of compressibility and thus helps in the development of more efficient lubricants for a particular application. We have found in the literature several works studying the thermophysical and tribological properties of mineral and synthetic oils. Gold et al. [ 11 ] studied the viscosity– pressure–temperature behavior of several gear oils and hydraulic oils up to 0.8 GPa. Fernández Rico et al. [ 12 ] reported the contact angle of mineral and synthetic oils, showing that mineral oil has a higher value than that of synthetic oil. Grandelli et al. [ 13 ] determined the high-pressure volumetric properties of three commonly used poly( α -olefin) base oils, PAO 2, PAO 4, and PAO 8, using a special variable volume view cell, which permits continuous pressure scan and volume measurements. These authors [ 13 ] determined the densities at several temperatures and pressures up to 40 MPa. Dickmann et al. [ 14 ] carried out a comprehensive evaluation of the volumetric and viscous properties of various mineral and synthetic base oils. These authors used a variable volume display cell to obtain densities and a high-pressure rotational viscometer to obtain viscosities at shear rates between 480 and 1270 s −1 . Wang et al. [ 15 ] determined the pressure–viscosity coefficients of several mineral and synthetic oils with the aim of improving the rolling fatigue lives. Recently, Teh et al. [ 16 ] published a review on the tribological performance of non-water miscible lubricants, such as vegetable oil, blend oil, synthetic oil, and ionic liquids. In order to analyze the effects of the chemical nature and of the viscosity grade on the thermophysical properties, the present work provides high-accurate experimental data on density, isothermal compressibility, thermal expansion coefficient, and viscosity over a temperature range from 278.15 to 373.15 K at a high pressure (up to 100 MPa for density and 150 MPa for viscosity) as well as contact angle values at atmospheric pressure of eight base lubricants. The thermophysical properties of the synthetic oils (polyalphaolefin and ester) are compared with those obtained for the mineral oils (paraffinic and naphthenic). 2. Experimental Procedure and Methodology The base oils analyzed in this work were four mineral base oils and four synthetic base oils: two paraffinic oils (PARA#1 and PARA#2), two naphthenic oils (NAPH#1 and NAPH#2), two ester oils (ESTER#1 and ESTER#2), and two polyalphaolefin oils (PAO4 and PAO16). These lubricants were kindly provided by Verkol Lubricantes. PARA#1 and PARA#2 are paraffinic mineral solvent neutral classified as API Group I. NAPH#1 is a mid- Lubricants 2023,11, 55 3 of 24 viscosity hydrotreated naphthenic base oil and NAPH#2 is a high viscosity hydrotreated naphthenic base. ESTER#1 is an adipic acid diester of long chain length alcohols and ESTER#2 is a mixture of adipic acid diester and pentaerythritol ester. NAPH#1, NAPH#2, ESTER#1 and ESTER#2 are categorized as API Group V. PAO4 is a low viscosity isoparaffinic polyalphaolefin and PAO16 is a mixture of high and low viscosity isoparaffinic polyalphaolefins. Both PAOs are classed as API Group IV. The eight base oils can be classified in two groups depending on their viscosity grade. Thus, the oils with kinematic viscosity around 20 mm 2 s −1 , at 313.15 K and 0.1 MPa (low-viscosity grade, ISO VG22) were PARA#1, NAPH#1, ESTER#1, and PAO4, and those with kinematic viscosity, at 313.15 K and 0.1 MPa, around 100 mm 2 s −1 (high-viscosity grade, ISO VG100) were PARA#2, NAPH#2, ESTER#2, and PAO16. Densities ( ρ ) and viscosities ( ν and η ) at atmospheric pressure were measured with the expanded uncertainties of 5 · 10 −4 g cm −3 and 1%, respectively, by using an Anton Paar Stabinger SVM3000 rotational viscometer (Anton Paar, Graz, Austria). A vibrating tube densimeter (HPM Anton Paar (Anton Paar, Graz, Austria)) was used to measure densities at high pressures with expanded uncertainties lower than 5 · 10 −3 g cm −3 . Dynamic viscosities ( η ) as a function of pressure were obtained with an uncertainty of 3.5% with a falling body viscometer. Contact angles ( θ ) were measured using the sessile drop method through a Phoenix MT(A) contact angle analyzer with an expanded uncertainty of 1 º . Other details regarding the experimental setups of density [ 17 ], viscosity [ 18 ], and contact angle [19] have been further reported in previous articles. For industry applications, it is useful to have a correlation that permits the interpolation of the density of these oils at temperatures and pressures different than those studied in this paper. For this reason, the density of each oil, as a function of both the temperature and the pressure, were correlated trough the Tammann–Tait empirical equation of state: ρ(T,p)=A0+A1T+A2T2+A3T3 1−ClnB0+B1T+B2T2+p B0+B1T+B2T2+0.1 MPa(1) Using basic thermodynamic relations, it is possible to obtain the thermal expansion coefficient ( αp ) and isothermal compressibility ( κT ) from density data at different temperatures and pressures. Generally, these properties are used to provide more specific information on the dependence of fluid density on temperature and pressure. The thermal expansion coefficient describes the effect of the temperature on the density at a constant pressure, and is defined as follows: αp=1 V∂V ∂TP =−1 ρ∂ρ ∂Tp (2) where αp is the volumetric thermal expansion coefficient, ρ the density, Vthe volume, Tthe temperature, and pthe pressure. If Equation (1) is used to represent the surface ρ (T,p) for each base oil, the isobaric thermal expansivity can be obtained as follows: αp(p,T)=−A1+2A2T ρ0(T,0.1MPa)−C(0.1MPa −p) (B(T) + p)(B(T) + 0.1MPa) B1+2B2T h1−C lnB(T)+p B(T)+0.1MPai(3) Changes in volume that occur with changes in pressure are often characterized using the isothermal compressibility (κT), which is defined as: κT=−1 V∂V ∂PT =1 ρ∂ρ ∂PT (4) Lubricants 2023,11, 55 4 of 24 If Equation (1) is used to represent the surface ρ (T,p) for each base oil, the isothermal compressibility can be obtained as follows: κT(p,T)=C (B0+B1T+B2T2+p)h1−C lnB0+B1T+B2T2+p B0+B1T+B2T2+0.1 MPai (5) The estimated uncertainty for the thermal expansion coefficient and the isothermal compressibility are around 0.3 · 10 −4 K −1 and 0.06 · 10 −4 MPa −1 , respectively. For each base oils, the experimental dynamic viscosity data as a function of pressure, η (p), were fitted at each temperature to the following equation: η(p) = η0expAlnB+p B+0.1 MPa (6) where η0 is the dynamic viscosity value obtained with the Anton Paar Stabinger viscometer at 0.1 MPa at each temperature) and A, B, and C are adjustable parameters. From Equation (6), it is possible to calculate the pressure–viscosity coefficient ( α ), which is another relevant property in lubrication [ 20 – 23 ]. In the present work, the procedure proposed by Bair et al. [23] was used to determine the pressure–viscosity coefficient using these equations: α=αf ilm =1−exp(−3) piv(3/α∗)(7) where piv the isoviscous pressure given by: piv =Zp00 0 η(p0=0)dp0 η(p0)(8) and α∗is the reciprocal asymptotic isoviscous pressure coefficient: α∗=1 piv(∞)=Z‘∞ 0 η(p=0)dp η(p)−1 (9) The pressure–viscosity coefficient for the eight base oils was also estimated from the following equation proposed by Gold et al. [ 11 ], which relates this coefficient with the kinematic viscosity, v, at 0.1 MPa: αGold =sνt(10) Gold et al. [ 11 ] used a database of 28 lubricants, including mineral, synthetic, and vegetable oils, to determine sand tvalues for six lubricant types. These parameters are valid from 278.15 to 353.15 K. There are several studies [ 23 , 24 ] concerning the relation between the pressure–viscosity coefficient ( α ) and the central film thickness (h 0 ). According to the American Gear Manufacturers Association (AGMA), under full-film elastohydrodynamic lubrication at speed U, the central film thickness is given by: h0=fη0.69 0α0.56U0.69 (11) where the parameter fis a function of the surface geometry, the applied load, and the elastic parameters of the rolling elements, and η0 is the dynamic viscosity at atmospheric pressure. In Equation (11), for α , we chose the universal pressure–viscosity coefficient ( αfilm ) obtained from Equation (7), as in a previous work [ 25 ]. From Equation (11), it can be concluded that, at a fixed temperature, comparing fluids with the same viscosity, the base oils that provide a better protection (thicker film) at extreme pressures are those with a higher pressure–viscosity coefficient. Nevertheless, to ensure a better efficiency, other factors should be considered, such as the reduction in wear, friction, sub-surface stress and pressure peaks [ 26 – 28 ]. Moreover, that the film thickness changes as little as possible with the temperature is desirable. Lubricants 2023,11, 55 5 of 24 3. Results and Discussion Table 1reports the densities at 0.1 MPa from 278.15 to 373.15 K for the eight oils measured with the SVM3000 apparatus (Anton Paar, Graz, Austria). As can be seen in Figure 1, the densities of all eight base oils decrease linearly with increasing temperature at atmospheric pressure. The following sequence is observed for the density at atmospheric pressure for both groups, the low-viscosity-grade base oils (NAPH#1, PARA#1, PAO4, and ESTER#1) and the high-viscosity-grade base oils (NAPH#2, PARA#2, PAO16, and ESTER#2): ESTER> NAPH> PARA> PAO. Thus, at atmospheric pressure, the polyalphaolefin oils (PAO4 and PAO16) have the lowest density values, followed by the mineral base oil PARA#1. On the contrary, esters are the densest fluids in each group. At 0.1 MPa, the decrease in density from 278.15 to 373.15 K is around 7% for all the base oils. Table 1. Density, ρ , kinematic viscosity, ν , and dynamic viscosity, η ,for the eight base oils at different temperatures, T/K, and at 0.1 MPa measured with SVM3000 Stabinger. T/K ρ/g cm−3ν/mm2s−1η/mPa s T/K ρ/g cm−3ν/mm2s−1η/mPa s PARA#1 PARA#2 278.15 0.8695 99.41 86.44 278.15 0.8984 1403.3 1260.6 283.15 0.8664 73.32 63.53 283.15 0.8953 913.2 817.6 288.15 0.8633 55.44 47.86 288.15 0.8923 614.3 548.1 293.15 0.8601 42.80 36.82 293.15 0.8892 424.9 377.8 298.15 0.8570 33.66 28.85 298.15 0.8862 301.2 266.9 303.15 0.8538 26.94 23.00 303.15 0.8832 218.5 192.9 308.15 0.8506 21.90 18.63 308.15 0.8802 161.8 142.4 313.15 0.8475 18.07 15.31 313.15 0.8772 122.3 107.2 318.15 0.8443 15.10 12.75 318.15 0.8742 94.06 82.23 323.15 0.8411 12.77 10.74 323.15 0.8712 73.60 64.12 328.15 0.8379 10.92 9.152 328.15 0.8682 58.50 50.79 333.15 0.8347 9.428 7.870 333.15 0.8651 47.17 40.81 338.15 0.8315 8.217 6.832 338.15 0.8620 38.55 33.23 343.15 0.8283 7.217 5.978 343.15 0.8590 31.91 27.41 348.15 0.8251 6.388 5.271 348.15 0.8559 26.73 22.87 353.15 0.8218 5.693 4.679 353.15 0.8528 22.60 19.27 358.15 0.8186 5.107 4.181 358.15 0.8497 19.31 16.40 363.15 0.8154 4.607 3.757 363.15 0.8467 16.64 14.09 368.15 0.8122 4.179 3.394 368.15 0.8436 14.46 12.20 373.15 0.8089 3.807 3.080 373.15 0.8405 12.66 10.64 NAPH#1 NAPH#2 278.15 0.9072 206.2 187.1 278.15 0.9227 2174.4 2006.3 283.15 0.9040 136.3 123.2 283.15 0.9196 1261.5 1160.1 288.15 0.9009 93.87 84.57 288.15 0.9165 768.3 704.1 293.15 0.8977 66.85 60.02 293.15 0.9133 487.3 445.1 298.15 0.8945 49.05 43.88 298.15 0.9103 320.5 291.7 303.15 0.8914 36.98 32.96 303.15 0.9072 218.0 197.7 308.15 0.8882 28.56 25.37 308.15 0.9041 152.8 138.1 313.15 0.8849 22.54 19.94 313.15 0.9011 110.1 99.20 318.15 0.8817 18.12 15.98 318.15 0.8980 81.37 73.07 323.15 0.8785 14.83 13.02 323.15 0.8949 61.54 55.07 328.15 0.8752 12.31 10.78 328.15 0.8918 47.53 42.39 333.15 0.8720 10.37 9.046 333.15 0.8887 37.43 33.26 338.15 0.8687 8.840 7.679 338.15 0.8855 29.97 26.54 343.15 0.8655 7.614 6.590 343.15 0.8824 24.39 21.52 348.15 0.8622 6.626 5.713 348.15 0.8793 20.13 17.70 Lubricants 2023,11, 55 6 of 24 Table 1. Cont. T/K ρ/g cm−3ν/mm2s−1η/mPa s T/K ρ/g cm−3ν/mm2s−1η/mPa s 353.15 0.8589 5.815 4.995 353.15 0.8761 16.83 14.75 358.15 0.8557 5.142 4.400 358.15 0.8730 14.24 12.43 363.15 0.8524 4.586 3.909 363.15 0.8698 12.17 10.59 368.15 0.8491 4.114 3.493 368.15 0.8667 10.51 9.109 373.15 0.8458 3.712 3.140 373.15 0.8635 9.156 7.907 ESTER#1 ESTER#2 278.15 0.9202 158.8 146.1 278.15 0.9299 844.6 785.4 283.15 0.9168 114.6 105.0 283.15 0.9266 584.1 541.3 288.15 0.9134 85.03 77.67 288.15 0.9233 415.2 383.3 293.15 0.9100 64.64 58.82 293.15 0.9200 301.9 277.7 298.15 0.9066 50.22 45.53 298.15 0.9168 224.2 205.6 303.15 0.9032 39.74 35.89 303.15 0.9135 170.0 155.3 308.15 0.8998 32.02 28.81 308.15 0.9103 131.2 119.4 313.15 0.8964 26.20 23.49 313.15 0.9071 103.0 93.39 318.15 0.8930 21.75 19.43 318.15 0.9039 82.08 74.18 323.15 0.8896 18.29 16.28 323.15 0.9006 66.37 59.77 328.15 0.8862 15.56 13.79 328.15 0.8974 54.37 48.79 333.15 0.8828 13.38 11.81 333.15 0.8941 45.10 40.32 338.15 0.8793 11.61 10.21 338.15 0.8909 37.82 33.69 343.15 0.8759 10.17 8.905 343.15 0.8876 32.04 28.44 348.15 0.8725 8.969 7.825 348.15 0.8843 27.41 24.24 353.15 0.8690 7.969 6.926 353.15 0.8811 23.65 20.84 358.15 0.8656 7.129 6.171 358.15 0.8778 20.59 18.07 363.15 0.8621 6.415 5.530 363.15 0.8745 18.03 15.77 368.15 0.8587 5.804 4.984 368.15 0.8712 15.91 13.86 373.15 0.8552 5.277 4.513 373.15 0.8680 14.13 12.26 PAO4 PAO16 278.15 0.8252 82.54 68.11 278.15 0.8439 826.8 697.8 283.15 0.8221 63.20 51.96 283.15 0.8409 590.1 496.2 288.15 0.8190 49.31 40.38 288.15 0.8379 430.7 360.9 293.15 0.8159 39.10 31.90 293.15 0.8349 320.6 267.7 298.15 0.8128 31.47 25.58 298.15 0.8319 243.0 202.2 303.15 0.8097 25.68 20.79 303.15 0.8289 187.3 155.3 308.15 0.8065 21.23 17.12 308.15 0.8259 146.6 121.1 313.15 0.8034 17.76 14.27 313.15 0.8230 116.4 95.83 318.15 0.8003 15.02 12.02 318.15 0.8200 93.71 76.84 323.15 0.7971 12.83 10.23 323.15 0.8170 76.36 62.39 328.15 0.7939 11.06 8.782 328.15 0.8140 62.95 51.24 333.15 0.7908 9.616 7.604 333.15 0.8109 52.41 42.50 338.15 0.7876 8.504 6.698 338.15 0.8079 44.11 35.63 343.15 0.7844 7.466 5.857 343.15 0.8049 37.46 30.15 348.15 0.7812 6.627 5.177 348.15 0.8018 32.09 25.73 353.15 0.7780 5.919 4.605 353.15 0.7988 27.72 22.14 358.15 0.7749 5.319 4.121 358.15 0.7957 24.13 19.20 363.15 0.7717 4.802 3.706 363.15 0.7927 21.15 16.76 368.15 0.7685 4.359 3.350 368.15 0.7897 18.64 14.72 373.15 0.7653 3.976 3.043 373.15 0.7866 16.53 13.00 Lubricants 2023,11, 55 7 of 24 Lubricants 2023, 11, x FOR PEER REVIEW 7 of 25 363.15 0.7717 4.802 3.706 363.15 0.7927 21.15 16.76 368.15 0.7685 4.359 3.350 368.15 0.7897 18.64 14.72 373.15 0.7653 3.976 3.043 373.15 0.7866 16.53 13.00 The experimental results of the densities at high pressures for the mineral and synthetic base oils are reported in Table 2 at a temperature range from 298.15 to 373.15 K and at pressures up to 100 MPa. The density values measured with the pρT apparatus at 0.1 MPa for the eight base oils were compared with those obtained with SVM3000 Stabinger apparatus over the temperature interval from 298.15 to 373.15 K. Relative deviations between 0.03% and 0.12% for the temperature of 298.15 K and from 0.01% to 0.08% for the highest temperature, 373.15 K, were found. These good results (very-low relative deviations between both apparatuses) are also a way to check and confirm the reliability of the pρT apparatus. The density of the eight base oils varies from 0.7646 to 0.9600 g cm −3 during the entirety of the pressure and the temperature interval. In Figure 2a, the density of all the base oils was plotted at a fixed pressure (60 MPa) against the temperature. This figure can be compared with Figure 1, where the data obtained with the SVM3000 apparatus at a low pressure (0.1 MPa) are also plotted as a function of the temperature. The same trend with temperature was observed for all the base oils over both isobars (0.1 and 60 MPa). It was found that, at a fixed temperature, the ESTER#2 oil has the highest densities in the entire pressure range; so, for example, at 333.15 K, the density of this oil changes from 0.8934 g cm −3 at 0.1 MPa to 0.9422 g cm −3 at 100 MPa. On the contrary, PAO4 has the lowest densities, ranging from 0.7896 g cm −3 at 0.1 MPa to 0.8400 g cm −3 at 100 MPa at the same temperature. For all the temperatures and pressures, the densities of the polyalphaolefins are around 11% (PAO4) and 9% (PAO16) lower than those of ESTER#2. The other synthetic oil (ESTER#1) has densities slightly lower (around 1%) than those of ESTER#2. Concerning mineral oils, naphthenic oils have higher densities than paraffinic oils. In Figure 2b, the dependence of the density with pressure is plotted at 333.15 K for the eight oils. Densities at 100 MPa are around 5% higher than those at 0.1 MPa for all the base oils for all the isotherms. This increase in density due to pressure must be considered in the design of the machinery that works under high loads. Figure 1. Densities, ρ , obtained with the SVM300 apparatus at 0.1 MPa for the eight oils versus the temperature function. The solid lines are for guidance. Figure 1. Densities, ρ , obtained with the SVM300 apparatus at 0.1 MPa for the eight oils versus the temperature function. The solid lines are for guidance. The experimental results of the densities at high pressures for the mineral and synthetic base oils are reported in Table 2at a temperature range from 298.15 to 373.15 K and at pressures up to 100 MPa. The density values measured with the p ρ T apparatus at 0.1 MPa for the eight base oils were compared with those obtained with SVM3000 Stabinger apparatus over the temperature interval from 298.15 to 373.15 K. Relative deviations between 0.03% and 0.12% for the temperature of 298.15 K and from 0.01% to 0.08% for the highest temperature, 373.15 K, were found. These good results (very-low relative deviations between both apparatuses) are also a way to check and confirm the reliability of the p ρ T apparatus. The density of the eight base oils varies from 0.7646 to 0.9600 g cm−3 during the entirety of the pressure and the temperature interval. In Figure 2a, the density of all the base oils was plotted at a fixed pressure (60 MPa) against the temperature. This figure can be compared with Figure 1, where the data obtained with the SVM3000 apparatus at a low pressure (0.1 MPa) are also plotted as a function of the temperature. The same trend with temperature was observed for all the base oils over both isobars (0.1 and 60 MPa ). It was found that, at a fixed temperature, the ESTER#2 oil has the highest densities in the entire pressure range; so, for example, at 333.15 K, the density of this oil changes from 0.8934 g cm−3 at 0.1 MPa to 0.9422 g cm −3 at 100 MPa. On the contrary, PAO4 has the lowest densities, ranging from 0.7896 g cm −3 at 0.1 MPa to 0.8400 g cm −3 at 100 MPa at the same temperature. For all the temperatures and pressures, the densities of the polyalphaolefins are around 11% (PAO4) and 9% (PAO16) lower than those of ESTER#2. The other synthetic oil (ESTER#1) has densities slightly lower (around 1%) than those of ESTER#2. Concerning mineral oils, naphthenic oils have higher densities than paraffinic oils. In Figure 2b, the dependence of the density with pressure is plotted at 333.15 K for the eight oils. Densities at 100 MPa are around 5% higher than those at 0.1 MPa for all the base oils for all the isotherms. This increase in density due to pressure must be considered in the design of the machinery that works under high loads. The coefficients Ai(i= 0, 1, 2) of Equation (1) were determined for each base oil in a preliminary fit of the density at 0.1 MPa as a function of the temperature. The coefficients Bj(j= 0, 1, 2) and C were fitted to the density measurements, at pressures different than 0.1 MPa, using the Levenberg–Marquardt algorithm. The parameter values are presented Lubricants 2023,11, 55 8 of 24 in Table 3. Comparing the experimental density data and those obtained from Equation (1), we can observe that yield standard deviations ( σ ) are lower than 6.5 · 10 −4 g cm −3 , which is a measure of the dispersion of the data. The σ values for all the oils are lower than the estimated experimental uncertainty (5 · 10 −3 g cm −3 ). As an example, Figure 3shows, for NAPH#2, the ρ (T,p) surface obtained with Equation (1) together with the experimental data measured with the HPM densimeter. Table 2. Experimental density data, ρ /g cm −3 , measured with the Anton Paar HPM densimeter of the eight base oils as a function of temperature (T) and pressure (P). P/MPa T/K PARA#1 NAPH#1 ESTER#1 PAO4 PARA#2 NAPH#2 ESTER#2 PAO16 298.15 0.1 0.8573 0.8945 0.9065 0.8121 0.8870 0.9107 0.9168 0.8308 1 0.8578 0.8950 0.9070 0.8127 0.8875 0.9111 0.9173 0.8313 5 0.8601 0.8973 0.9093 0.8150 0.8896 0.9132 0.9195 0.8335 10 0.8628 0.9000 0.9121 0.8178 0.8922 0.9158 0.9221 0.8362 20 0.8681 0.9052 0.9175 0.8232 0.8971 0.9207 0.9272 0.8412 40 0.8777 0.9148 0.9276 0.8328 0.9061 0.9298 0.9367 0.8504 60 0.8863 0.9234 0.9368 0.8415 0.9143 0.9380 0.9453 0.8587 80 0.8942 0.9313 0.9449 0.8494 0.9218 0.9455 0.9531 0.8665 100 0.9016 0.9386 0.9521 0.8571 0.9287 0.9525 0.9600 0.8744 313.15 0.1 0.8473 0.8845 0.8958 0.8024 0.8774 0.9008 0.9069 0.8219 1 0.8479 0.8850 0.8964 0.8030 0.8779 0.9013 0.9074 0.8225 5 0.8503 0.8874 0.8988 0.8055 0.8801 0.9036 0.9097 0.8248 10 0.8532 0.8903 0.9017 0.8085 0.8829 0.9063 0.9125 0.8277 20 0.8588 0.8958 0.9074 0.8142 0.8881 0.9115 0.9179 0.8330 40 0.8689 0.9059 0.9181 0.8245 0.8976 0.9211 0.9279 0.8427 60 0.8780 0.9149 0.9278 0.8336 0.9062 0.9298 0.9370 0.8514 80 0.8863 0.9232 0.9365 0.8418 0.9141 0.9377 0.9452 0.8595 100 0.8939 0.9308 0.9443 0.8497 0.9213 0.9450 0.9525 0.8674 333.15 0.1 0.8340 0.8711 0.8819 0.7896 0.8646 0.8878 0.8934 0.8099 1 0.8347 0.8717 0.8824 0.7902 0.8651 0.8884 0.8939 0.8105 5 0.8373 0.8743 0.8850 0.7929 0.8676 0.8908 0.8964 0.8131 10 0.8405 0.8774 0.8881 0.7962 0.8705 0.8938 0.8994 0.8161 20 0.8465 0.8834 0.8942 0.8024 0.8762 0.8994 0.9052 0.8220 40 0.8574 0.8942 0.9056 0.8135 0.8864 0.9097 0.9161 0.8324 60 0.8671 0.9038 0.9161 0.8232 0.8956 0.9190 0.9259 0.8416 80 0.8758 0.9125 0.9255 0.8319 0.9039 0.9274 0.9346 0.8500 100 0.8838 0.9206 0.9340 0.8400 0.9115 0.9351 0.9422 0.8581 348.15 0.1 0.8242 0.8611 0.8716 0.7800 0.8551 0.8782 0.8834 0.8009 1 0.8248 0.8618 0.8722 0.7807 0.8557 0.8788 0.8840 0.8015 5 0.8276 0.8645 0.8749 0.7835 0.8583 0.8814 0.8866 0.8042 10 0.8310 0.8679 0.8781 0.7870 0.8614 0.8846 0.8898 0.8075 20 0.8375 0.8742 0.8845 0.7936 0.8674 0.8906 0.8960 0.8136 40 0.8489 0.8856 0.8965 0.8053 0.8782 0.9014 0.9074 0.8247 60 0.8591 0.8957 0.9075 0.8156 0.8877 0.9110 0.9177 0.8343 80 0.8682 0.9048 0.9175 0.8246 0.8964 0.9198 0.9268 0.8430 100 0.8764 0.9131 0.9265 0.8330 0.9043 0.9279 0.9347 0.8512 353.15 0.1 0.8209 0.8578 0.8682 0.7768 0.8519 0.8750 0.8801 0.7978 1 0.8215 0.8585 0.8688 0.7775 0.8525 0.8756 0.8807 0.7984 5 0.8244 0.8613 0.8715 0.7804 0.8552 0.8783 0.8834 0.8012 10 0.8279 0.8647 0.8748 0.7840 0.8584 0.8815 0.8866 0.8045 20 0.8345 0.8712 0.8813 0.7907 0.8645 0.8876 0.8929 0.8108 Lubricants 2023,11, 55 9 of 24 Table 2. Cont. P/MPa T/K PARA#1 NAPH#1 ESTER#1 PAO4 PARA#2 NAPH#2 ESTER#2 PAO16 40 0.8462 0.8828 0.8934 0.8026 0.8754 0.8987 0.9046 0.8221 60 0.8564 0.8930 0.9046 0.8130 0.8852 0.9085 0.9150 0.8319 80 0.8657 0.9022 0.9148 0.8223 0.8940 0.9173 0.9242 0.8407 100 0.8740 0.9107 0.9241 0.8307 0.9020 0.9255 0.9323 0.8489 373.15 0.1 0.8083 0.8452 0.8553 0.7646 0.8400 0.8630 0.8677 0.7861 1 0.8084 0.8453 0.8554 0.7648 0.8400 0.8631 0.8678 0.7862 5 0.8116 0.8485 0.8582 0.7679 0.8429 0.8660 0.8706 0.7892 10 0.8154 0.8523 0.8617 0.7718 0.8464 0.8695 0.8742 0.7928 20 0.8225 0.8594 0.8686 0.7790 0.8530 0.8762 0.8809 0.7996 40 0.8351 0.8719 0.8815 0.7920 0.8647 0.8879 0.8933 0.8118 60 0.8461 0.8827 0.8934 0.8031 0.8750 0.8983 0.9044 0.8223 80 0.8558 0.8924 0.9044 0.8130 0.8843 0.9076 0.9141 0.8316 100 0.8646 0.9013 0.9144 0.8218 0.8927 0.9162 0.9225 0.8401 Lubricants 2023, 11, x FOR PEER REVIEW 10 of 25 Figure 2. Density at high pressure obtained with the Anton Paar apparatus, (a) as a function of temperature at 60 MPa and (b) as a function of pressure at 333.15 K, for the eight base oils. The solid lines are for guidance. Figure 3. pρT surface as a function of the temperature and pressure for NAPH#2 base oil. The dots represent the density measurements obtained with the Anton Paar apparatus, and the surface the correlation using Equation (1) with a standard deviation of 5·10−4 g cm−3. 0.78 0.81 0.84 0.87 0.90 0.93 0.96 0.99 298.15 318.15 338.15 358.15 378.15 PARA#1 PARA#2 NAPH#1 NAPH#2 ESTER#1 ESTER#2 PAO4 PAO16 T/K ρ/ g cm - ³ (a) 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0 102030405060 PARA#1 PARA#2 NAPH#1 NAPH#2 ESTER#1 ESTER#2 PAO4 PAO16 p/ MPa ρ/ g cm - ³ (b) Figure 2. Density at high pressure obtained with the Anton Paar apparatus, ( a ) as a function of temperature at 60 MPa and ( b ) as a function of pressure at 333.15 K, for the eight base oils. The solid lines are for guidance. Lubricants 2023,11, 55 16 of 24 Lubricants 2023, 11, x FOR PEER REVIEW 16 of 25 Figure 7. Images of the sessile drop evolution for all mineral and synthetic oils at 298.15 K. Coelho de Sousa Marques et al. [7] measured the contact angle for different base oils on AISI 420 stainless steel surface from 293.15 to 323.15 K. They reported the contact angle for four different polyalphaolefins (PAO6, PAO20, PAO32, and PAO40) and for four esterbased lubricants (TMPTO, TOTM, TTM, and BIOE). These authors [7] measured the contact angle at 5 s after the droplet fall, finding 6.8° and 12.6° for PAO6 and PAO20 at 323.15 K, respectively. In the present work, PAO4 and PAO16 provided contact angles at the same droplet fall time (5 s) and at 323.15 K of 5.4° and 15.0°, respectively. Thus, we observed a good agreement considering the uncertainty of the two measurements. Figure 7. Images of the sessile drop evolution for all mineral and synthetic oils at 298.15 K. Lubricants 2023,11, 55 17 of 24 Lubricants 2023, 11, x FOR PEER REVIEW 17 of 25 Figure 8. Average steady-state contact angle (θ) of the eight base oils at 298.15 K (filled bars) and 323.15 K (clear bars). The kinematic and dynamic viscosities for the eight oils measured with SVM3000 apparatus are reported in Table 1. The dynamic viscosities at 0.1 MPa of all the base oils with low-viscosity grades (PARA#1, NAPH#1, ESTER#1, and PAO4) range along the entire temperature interval, from around 3 mPa s to 187 mPa s. Five of the base oils studied in this work (PARA#1, NAPH#1, ESTER#1, PAO4, and NAPH#2) had kinematic viscosities at 373.15 K and 0.1 MPa, between 3 mm 2 s −1 and 10 mm 2 s −1 , which means that they could be used in the formulation of automatic transmission fluids (ATF) for electric vehicles, with configurations where the ATF and the electric motor are in contact due to the latter being inside the transmission housing [34]. From Figure 9, where the logarithm of the dynamic viscosity is plotted against temperature, we can observe that PARA#1, NAPH#1, and PAO4 had very similar viscosities over the temperature range (343.15– 373.15 K). Moreover, the ester oil ESTER#1 presented the higher viscosities within the temperature interval (298.15–373.15 K). On the contrary, at temperatures lower than 298.15 K, the naphthenic oil (NAPH#1) was more viscous that the other three oils; thus, the following trend is obtained: NAPH#1 > ESTER#1 > PARA#1 > PAO4. For the base oils with a high-viscosity grade (PARA#2, NAPH#2, ESTER#2, and PAO16), the dynamic viscosity at 0.1 MPa ranged from 8 mPa s to 2006 mPa s over the entire temperature interval. We observed that, for temperatures lower than 308.15 K, the naphthenic oil (NAPH#2) was more viscous that the other three oils (PARA#2, ESTER#2, and PAO16). Over the entire temperature interval (308.15–318.15 K), the dynamic viscosity of the base oils with a high-viscosity grade were quite similar. However, the trend found for temperatures higher than 318.15 K was PAO16 > ESTER#2 > PARA#2 > NAPH#2. Figure 8. Average steady-state contact angle ( θ ) of the eight base oils at 298.15 K (filled bars) and 323.15 K (clear bars). The viscosity index obtained for the eight base oils is reported in Figure 10. The ester and polyalphaolefin oils (synthetic oils) have the highest viscosity index (VI from 122 to 154), that is, they present the lower dependence of the viscosity with the temperature. Both esters have a similar viscosity index (VI = 140), even if both oils have very different viscosity grades. Thus, the viscosity of these synthetic oils is less dependent on temperature changes than that of mineral oils. The very-low values obtained for the VI of the naphthenic base oils were checked measuring the viscosity index three times, obtaining the same results. The VI of the naphthenic base oils indicates that, for these oils, it is necessary to use VI improvers, also known as viscosity modifiers. However, the use of additives as viscosity improvers has some drawbacks, for example, using polymers with a higher molecular weight as additives would improve the thickening properties, but they show less resistance to mechanical shearing. This highlights the great difficulty involved in formulating new lubricants, since the use of one additive can improve one property, but, at the same time, worsen another. In other words, it is necessary to strike a strict balance between the different properties that are to be achieved for the final lubricant. Lubricants 2023,11, 55 18 of 24 Lubricants 2023, 11, x FOR PEER REVIEW 18 of 25 Figure 9. Dynamic viscosity (ln η) versus temperature at 0.1 MPa for the eight studied oils. The viscosity index obtained for the eight base oils is reported in Figure 10. The ester and polyalphaolefin oils (synthetic oils) have the highest viscosity index (VI from 122 to 154), that is, they present the lower dependence of the viscosity with the temperature. Both esters have a similar viscosity index (VI = 140), even if both oils have very different viscosity grades. Thus, the viscosity of these synthetic oils is less dependent on temperature changes than that of mineral oils. The very-low values obtained for the VI of the naphthenic base oils were checked measuring the viscosity index three times, obtaining the same results. The VI of the naphthenic base oils indicates that, for these oils, it is necessary to use VI improvers, also known as viscosity modifiers. However, the use of additives as viscosity improvers has some drawbacks, for example, using polymers with a higher molecular weight as additives would improve the thickening properties, but they show less resistance to mechanical shearing. This highlights the great difficulty involved in formulating new lubricants, since the use of one additive can improve one property, but, at the same time, worsen another. In other words, it is necessary to strike a strict balance between the different properties that are to be achieved for the final lubricant. Figure 9. Dynamic viscosity (ln η) versus temperature at 0.1 MPa for the eight studied oils. Lubricants 2023, 11, x FOR PEER REVIEW 19 of 25 Figure 10. Viscosity index (VI) for the eight studied base oils: four mineral (PARAs and NAPHs) and four synthetic (PAOs and ESTERs) oils. The dynamic viscosities at high pressures for the eight base oils are reported in Table 6. As Figure 11 shows, at 323.15 K and for pressures lower than 50 MPa, the dependence of the viscosity with pressure was quite similar for the eight oils. For pressures higher than 50 MPa, the bigger increase in the viscosity with pressure occurred for the mineral naphthenic oils: NAPH#2 (viscosity at 150 MPa around 40 times higher than that at 0.1 MPa), followed by NAPH#1 (viscosity at 150 MPa around 30 times higher than that at 0.1 MPa). The studied synthetic polyalphaolefin oils (PAO4 and PAO16) had the lowest dependence of the viscosity with pressure (viscosity at 150 MPa/viscosity at 0.1 MPa ≤ 10). At 353.15 K, for the oils with the highest viscosity grade (PARA#2, NAPH#2, ESTER#2, and PAO16), the pressure dependence of the viscosity was quite similar, up to 75 MPa. For pressures higher than 75 MPa, once again mineral oils, especially NAPH#2, had the biggest increase in the viscosity with pressure. For the oils with a lower ISO VG grade at 353.15 K, ESTER#1 had the highest viscosity values at a pressure up to 75 MPa and, for pressures higher or equal than 100 MPa, NAPH#1 is the most viscous fluid. The experimental dynamic viscosity data as a function of pressure, η (p), were fitted using Equation (6), where η 0 is the dynamic viscosity value obtained with the Anton Paar Stabinger viscometer at 0.1 MPa at each temperature (reported in Table 1), and A, B, and C are adjustable parameters. The values of these parameters and the standard deviation of the fit are reported in Table 7. Equation (6) with the values of the parameters of Table 7 reproduces the experimental dynamic viscosity values with a standard deviation lower than 5 mPa s. Figure 10. Viscosity index (VI) for the eight studied base oils: four mineral (PARAs and NAPHs) and four synthetic (PAOs and ESTERs) oils. The dynamic viscosities at high pressures for the eight base oils are reported in Table 6. As Figure 11 shows, at 323.15 K and for pressures lower than 50 MPa , the dependence of the viscosity with pressure was quite similar for the eight oils. For pressures higher than 50 MPa , the bigger increase in the viscosity with pressure occurred for the mineral naphthenic oils: NAPH#2 (viscosity at 150 MPa around 40 times higher than that at 0.1 MPa ), followed by NAPH#1 (viscosity at 150 MPa around 30 times higher than that at 0.1 MPa ). The studied synthetic polyalphaolefin oils (PAO4 and PAO16) had the lowest dependence of the viscosity with pressure (viscosity at 150 MPa/viscosity at 0.1 MPa ≤10 ). At 353.15 K, for the oils with the highest viscosity grade (PARA#2, NAPH#2, ESTER#2, and Lubricants 2023,11, 55 19 of 24 PAO16), the pressure dependence of the viscosity was quite similar, up to 75 MPa. For pressures higher than 75 MPa, once again mineral oils, especially NAPH#2, had the biggest increase in the viscosity with pressure. For the oils with a lower ISO VG grade at 353.15 K, ESTER#1 had the highest viscosity values at a pressure up to 75 MPa and, for pressures higher or equal than 100 MPa, NAPH#1 is the most viscous fluid. Table 6. Dynamic viscosity, η /mPa s, at different temperatures, T/K, and pressures, P/MPa, measured with the high-pressure falling body viscometer. T/K 323.15 353.15 323.15 353.15 323.15 353.15 323.15 353.15 P/MPa PARA#1 PARA#2 NAPH#1 NAPH#2 10 12.28 5.148 72.35 21.38 14.31 6.005 63.77 16.56 15 13.57 5.614 82.02 23.71 16.57 6.566 72.73 18.21 25 16.42 6.620 103.9 28.85 21.83 7.835 94.19 22.07 50 25.34 9.618 176.5 45.19 40.75 12.09 176.8 36.32 75 37.59 13.47 284.7 68.09 72.21 18.50 327.0 60.77 100 54.41 18.40 446.2 100.2 124.5 28.2 600.3 102.7 125 77.51 24.74 687.1 145.2 211.5 42.7 1098.3 174.8 150 109.3 32.9 1047.1 208.3 356.5 64.7 2006.1 298.7 P/MPa ESTER#1 ESTER#2 PAO4 PAO16 10 19.09 7.894 66.80 22.58 11.67 5.132 71.05 25.08 15 20.96 8.534 73.34 24.56 12.69 5.548 78.32 27.20 25 25.09 9.914 87.70 28.83 14.91 6.432 94.14 31.79 50 37.95 14.04 132.5 41.54 21.58 8.971 142.5 45.6 75 55.54 19.36 193.7 57.83 30.25 12.07 206.6 63.4 100 79.58 26.21 277.3 78.70 41.52 15.84 291.6 86.4 125 112.5 35.03 391.6 105.4 56.18 20.44 404.4 116.3 150 157.5 46.41 547.9 139.8 75.24 26.05 554.2 155.0 The experimental dynamic viscosity data as a function of pressure, η (p), were fitted using Equation (6), where η0 is the dynamic viscosity value obtained with the Anton Paar Stabinger viscometer at 0.1 MPa at each temperature (reported in Table 1), and A, B, and C are adjustable parameters. The values of these parameters and the standard deviation of the fit are reported in Table 7. Equation (6) with the values of the parameters of Table 7 reproduces the experimental dynamic viscosity values with a standard deviation lower than 5 mPa s. Using Equations (6)–(9), the values of αfilm and α∗ at different temperatures for the eight base oils studied in this work were determined. These values are reported in Table 8. As can be observed in Figure 12, the highest αfilm values were obtained for the naphthenic base oils (NAPH#1 and NAPH#2), followed by the paraffinic oils (PARA#1 and PARA#2). The universal pressure–viscosity coefficient ( αfilm ) for ESTER#1, ESTER#2, and PAO16 are very similar, around 15 GPa −1 at 323.15 K and around 13 GPa −1 at 353.15 K. The lowest αfilm values were obtained for PAO4. As expected, both coefficients ( αfilm and α∗ ) decreased with temperature. The values reported in Table 8agree with the previously published data for other mineral and synthetic oils [25,35]. Lubricants 2023,11, 55 20 of 24 Lubricants 2023, 11, x FOR PEER REVIEW 20 of 25 Figure 11. Viscosity as a function of pressure for the eight studied base oils: four mineral (PARAs and NAPHs) and four synthetic (PAOs and ESTERs) oils. Using Equations (6)–(9), the values of αfilm and α* at different temperatures for the eight base oils studied in this work were determined. These values are reported in Table 8. As can be observed in Figure 12, the highest αfilm values were obtained for the naphthenic base oils (NAPH#1 and NAPH#2), followed by the paraffinic oils (PARA#1 and PARA#2). The universal pressure–viscosity coefficient (αfilm) for ESTER#1, ESTER#2, and PAO16 are very similar, around 15 GPa−1 at 323.15 K and around 13 GPa−1 at 353.15 K. The lowest αfilm values were obtained for PAO4. As expected, both coefficients (αfilm and α*) decreased with temperature. The values reported in Table 8 agree with the previously published data for other mineral and synthetic oils [25,35]. 0 50 100 150 200 250 300 350 400 050100150 PARA#1 NAPH#1 ESTER#1 PAO4 η/ mPa·s P/ MPa 323.15 K 0 500 1000 1500 2000 2500 050100150 PARA#2 ESTER#2 PAO16 NAPH#2 P/ MPa η/ mPa·s 323.15 K 0 10 20 30 40 50 60 70 050100150 PARA#1 NAPH#1 ESTER#1 PAO4 η/ mPa·s P/ MPa 353.15 K 0 50 100 150 200 250 300 350 050100150 PARA#2 PAO16 ESTER#2 NAPH#2 P/ MPa η/ mPa·s 353.15 K Figure 11. Viscosity as a function of pressure for the eight studied base oils: four mineral (PARAs and NAPHs) and four synthetic (PAOs and ESTERs) oils. Table 7. Parameters and deviations for the viscosity correlation by using Equation (6). T/K 323.15 353.15 323.15 353.15 323.15 353.15 323.15 353.15 PARA#1 PARA#2 NAPH#1 NAPH#2 A 7.58652 6.11536 11.009 10.431 24.685 30.881 80.8 92.3 B 419.07 398.94 519.04 584.55 1044.62 1733.57 3305.6 4699.7 σ/mPa s 0.3 0.2 3.6 0.9 1.2 0.07 4.7 4.0 ESTER#1 ESTER#2 PAO4 PAO16 A 7.219 6.050 9.552 7.041 5.915 4.005 5.893 6.226 B 405.830 405.78 574.04 482.55 373.62 276.70 334.11 408.60 σ/mPa s 0.3 0.07 1.9 0.8 0.15 0.1 1.6 0.3 The pressure–viscosity coefficient of the eight base oils were also determined from the equation proposed by Gold et al. [ 11 ]. The kinematic viscosity needed in Equation (10) was obtained from Table 1. The pressure–viscosity coefficients obtained from both the procedure proposed by Bair et al. ( αfilm ) and Equation (10) ( αGold ) decrease when the temperature rises. It was observed that αfilm values were higher than the αGold values for all the base oils studied in this work, except for NAPH#2, for which the α value obtained from the Gold method is around 8% higher than the αfilm value. For the mineral base oils (PARA#1, PARA#2, NAPH#1, and NAPH#2), average deviations around 10% at 323.15 K and 5% at 353.15 K between αfilm and αGold values were found. These deviations are higher for the synthetic base oils (ESTER#1, ESTER#2, PAO4, and PAO16), and thus average deviations around Lubricants 2023,11, 55 21 of 24 25% at 323.15 K and 22% at 353.15 K were obtained, respectively. We must emphasize that, in the database used by Gold et al. to determine the sand mparameters, the lubricants used were in the range from ISO VG32 to ISO VG 460, which means they used oils with a kinematic viscosity higher than 30 mm 2 s −1 at 313.15 K. As can be observed in Table 1, the kinematic viscosities of PARA#1, NAPH#1, ESTER#1, and PAO4 at 313.15 K were lower than this value. Table 8. Universal pressure–viscosity coefficient αfilm and reciprocal asymptotic isoviscous pressure coefficient α∗for the base oils. Base Oils T/K αfilm/GPa−1α∗/GPa−1 PARA#1 323.15 16.3 15.2 353.15 13.4 12.8 PARA#2 323.15 19.7 19.2 353.15 16.5 16.1 NAPH#1 323.15 22.8 22.6 353.15 17.3 17.2 NAPH#2 323.15 24.1 24.1 353.15 19.4 19.4 ESTER#1 323.15 15.9 15.3 353.15 13.3 12.4 ESTER#2 323.15 15.3 14.9 353.15 13.0 12.5 PAO4 323.15 13.8 13.2 353.15 11.8 11.0 PAO16 323.15 15.4 14.6 353.15 13.4 12.8 Lubricants 2023, 11, x FOR PEER REVIEW 21 of 25 Figure 12. Universal pressure–viscosity coefficient (α film ) for the eight studied base oils: four mineral (PARAs and NAPHs) and four synthetic (PAOs and ESTERs) oils. () 323.15 K and () 353.15 K. The pressure–viscosity coefficient of the eight base oils were also determined from the equation proposed by Gold et al. [11]. The kinematic viscosity needed in Equation (10) was obtained from Table 1. The pressure–viscosity coefficients obtained from both the procedure proposed by Bair et al. ( α film ) and Equation (10) (α Gold ) decrease when the temperature rises. It was observed that α film values were higher than the α Gold values for all the base oils studied in this work, except for NAPH#2, for which the α value obtained from the Gold method is around 8% higher than the α film value. For the mineral base oils (PARA#1, PARA#2, NAPH#1, and NAPH#2), average deviations around 10% at 323.15 K and 5% at 353.15 K between α film and α Gold values were found. These deviations are higher for the synthetic base oils (ESTER#1, ESTER#2, PAO4, and PAO16), and thus average deviations around 25% at 323.15 K and 22% at 353.15 K were obtained, respectively. We must emphasize that, in the database used by Gold et al. to determine the s and m parameters, the lubricants used were in the range from ISO VG32 to ISO VG 460, which means they used oils with a kinematic viscosity higher than 30 mm 2 s −1 at 313.15 K. As can be observed in Table 1, the kinematic viscosities of PARA#1, NAPH#1, ESTER#1, and PAO4 at 313.15 K were lower than this value. Table 6. Dynamic viscosity, η/ mPa s, at different temperatures, T/K, and pressures, P/MPa, measured with the high-pressure falling body viscometer. T/K 323.15 353.15 323.15 353.15 323.15 353.15 323.15 353.15 P/MPa PARA#1 PARA#2 NAPH#1 NAPH#2 10 12.28 5.148 72.35 21.38 14.31 6.005 63.77 16.56 15 13.57 5.614 82.02 23.71 16.57 6.566 72.73 18.21 25 16.42 6.620 103.9 28.85 21.83 7.835 94.19 22.07 50 25.34 9.618 176.5 45.19 40.75 12.09 176.8 36.32 75 37.59 13.47 284.7 68.09 72.21 18.50 327.0 60.77 100 54.41 18.40 446.2 100.2 124.5 28.2 600.3 102.7 125 77.51 24.74 687.1 145.2 211.5 42.7 1098.3 174.8 150 109.3 32.9 1047.1 208.3 356.5 64.7 2006.1 298.7 Figure 12. Universal pressure–viscosity coefficient ( αfilm ) for the eight studied base oils: four mineral (PARAs and NAPHs) and four synthetic (PAOs and ESTERs) oils. ( Lubricants 2023, 11, x FOR PEER REVIEW 23 of 25 353.15 K. Finally, we must emphasize that the naphthenic base oils presented the highest variation of 𝜂 .𝛼. with temperature, mainly due to their low-viscosity index. Figure 13. 𝜂 .𝛼. for the eight studied base oils: four mineral (PARAs and NAPHs) and four synthetic (PAOs and ESTERs) oils. () 323.15 K and () 353.15 K. 4. Conclusions Several thermophysical properties of eight mineral and synthetic base oils were experimentally determined. The following features were observed: 1. The densities of the synthetic oils were the highest (ESTERs) and the lowest (PAOs) of all the base oils. The following sequence was observed: ESTER > NAPH > PARA > PAO for both the ISO VG22 and ISO VG100 base oils. Densities at 100 MPa were around 5% higher than those at 0.1 MPa for all the base oils for all the isotherms. 2. Decreases with pressure around 20% at 298.15 K and around 35% at 373.15 K were observed for the isobaric thermal expansivity and 35% and 45%, respectively, for the isothermal compressibility, over the range of 0.1–100 MPa. The more compressible base oil was ESTER#2, so a priori, the risk surface fatigue would be lower with this base oil, although this must be verified by performing tribological tests. 3. The lowest contact angle corresponded to PAO4 and the highest to PARA#2. Base oils with an ISO VG100 grade had a higher contact angle than base oils with ISO VG22, which suggests the poorer wetting of the high-viscosity base oils. 4. Mineral naphthenic oils presented the highest increase in the viscosity with pressure and the synthetic polyalphaolefin oils the lowest. The highest α film values were obtained for naphthenic base oils (NAPH#1 and NAPH#2), followed by the paraffinic oils (PARA#1 and PARA#2), with the lowest α film values being obtained for PAO4. Average deviations between 5% and 25% were obtained between the αfilm and αGold values for the eight base oils. 5. The naphthenic base oils (NAPH#1 and NAPH#2) presented the highest variation of 𝜂 .𝛼. with the temperature, which means that they could diminish the efficiency of the machinery in comparison with other base oils. ) 323.15 K and ( Lubricants 2023, 11, x FOR PEER REVIEW 23 of 25 353.15 K. Finally, we must emphasize that the naphthenic base oils presented the highest variation of 𝜂 .𝛼. with temperature, mainly due to their low-viscosity index. Figure 13. 𝜂 .𝛼. for the eight studied base oils: four mineral (PARAs and NAPHs) and four synthetic (PAOs and ESTERs) oils. () 323.15 K and () 353.15 K. 4. Conclusions Several thermophysical properties of eight mineral and synthetic base oils were experimentally determined. The following features were observed: 1. The densities of the synthetic oils were the highest (ESTERs) and the lowest (PAOs) of all the base oils. The following sequence was observed: ESTER > NAPH > PARA > PAO for both the ISO VG22 and ISO VG100 base oils. Densities at 100 MPa were around 5% higher than those at 0.1 MPa for all the base oils for all the isotherms. 2. Decreases with pressure around 20% at 298.15 K and around 35% at 373.15 K were observed for the isobaric thermal expansivity and 35% and 45%, respectively, for the isothermal compressibility, over the range of 0.1–100 MPa. The more compressible base oil was ESTER#2, so a priori, the risk surface fatigue would be lower with this base oil, although this must be verified by performing tribological tests. 3. The lowest contact angle corresponded to PAO4 and the highest to PARA#2. Base oils with an ISO VG100 grade had a higher contact angle than base oils with ISO VG22, which suggests the poorer wetting of the high-viscosity base oils. 4. Mineral naphthenic oils presented the highest increase in the viscosity with pressure and the synthetic polyalphaolefin oils the lowest. The highest α film values were obtained for naphthenic base oils (NAPH#1 and NAPH#2), followed by the paraffinic oils (PARA#1 and PARA#2), with the lowest α film values being obtained for PAO4. Average deviations between 5% and 25% were obtained between the αfilm and αGold values for the eight base oils. 5. The naphthenic base oils (NAPH#1 and NAPH#2) presented the highest variation of 𝜂 .𝛼. with the temperature, which means that they could diminish the efficiency of the machinery in comparison with other base oils. ) 353.15 K. The results obtained for η0.69 0α0.56 for the eight base oils studied in the present work are shown in Figure 13 at 323.15 K and 353.15 K. At 323.15 K, for the base oils with the highest viscosity (PARA#2, NAPH#2, ESTER#2, and PAO16), we observed that PARA#2 and NAPH#2 had higher values than ESTER#2 and PAO16. This means that, at 323.15 K, the mineral base oils generate a thicker film than the synthetic ones. At 353.15 K, regarding the four high-viscosity oils, PARA#2 and PAO16 had slightly higher η0.69 0α0.56 values than Lubricants 2023,11, 55 22 of 24 NAPH#2 and ESTER#2. For the low-viscosity base oils (PARA#1, NAPH#1, ESTER#1, and PAO4), it can be observed in Figure 13 that NAPH#1 and ESTER#1 presented similar and higher η0.69 0α0.56 values than PARA#1 and PAO4 for both temperatures 323.15 and 353.15 K. Finally, we must emphasize that the naphthenic base oils presented the highest variation of η0.69 0α0.56 with temperature, mainly due to their low-viscosity index. Lubricants 2023, 11, x FOR PEER REVIEW 23 of 25 353.15 K. Finally, we must emphasize that the naphthenic base oils presented the highest variation of 𝜂 .𝛼. with temperature, mainly due to their low-viscosity index. Figure 13. 𝜂 .𝛼. for the eight studied base oils: four mineral (PARAs and NAPHs) and four synthetic (PAOs and ESTERs) oils. () 323.15 K and () 353.15 K. 4. Conclusions Several thermophysical properties of eight mineral and synthetic base oils were experimentally determined. The following features were observed: 1. The densities of the synthetic oils were the highest (ESTERs) and the lowest (PAOs) of all the base oils. The following sequence was observed: ESTER > NAPH > PARA > PAO for both the ISO VG22 and ISO VG100 base oils. Densities at 100 MPa were around 5% higher than those at 0.1 MPa for all the base oils for all the isotherms. 2. Decreases with pressure around 20% at 298.15 K and around 35% at 373.15 K were observed for the isobaric thermal expansivity and 35% and 45%, respectively, for the isothermal compressibility, over the range of 0.1–100 MPa. The more compressible base oil was ESTER#2, so a priori, the risk surface fatigue would be lower with this base oil, although this must be verified by performing tribological tests. 3. The lowest contact angle corresponded to PAO4 and the highest to PARA#2. Base oils with an ISO VG100 grade had a higher contact angle than base oils with ISO VG22, which suggests the poorer wetting of the high-viscosity base oils. 4. Mineral naphthenic oils presented the highest increase in the viscosity with pressure and the synthetic polyalphaolefin oils the lowest. The highest α film values were obtained for naphthenic base oils (NAPH#1 and NAPH#2), followed by the paraffinic oils (PARA#1 and PARA#2), with the lowest α film values being obtained for PAO4. Average deviations between 5% and 25% were obtained between the αfilm and αGold values for the eight base oils. 5. The naphthenic base oils (NAPH#1 and NAPH#2) presented the highest variation of 𝜂 .𝛼. with the temperature, which means that they could diminish the efficiency of the machinery in comparison with other base oils. Figure 13. η0.69 0α0.56 for the eight studied base oils: four mineral (PARAs and NAPHs) and four synthetic (PAOs and ESTERs) oils. ( Lubricants 2023, 11, x FOR PEER REVIEW 23 of 25 353.15 K. Finally, we must emphasize that the naphthenic base oils presented the highest variation of 𝜂 .𝛼. with temperature, mainly due to their low-viscosity index. Figure 13. 𝜂 .𝛼. for the eight studied base oils: four mineral (PARAs and NAPHs) and four synthetic (PAOs and ESTERs) oils. () 323.15 K and () 353.15 K. 4. Conclusions Several thermophysical properties of eight mineral and synthetic base oils were experimentally determined. The following features were observed: 1. The densities of the synthetic oils were the highest (ESTERs) and the lowest (PAOs) of all the base oils. The following sequence was observed: ESTER > NAPH > PARA > PAO for both the ISO VG22 and ISO VG100 base oils. Densities at 100 MPa were around 5% higher than those at 0.1 MPa for all the base oils for all the isotherms. 2. Decreases with pressure around 20% at 298.15 K and around 35% at 373.15 K were observed for the isobaric thermal expansivity and 35% and 45%, respectively, for the isothermal compressibility, over the range of 0.1–100 MPa. The more compressible base oil was ESTER#2, so a priori, the risk surface fatigue would be lower with this base oil, although this must be verified by performing tribological tests. 3. The lowest contact angle corresponded to PAO4 and the highest to PARA#2. Base oils with an ISO VG100 grade had a higher contact angle than base oils with ISO VG22, which suggests the poorer wetting of the high-viscosity base oils. 4. Mineral naphthenic oils presented the highest increase in the viscosity with pressure and the synthetic polyalphaolefin oils the lowest. The highest α film values were obtained for naphthenic base oils (NAPH#1 and NAPH#2), followed by the paraffinic oils (PARA#1 and PARA#2), with the lowest α film values being obtained for PAO4. Average deviations between 5% and 25% were obtained between the αfilm and αGold values for the eight base oils. 5. The naphthenic base oils (NAPH#1 and NAPH#2) presented the highest variation of 𝜂 .𝛼. with the temperature, which means that they could diminish the efficiency of the machinery in comparison with other base oils. ) 323.15 K and ( Lubricants 2023, 11, x FOR PEER REVIEW 23 of 25 353.15 K. Finally, we must emphasize that the naphthenic base oils presented the highest variation of 𝜂 .𝛼. with temperature, mainly due to their low-viscosity index. Figure 13. 𝜂 .𝛼. for the eight studied base oils: four mineral (PARAs and NAPHs) and four synthetic (PAOs and ESTERs) oils. () 323.15 K and () 353.15 K. 4. Conclusions Several thermophysical properties of eight mineral and synthetic base oils were experimentally determined. The following features were observed: 1. The densities of the synthetic oils were the highest (ESTERs) and the lowest (PAOs) of all the base oils. The following sequence was observed: ESTER > NAPH > PARA > PAO for both the ISO VG22 and ISO VG100 base oils. Densities at 100 MPa were around 5% higher than those at 0.1 MPa for all the base oils for all the isotherms. 2. Decreases with pressure around 20% at 298.15 K and around 35% at 373.15 K were observed for the isobaric thermal expansivity and 35% and 45%, respectively, for the isothermal compressibility, over the range of 0.1–100 MPa. The more compressible base oil was ESTER#2, so a priori, the risk surface fatigue would be lower with this base oil, although this must be verified by performing tribological tests. 3. The lowest contact angle corresponded to PAO4 and the highest to PARA#2. Base oils with an ISO VG100 grade had a higher contact angle than base oils with ISO VG22, which suggests the poorer wetting of the high-viscosity base oils. 4. Mineral naphthenic oils presented the highest increase in the viscosity with pressure and the synthetic polyalphaolefin oils the lowest. The highest α film values were obtained for naphthenic base oils (NAPH#1 and NAPH#2), followed by the paraffinic oils (PARA#1 and PARA#2), with the lowest α film values being obtained for PAO4. Average deviations between 5% and 25% were obtained between the αfilm and αGold values for the eight base oils. 5. The naphthenic base oils (NAPH#1 and NAPH#2) presented the highest variation of 𝜂 .𝛼. with the temperature, which means that they could diminish the efficiency of the machinery in comparison with other base oils. ) 353.15 K. 4. Conclusions Several thermophysical properties of eight mineral and synthetic base oils were experimentally determined. The following features were observed: 1. The densities of the synthetic oils were the highest (ESTERs) and the lowest (PAOs) of all the base oils. The following sequence was observed: ESTER > NAPH > PARA > PAO for both the ISO VG22 and ISO VG100 base oils. Densities at 100 MPa were around 5% higher than those at 0.1 MPa for all the base oils for all the isotherms. 2. Decreases with pressure around 20% at 298.15 K and around 35% at 373.15 K were observed for the isobaric thermal expansivity and 35% and 45%, respectively, for the isothermal compressibility, over the range of 0.1–100 MPa. The more compressible base oil was ESTER#2, so a priori, the risk surface fatigue would be lower with this base oil, although this must be verified by performing tribological tests. 3. The lowest contact angle corresponded to PAO4 and the highest to PARA#2. Base oils with an ISO VG100 grade had a higher contact angle than base oils with ISO VG22, which suggests the poorer wetting of the high-viscosity base oils. 4. Mineral naphthenic oils presented the highest increase in the viscosity with pressure and the synthetic polyalphaolefin oils the lowest. The highest αfilm values were obtained for naphthenic base oils (NAPH#1 and NAPH#2), followed by the paraffinic oils (PARA#1 and PARA#2), with the lowest αfilm values being obtained for PAO4. Average deviations between 5% and 25% were obtained between the αfilm and αGold values for the eight base oils. Lubricants 2023,11, 55 23 of 24 5. The naphthenic base oils (NAPH#1 and NAPH#2) presented the highest variation of η0.69 0α0.56 with the temperature, which means that they could diminish the efficiency of the machinery in comparison with other base oils. Author Contributions: Conceptualization, F.U. and J.F.; methodology, A.V., M.J.G.G., J.M.L.d.R. and F.M.; software, F.M.; validation, M.J.P.C. and A.V.; formal analysis, J.F. and F.U.; investigation, A.V., M.J.G.G., J.M.L.d.R. and M.J.P.C.; resources, F.U. and R.U.; data curation, A.V.; writing—original draft preparation, M.J.P.C.; writing—review and editing, M.J.P.C.; visualization, J.F. and M.J.P.C.; supervision, F.U.; project administration, J.F.; funding acquisition, J.F. and F.U. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by MCIN/AEI/10.13039/501100011033 and by the European Regional Development Fund (ERDF, a way of making Europe) through the ENE2017-86425-C2-2-R and the PID2020-112846RB-C22 projects as well as by Xunta de Galicia (ED431C 2020/10). JoséM. Liñeira del Río acknowledges the grant of the Margarita Salas program, funded by MCIN/AEI/10.13039/501100011033 and “European Union NextGenerationEU/PRTR” María J. G. Guimarey acknowledges a postdoctoral fellowship (ED481B-2019-015) from the Xunta de Galicia (Spain). Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. References 1. Chowdary, K.; Kotia, A.; Lakshmanan, V.; Elsheikh, A.H.; Ali, M.K.A. A Review of the Tribological and Thermophysical Mechanisms of Bio-Lubricants Based Nanomaterials in Automotive Applications. J. Mol. Liq. 2021,339, 116717. [CrossRef] 2. Quinchia, L.; Delgado, M.; Reddyhoff, T.; Gallegos, C.; Spikes, H.A. Tribological Studies of Potential Vegetable Oil-Based Lubricants Containing Environmentally Friendly Viscosity Modifiers. Tribol. Int. 2014,69, 110–117. [CrossRef] 3. Boyde, S. Green Lubricants. Environmental Benefits and Impacts of Lubrication. Green Chem. 2002,4, 293–307. [CrossRef] 4. 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