Compressibilities and Viscosities of Reference, Vegetable, and

Article pubs.acs.org/IECR

Compressibilities and Viscosities of Reference, Vegetable, and Synthetic Gear Lubricants Teresa Regueira,† Luis Lugo,‡ and Josefa Fernández* Laboratorio de Propiedades Termofísicas de Fluidos y Biomateriales, Departamento de Física Aplicada, Facultad de Física, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain ABSTRACT: Nowadays, one of the primary choices of base oils for environmentally aware lubricants is vegetable oils. This is due to their good natural biodegradability and very low toxicity in combination with very good lubricity characteristics. The development of new vegetable-based lubricants requires the knowledge of their thermophysical properties such as their viscosity or density, among others. Regarding this issue, in this work, we have carried out density measurements between 278.15 and 398.15 K and pressures up to 120 MPa and calculated the isothermal compressibility and isobaric thermal expansivity values of six gear lubricants, two of them reference mineral oils and the other four developed biodegradable oils based in high oleic sunflower oil or in synthetic esters. It was found that all of the lubricants have both similar compressibilities and similar expansivities. Dowson and Higginson, Zhu and Wen, Jacobson and Vinet equations of state predict the experimental density values with absolute average deviations (AADs), that is, AAD % lower than 0.3, 0.4, and 0.6%, respectively, whereas Tammann− Tait and the modified Tait equations correlate these experimental densities with AAD % of 0.02 and 0.06%. Dowson and Higginson and Zhu and Wen equations of state do not predict well the isothermal compressibilities, with AAD % being around 45% for both equations. Moreover, the viscosities were measured in the temperature range from 278.15 to 373.15 K at atmospheric pressure for these oils, and the viscosity index was also determined. New formulated oils present the highest viscosity indexes and the lowest viscosity data at low temperatures; therefore, they become the most suitable for machinery cold start.

1. INTRODUCTION Despite the impact of recession that gave rise to a minimum in the world lubricant demand in 2009, Gosalia1 states that the regional lube market dynamics of the past 10 years in terms of quantity and quality will continue in the future. Thus, the global lubricant demand in 2011 was, according to Gosalia,1 35.1 million tonnes, and it increased 1.9% compared with the previous year. In the past 10 years overall, in volume terms, Europe and America together lost what Asia-Pacific and the rest of world gained, and these latter regions now share close to 44% of the global lubricant market.2 The environment must be protected against pollution caused by lubricants based on petroleum oils. The pollution problem is so severe that approximately 50% of all lubricants sold worldwide end up in the environment via volatility, spills, or total loss applications. This threat to the environment can be avoided by either preventing undesirable losses, reclaiming and recycling mineral oil lubricants, or using environmentally friendly lubricants.3 To initiate and boost the use of biodegradable products, government incentives and mandatory regulations are needed to put pressure on the industries that release lubricants into the environment.2 Thus, the EU Ecolabel is a voluntary award scheme intended to promote products with a reduced environmental impact during their entire life cycle. The EU established in 2011 the latest ecological criteria for the award of the EU Ecolabel to lubricants.4 In this context, one of the primary choices of base oils for environmentally aware lubricants is vegetable oils. This is due to their good natural biodegradability and very low toxicity in combination with very good lubricity characteristics.5−9 The triglyceride structure gives these esters a high natural viscosity © 2014 American Chemical Society

and viscosity index (VI) and is also responsible for structural stability over reasonably operating temperature ranges. However, they have poor oxidative stability compared to mineral oils, and in general they cannot withstand reservoir temperatures over 80 °C, even though the use of appropriate antioxidants or control of the feedstock composition can combat this fact.2,10 Gear lubrication oils are a machine component of particular significance for transmissions, i.e., in gearboxes of wind turbines or in agricultural tractors. Elastohydrodynamic lubrication (EHL) prevails in lubricated contacts where the external load per unit area is high compared to the stiffness of the material and the contact surfaces are nonconformal, i.e., they do not fit well together. Gears are a typical example of highly loaded elastohydrodynamic contacts.11 In EHL, for severe operating conditions, the temperature increase in conjunctions may not be ignored. Neglecting the heat generation in EHL contacts operating under severe conditions leads to an overestimation of both film thicknesses and friction coefficients. Temperature variations lead to both viscosity, η, and density, ρ, changes throughout the lubricant film.12 The effect of the density−pressure relationship on the EHL parameters such as the film thickness and pressure spikes has been studied by several authors. It has been shown that compressibility has a very small effect on the minimum film Received: Revised: Accepted: Published: 4499

October 11, 2013 January 26, 2014 February 18, 2014 February 18, 2014 dx.doi.org/10.1021/ie4034285 | Ind. Eng. Chem. Res. 2014, 53, 4499−4510

Industrial & Engineering Chemistry Research

Article

thickness, whereas the film thickness at the center of the contact becomes minor in the case of highly compressible lubricants.11 Kweh et al.13 demonstrate that in a circular contact the reduction in the central film thickness due to compressibility can be correlated with the increase in the density at the local pressure in the center of the contact. Moreover, Venner and Bos14 showed that, although compressibility is not one of the predominant effects accounting for film formation, it does determine to a great extent the shape of the lubricant film in the central region of the contact. Hamrock et al.15 studied the influence of compressibility on the pressure spike and found that an incompressible lubricant gives rise to much higher pressure at the pressure spike than lubricants that are compressible. Furthermore, the risk of surface fatigue is much greater for a lubricant with low compressibility than for more compressible lubricants.11 In EHL, more effort has been directed toward a better understanding of shear response than to the study of the compressibility of EHL lubricants; however, the pursuit of higher precision is necessary to enable the theory to cope with film thicknesses on the order of nanometers, which are encountered in the mixed lubrication and partial EHL regimes. Consequently, it is appropriate to give more attention to descriptions of the density, pressure, and temperature relationships for fluid lubricants.16 Regarding the density behavior of lubricants and vegetable base oils at elevated pressures, the articles reported by Bamgbade et al.17,18 are noteworthy. These authors reported density data for bis(2-ethylhexyl) phthalate and poly(perfluoropropyl ether) in a broad temperature range and up to 275 MPa. Acosta et al.19 have reported pVT data of up to 140 MPa for different vegetable oils and fats, finding that, above their melting points, their results are coherent with their fatty acid composition, whereas Freitas et al.20 reported densities for seven vegetable oils from 283.15 to 363.15 K and up to 45 MPa. Guignon et al.21,22 have published densities for sunflower, olive, castor, and silicon oils as well as for two glycols under pressures of up to 350 MPa. Grandelli et al.23 described the high-pressure volumetric properties of three poly(α-olefin) base oils from 298 to 398 K at pressures of up to 40 MPa. Sagedev et al.24 have also measured the densities of several glycols from 293 to 465 K and at pressures of up to 245 MPa. Bair25 has reported values of the relative volumes up to pressures of 424 MPa for nine lubricants. Densities for lubricating oils to 1 GPa and 490 K measured in the laboratory of the Nobel laureate Bridgman are reported in an ASME report published in 1953.26 Moreover, the experimental and theoretical studies27−36 on the density−pressure behavior in broad temperature and pressure ranges performed in our research group for several polyolesters, polyglycols, and vegetable, mineral, and synthetic oils in the past decade should be mentioned. In the present work, we have carried out density measurements in a temperature range between 278.15 and 398.15 K and pressures up to 120 MPa of two mineral gear oils, three biodegradable oils based in high oleic sunflower oil, and a synthetic biodegradable oil. The mineral oils are considered to be reference lubricants because one of them is currently used in wind turbines and the other in agricultural tractors, whereas the biodegradable oils were specifically developed to replace them. Besides, the correlation ability of two different equations for fitting experimental density values as a function of the temperature and pressure was checked. Additionally, the density predictive capability of the equation of state (EoS)

from Dowson and Higginson,37 Zhu and Wen,38 and Jacobson and Vinet39 was also analyzed for the studied lubricants. Furthermore, compressibility values of the lubricants were calculated from the correlation of the experimental density data. Moreover, viscosity data for these oils were determined under a temperature range from 278.15 to 373.15 K, and their corresponding VIs are also reported. This work was carried out in the framework of a Spanish singular and strategic project, BIOVESIN, aiming to develop a formulation of a new range of environmentally friendly biodegradable lubricants from vegetable oils35,40−45 for wind energy and agricultural sectors.

2. EXPERIMENTAL SECTION 2.1. Materials. The gear lubricants have been provided by some of the Spanish companies involved in the BIOVESIN project: Verkol Lubricantes, Agria Hispania, and Indra. All of them are presented in Table 1, along with their density and Table 1. Characteristics of the Gear Lubricants Studied in This Work lubricant

ν/mm2·s−1 (313.15 K)

VI

329.29

139.4

tractor 0.8838 182.64 transmission Developed Biodegradable Lubricants wind turbine 0.9261 244.56

96.7

description mineral

BIOG00 BIOG01 BIOG02 SYNG01

25% HOSOa 50% HOSOa 45% HOSOa synthetic esters

a

ρ/g·cm−3 (313.15 K)

Reference Lubricants wind turbine 0.8600

MING01 MING02

mineral

application

158.2

wind turbine

0.9207

221.80

189.3

tractor transmission wind turbine

0.9203

148.56

165.8

0.9269

254.35

149.6

HOSO is high oleic sunflower oil.

kinematic viscosity at 313.15 K and their VI. Three of the biodegradable oils, BIO-G00, BIO-G01, and BIO-G02, are based in high oleic sunflower oil (HOSO), and the last one, SYN-G01, is composed of synthetic esters. These biodegradable lubricants were developed by Verkol Lubricantes to substitute for the reference mineral oils. Thus, the oils BIO-G00, BIOG01, and BIO-G02 were developed to replace the mineral oils MIN-G,35 MIN-G01, and MIN-G02, respectively. 2.2. Experimental Procedure. The VI and viscosity values between 278.15 and 373.15 K were measured with an automated Anton Paar rotational Stabinger SVM 3000 device.46 The basic operating principles and schematic setup of this equipment are described in a European patent.46 This apparatus, which has also a glass vibrating tube, allows density measurements and was used to measure the densities of the studied oils at atmospheric pressure. The SVM 3000 uses Peltier elements for fast and efficient thermostatting. The temperature uncertainty is 0.02 K from 288.15 to 378.15 K and 0.05 K outside this range. The uncertainty of the dynamic viscosity is 1%, whereas the density is measured with an uncertainty of 0.0005 g·cm−3.47,48 Density measurements up to 120 MPa, in the temperature range from 278.15 to 398.15 K, were performed in a fully automated Anton Paar HPM vibrating-tube densimeter.36,49−53 This densimeter was previously used to characterize the density−pressure behavior of hydrocarbons, fuels, and 4500

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Table 2. Viscosity Values, η (mPa·s), at Atmospheric Pressure of the Gear Lubricants

lubricants.35,51−53 The temperature is measured by a Pt100 probe calibrated with an uncertainty of 0.02 K, whereas the pressure transducer was calibrated with an uncertainty of 0.02 MPa. Water, decane, and vacuum were used as reference fluids for density calibration, following the procedure described by Comuñas et al.54 Taking into account the uncertainties of the temperature, pressure, water and decane density, and oscillation period measurements for water, decane, vacuum, and the studied liquid, it was estimated36 that the expanded (k = 2) density uncertainty is 0.7 × 10−3 g·cm−3 for temperatures below T = 373.15 K, 5 × 10−3 g·cm−3 at T = 373.15 and 398.15 K and p = 0.1 MPa, and 3 × 10−3 g·cm−3 at T ≥ 373.15 K and p > 0.1 MPa. The higher uncertainty in the density for temperatures higher or equal to 373.15 K is due to the fact that in this temperature range it is necessary to use decane as a reference fluid in the calibration and literature data for this fluid have a higher uncertainty than those of water. More details about the experimental setup and uncertainty calculations were previously given.36

3. RESULTS AND DISCUSSION 3.1. Viscosity and Its Temperature Dependence. Table 1 shows the VIs of the lubricants studied in this work. The VI is a single number that indicates the temperature dependence of the kinematic viscosity of an oil, and it is calculated from its kinematic viscosities at 40 and 100 °C.55−57 These values were obtained according to ASTM D227056 and ISO 290957 by means of the automated Anton Paar Stabinger SVM 3000. Table 1 shows that the developed biodegradable lubricants present VIs higher than those of the reference mineral oils, indicating that their viscosity suffers lower changes with temperature, which is a desirable property for lubricant applications. Table 1 also indicates that, among the vegetablebased lubricants, the higher the HOSO content, the higher the VI. The synthetic oil composed of a mixture of biodegradable synthetic esters has a VI slightly lower than those of the HOSO-based lubricants. The viscosity values at atmospheric pressure of the studied lubricants were also obtained by using this device and are presented in Table 2. It can be seen that the developed oil BIOG01 has a viscosity similar to that of the reference oil MIN-G01 from 343.15 to 363.15 K because the biodegradable oil was developed to have a viscosity similar to that of the reference oil at the working wind turbine temperatures (343.15−353.15 K). Similarly, the developed oil for tractor transmission, BIO-G02, presents a viscosity value similar to that of the reference oil MIN-G02 at temperatures higher than 353.15 K. In Table 2 and Figure 1a, it can be observed that the developed oils BIO-G01 and BIO-G02 reach up to half viscosity values (at 278.15 K) compared to that of the corresponding reference oils MIN-G01 and MIN-G02. This fact is an important disadvantage of both reference mineral oils because, in cold starts, the lubricant film is too robust at low temperatures, and it will change in a noticeable way when the temperature rises, leading to a nonlinear power transmission.58 Viscosity values were correlated (Figure 1a) as a function of the temperature by means of the Vogel−Fulcher−Tammann (VFT)59−61 equation:

T/K

MING01

MING02

BIOG00

BIOG01

BIOG02

SYNG01

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15

3265 2140 1439 994 704 510 376 283 217 169 134 107 86.7 71.2 59.0 49.5 41.9 35.7 30.7 26.6

2121 1348 890 603 419 299 217 161 122 94.1 73.6 58.5 47.3 38.6 31.8 26.6 22.4 19.1 16.4 14.2

2144 1455 1013 721 524 389 294 226 177 140 113 92.1 76.0 63.4 53.4 45.4 39.0 33.7 29.3 25.7

1584 1110 796 584 438 334 259 204 163 133 109 90.3 75.8 64.3 55.0 47.4 41.2 36.1 31.8 28.2

1086 756 541 397 296 225 174 137 109 88.2 72.2 59.9 50.2 42.4 36.3 31.2 27.1 23.7 20.9 18.5

2472 1637 1118 786 563 413 309 236 183 144 116 93.8 77.0 64.0 53.7 45.5 38.9 33.6 29.2 25.5

where η is the dynamic viscosity in mPa·s, T is the temperature in K, and A, B (K), and T0 (K) are fit constants. The correlation parameters as well as the standard deviations and average absolute deviations, AAD %, are gathered in Table 3. 3.2. Density and Its Temperature and Pressure Dependence. We have also measured the density data at atmospheric pressure with the automated Anton Paar Stabinger SVM 3000, which are depicted in Figure 1b. Density values measured in the high-pressure densimeter are gathered in Table 4. The values at atmospheric pressure measured in this last device were compared with those obtained in the Stabinger SVM 3000, finding an agreement (AAD %) between both data sets of 0.08%, which is within the combined uncertainty of both apparatuses. The pρT values were correlated as a function of the temperature and pressure by means of the Tammann−Tait equation in the form used by Cibulka and Hnědkovský:62 ρ(T , 0.1)

ρ (T , p) =

(

1 − C ln

)

(2)

where T is the temperature in K, p is the pressure in MPa, and ρ(T,0.1) is the density as a function of the temperature at the reference pressure 0.1 MPa following the polynomial expression 3

ρ(T , 0.1) =

∑ Ai(T )i i=0

(3)

C is a parameter independent of the temperature and pressure and B(T) is a parameter depending on the temperature as a polynomial function: 2

B (T ) =

∑ Bj(T ) j j=0

B ln(η) = A + T − T0

B(T ) + p B(T ) + 0.1

(4)

Parameters obtained for the Tammann−Tait correlation are presented in Table 5, along with standard deviations σ for

(1) 4501



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Figure 1. (a) Experimental dynamic viscosity values, η, and (b) density values, ρ, at atmospheric pressure from Anton Paar Stabinger SVM 3000: MIN-G01 (□), MIN-G02 (◇), SYN-G01 (△), BIO-G01 (×), BIO-G00 (*), and BIO-G02 (○). The solid line is (a) the VFT correlation and (b) a third-order polynomial correlation.

those of the mineral oils, with the highest density values being those of the synthetic lubricant SYN-G01. This is due to the ester groups of the molecules of the four biodegradable oils, which increase the packing of the molecules because of attractive dipole intermolecular forces. Among the vegetablebased oils, the density sequence is the following: BIO-G00 > BIO-G02 > BIO-G01. Therefore, the density of these oils decreases with the HOSO content. This is due to the fact that the biodegradable and viscous esters included in their composition are denser than HOSO. On the other hand, we have found previously35 that HOSO is denser than mineral hydraulic oils. According to the Sieder−Tate equation, the higher the density value, the better the heat-transfer coefficient. Density values as a function of the temperature and pressure for the studied oils have been predicted by means of two methods. The first of them was the Dowson and Higginson37 EoS:

Table 3. Coefficients of the VFT Correlation (eq 1), Standard Deviation, σ, and AAD %

A B /K T0/K 103σ AAD %

MING01

MING02

BIOG00

BIOG01

BIOG02

SYNG01

−2.9559 1355.6 155.55 5.2 0.4

−3.5062 1297.3 162.09 7.7 0.6

−2.4919 1246.0 155.69 6.3 0.5

−1.8850 1135.4 155.54 3.8 0.3

−2.3471 1141.9 155.96 5.1 0.4

−2.4157 1196.4 161.30 5.4 0.4

ρ(T,0.1) and σ* for ρ(T,p), as well as AAD %, the definitions of which were calculated as explained in the Appendix. Additionally, density values as a function of the temperature and pressure were also correlated using the following modification of the Tait equation:63−65 ρ (T , p) = 1−

1 1 + K0 ′

ρ(T , 0.1) ⎡ ⎤ p ln⎢⎣1 + K exp(−β T ) (1 + K 0′)⎥⎦ 00 K

⎛ 0.6p ⎞ ρ(T , p) = ρ(T , 0.1)⎜1 + ⎟ 1 + 1.7p ⎠ ⎝

(5)

In this last expression, eq 3 was used for obtaining ρ(T,0.1), T is the temperature in K and p is the pressure in GPa. The other method consists of the use of the EoS from Zhu and Wen,38 which is defined as follows:

where T is the temperature in K, p is the pressure in MPa, K0′ is the pressure derivative of the bulk modulus at ambient pressure,66 K00 in MPa and βK in K−1 are the constants that define the exponential dependence of the bulk modulus at ambient pressure on the temperature,65 and finally ρ(T,0.1), the dependence of the density on the temperature at 0.1 MPa, is given by the following expression:63 ρ(T , 0.1) = ρR [1 − a p(T − TR )]

(7)

⎡ 0.6p ρ(T , p) = ρ(TR , 0.1)⎢1 + 1 + 1.7p ⎣ ⎤ − 0.65 × 10−3(T − TR )⎥ ⎦

(6)

where TR is a reference temperature and ρR is the measured density at TR and 0.1 MPa. In this fit, the reference temperature was considered as the lowest experimental temperature for each of the oils, i.e., 283.15 K for MIN-G02 and 278.15 K for the other oils. Fitting coefficients as well as standard deviations are presented in Table 6. The obtained standard deviations with this fit are lower than the uncertainty of the experimental density measurements but slightly higher than those of the fit with the Tammann−Tait equation. This is because eight parameters are used with the last equation but only four with eq 5. Moreover, density values from the Anton Paar HPM densimeter are plotted as a function of the pressure at 313.15 K (Figure 2a) and as a function of the temperature at 40 MPa (Figure 2b). It can be observed that the lubricants with the lowest densities are the reference mineral ones, whereas the densities of the vegetable-based lubricant as well as the synthetic lubricant are similar to each other and higher than

(8)

where T is the temperature in K, p is the pressure in GPa, and TR is a reference temperature. We have chosen TR = 293.15 K. When T=TR, this equation coincides with the Dowson and Higginson relation. Finally, the relation proposed by Jacobson and Vinet39 and employed by Venner and Bos14 in numerical EHL simulations was employed for prediction of the experimental pressure values as a function of the density as follows: ⎡ ⎡ ⎛ ρ ⎞−2/3⎡ ⎛ ρ ⎞1/3⎤ ⎛ ρ ⎞1/3⎤⎤ ⎢1 − ⎜ 0 ⎟ ⎥ exp⎢η′⎢1 − ⎜ 0 ⎟ ⎥⎥ p = 3B0 ⎜ 0 ⎟ ⎢ ⎢⎣ ⎢⎣ ⎝ρ⎠ ⎝ ρ ⎠ ⎥⎦ ⎝ ρ ⎠ ⎥⎦⎥⎦ ⎣ (9)

where B0 and η′ are characteristic parameters with values of 1.7 × 10−9 Pa and 10.0 for a mineral oil,14 respectively. The Jacobson and Vinet equation is slightly inconvenient for their 4502



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Table 4. Experimental Density Values, ρ (g·cm−3), of the Studied Lubricants at Different Temperatures and Pressures p/MPa T/K MIN-G01 278.15 298.15 313.15 333.15 348.15 373.15 398.15 MIN-G02 283.15 298.15 313.15 323.15 348.15 373.15 398.15 BIO-G00 278.15 298.15 313.15 333.15 348.15 373.15 398.15 BIO-G01 278.15 298.15 313.15 333.15 348.15 373.15 398.15 BIO-G02 278.15 298.15 313.15 333.15 348.15 373.15 398.15 SYN-G01 278.15 298.15 313.15 333.15 348.15 373.15 398.15

0.10

1.00

10.00

20.00

40.00

60.00

80.00

100.00

120.00

0.8828 0.8703 0.8606 0.8480 0.8388 0.8236 0.8082

0.8833 0.8707 0.8611 0.8486 0.8394 0.8240 0.8093

0.8878 0.8753 0.8660 0.8540 0.8452 0.8302 0.8164

0.8924 0.8803 0.8713 0.8597 0.8512 0.8369 0.8237

0.9008 0.8893 0.8809 0.8701 0.8622 0.8489 0.8366

0.9085 0.8975 0.8895 0.8793 0.8719 0.8593 0.8478

0.9156 0.9050 0.8974 0.8877 0.8806 0.8687 0.8577

0.9222 0.9120 0.9047 0.8954 0.8886 0.8773 0.8666

0.9277 0.9185 0.9115 0.9025 0.8960 0.8854 0.8750

0.9031 0.8937 0.8841 0.8777 0.8619 0.8464 0.8315

0.9035 0.8942 0.8846 0.8782 0.8625 0.8469 0.8316

0.9078 0.8988 0.8895 0.8833 0.8682 0.8532 0.8387

0.9124 0.9036 0.8947 0.8887 0.8741 0.8597 0.8458

0.9208 0.9126 0.9041 0.8985 0.8848 0.8713 0.8585

0.9287 0.9207 0.9127 0.9074 0.8944 0.8816 0.8695

0.9359 0.9282 0.9205 0.9155 0.9031 0.8908 0.8793

0.9427 0.9351 0.9276 0.9228 0.9110 0.8993 0.8882

0.9494 0.9417 0.9344 0.9297 0.9184 0.9071 0.8964

0.9504 0.9367 0.9268 0.9132 0.9032 0.8863 0.8693

0.9504 0.9368 0.9270 0.9135 0.9036 0.8873 0.8704

0.9548 0.9416 0.9321 0.9190 0.9095 0.8938 0.8777

0.9595 0.9466 0.9373 0.9247 0.9156 0.9005 0.8850

0.9681 0.9558 0.9471 0.9352 0.9266 0.9124 0.8980

0.9760 0.9643 0.9560 0.9448 0.9366 0.9230 0.9094

0.9834 0.9722 0.9642 0.9534 0.9456 0.9327 0.9197

0.9902 0.9795 0.9717 0.9614 0.9539 0.9414 0.9291

0.9965 0.9865 0.9788 0.9689 0.9616 0.9497 0.9388

0.9455 0.9308 0.9206 0.9071 0.8972 0.8812 0.8651

0.9459 0.9313 0.9212 0.9076 0.8978 0.8814 0.8652

0.9503 0.9361 0.9262 0.9131 0.9037 0.8879 0.8723

0.9550 0.9412 0.9316 0.9189 0.9098 0.8946 0.8796

0.9636 0.9505 0.9415 0.9294 0.9209 0.9067 0.8928

0.9716 0.9590 0.9504 0.9390 0.9309 0.9173 0.9042

0.9790 0.9668 0.9586 0.9477 0.9399 0.9269 0.9145

0.9858 0.9741 0.9662 0.9557 0.9482 0.9358 0.9239

0.9922 0.9809 0.9732 0.9633 0.9561 0.9441 0.9326

0.9465 0.9325 0.9224 0.9087 0.8987 0.8815 0.8651

0.9465 0.9326 0.9225 0.9090 0.8991 0.8826 0.8663

0.9510 0.9375 0.9277 0.9146 0.9050 0.8892 0.8735

0.9556 0.9425 0.9330 0.9204 0.9111 0.8959 0.8809

0.9643 0.9519 0.9428 0.9309 0.9222 0.9079 0.8939

0.9723 0.9605 0.9518 0.9405 0.9322 0.9185 0.9053

0.9797 0.9684 0.9600 0.9492 0.9413 0.9282 0.9156

0.9864 0.9757 0.9676 0.9572 0.9496 0.9370 0.9250

0.9929 0.9826 0.9747 0.9647 0.9574 0.9452 0.9336

0.9527 0.9388 0.9285 0.9150 0.9049 0.8879 0.8716

0.9527 0.9389 0.9287 0.9153 0.9053 0.8889 0.8727

0.9572 0.9438 0.9339 0.9209 0.9113 0.8955 0.8801

0.9618 0.9488 0.9392 0.9267 0.9175 0.9023 0.8875

0.9706 0.9582 0.9491 0.9373 0.9287 0.9145 0.9006

0.9786 0.9668 0.9581 0.9469 0.9387 0.9252 0.9121

0.9860 0.9748 0.9663 0.9556 0.9478 0.9349 0.9225

0.9928 0.9821 0.9740 0.9636 0.9560 0.9436 0.9318

0.9993 0.9891 0.9811 0.9711 0.9637 0.9517 0.9403

use as the EHL EoS because it cannot be easily inverted analytically. The Dowson and Higginson37 EoS predicts the density values of each oil with an AAD % ≤ 0.4%, whereas the prediction from the Zhu and Wen EoS38 gives rise to similar results, with AAD % being lower or equal to 0.3%. Finally, the method from Jacobson and Vinet39 predicts pressure values with an AAD % ranging from 18.8 to 28.3% (which corresponds to an AAD % in density ranging from 0.4 to 0.6%). The quality of the prediction of the three equations does

not depend on the oil type. The poorer prediction of the Jacobson and Vinet equation for the density of the studied oils could be explained by the fact that the empirical equation is based on considering that the bulk modulus is temperatureindependent, which is not the case for the six oils studied in this work. Besides, according to some authors,63 the experimental method used to determine the constants, B0 and η′, would not be considered accurate according to the rules set forth by Hayward.67 4503



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Table 5. Ai, Bi, C, Standard Deviations σ for ρ(T,0.1) and σ* for ρ(T,p), and AAD % from the Tammann−Tait equation A0 /g·cm−3 103A1 /g·cm−3·K−1 106A2 /g·cm−3·K−2 109A3 /g·cm−3·K−3 104σ/g·cm−3 102C B0 /MPa B1 /MPa·K−1 103B2 /MPa·K−2 104σ*/g·cm−3 102(AAD %)

MIN-G01

MIN-G02

BIO-G00

BIO-G01

BIO-G02

SYN-G01

1.1513 −1.441 2.307 −2.14 2.9 8.4 454.8 −1.438 1.26 2.3 1.9

0.9922 0.23 −2.742 2.89 0.4 8.4 508.9 −1.732 1.69 1.5 1.2

1.1797 −1.056 1.152 −1.15 0.9 8.6 510.2 −1.63 1.44 2.2 2.2

1.3169 −2.2077 4.1573 −3.672 1.1 8.78 550.3 −1.913 1.928 2.1 1.5

1.137 −0.6557 −0.192 0.31 1.8 8.4 512.17 −1.706 1.595 2.0 1.5

1.1443 −0.657 −0.218 0.37 1.3 8.25 501.3 −1.668 1.555 1.9 1.5

Table 6. Fitting Parameters of the Modified Tait Equation,63−65 ap, K0′, K00, and βK, Standard Deviations σ (eq 6) and σ* (eq 5), and AAD % 104ap/K−1 104σ/g·cm−3 K0′ K00/MPa 103βK/K−1 104σ*/g·cm−3 102(AAD %)

MIN-G01

MIN-G02

BIO-G00

BIO-G01

BIO-G02

SYN-G01

7.0755 3.0 10.888 8168.4 5.3695 3.3 3.2

6.9481 3.3 10.696 7672.6 5.0089 2.4 2.1

7.1065 0.9 10.445 8627.5 5.3036 2.4 1.9

7.1856 9.7 9.864 8560.4 5.2295 6.1 5.1

7.2063 2.9 10.658 8695.4 5.3706 3.5 3.1

7.1406 0.0 10.869 8821.2 5.4183 3.9 3.4

Figure 2. Experimental density values, ρ, from Anton Paar HPM of the lubricants measured in this work (a) as a function of the pressure at T = 313.15 K and (b) as a function of the temperature at p = 40 MPa: SYN-G01 (△); BIO-G00 (*); BIO-G02 (○); BIO-G01 (×); MIN-G02 (◇); MIN-G01 (□). The solid line is the Tammann−Tait correlation.

The above EoSs are employed to estimate film thicknesses in EHL. For this purpose, one needs to extrapolate this EoS up to around to 4 GPa. It is not easy to establish which equation gives the most reasonable results at extreme pressures. Recent efforts have been performed, but the proposed equations are too complicated to be included in EHL simulations.68,69 Because of the asymptotic limited density value, the Dowson and Higginson and Zhu and Wen equations are not realistic at high pressures for liquids below the glass transition pressure. Figure 3 shows that the experimental ρ(p,T)/ρ(0.1,T) values from Dick70 on viscous compounds such as ethylene glycol and glycerol up to 53.6 GPa increase with pressure more strongly than the corresponding curves obtained through the Dowson and Higginson equation. In EHL calculations, this effect is compensated for by neglect of the effect of the glass transition at high pressures.25 Using molecular simulations of hexadecane to determine the density−pressure behavior and the central thickness at 300, 350, and 400 K up to 4.5 GPa, Martini and Vadakkepatt71 concluded that the Dowson−Higginson model underestimates

the compressibility at high pressures, whereas the modified Tait equation (eq 5) predicts well that at lower temperatures, but at higher temperatures, the modified Tait equation underpredicts slightly the effect of the pressure on the density. Habchi and Bair63 have recently showed for a silicone oil that the Dowson and Higginson equation underpredicts the pressure effect on the density up to 2 GPa, in comparison with the results obtained through the modified Tait equation, interpolating up to 0.9 GPa and extrapolating for the higher pressures. Following a similar procedure, these authors found for a heavy naphthenic mineral oil that the Dowson and Higginson equation slightly overpredicts this effect at the lowest temperature analyzed (303.15 K) for pressures lower than 1.1 GPa. On the other hand, Jacobson and Vinet39 indicated that their model describes well the density as a function of the pressure for different types of lubricants up to the pressure limit of their high pressure chamber (2.2 GPa). We have also used these prediction methods, as well as the Tammann−Tait and the modified Tait63−65 correlations of the experimental density data, to predict the density values up to 4 4504



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κT(T , p) =

1 ⎛ ∂ρ ⎞ ⎜ ⎟ ρ ⎝ ∂p ⎠

(10)

T 72

This property is the inverse of the bulk modulus. The bulk modulus is a property also relevant to characterizing new, biobased, or intermediate fuels.72−76 The compressibility values are depicted in Figure 5 for the lubricants studied in this work.

Figure 3. Relative density, ρ(p,T)/ρ(0.1,T), as a function of the pressure for glycerol (□) and ethylene glycol (△) at 295 K. The solid line represents the Dowson and Higginson equation. Experimental values were taken from Dick.70

GPa, as can be observed in Figure 4 for MIN-G02 and BIOG02 at 313.15 K. As expected, asymptotic behavior is observed

Figure 4. Experimental density values of MIN-G02 (◇) and BIO-G02 (○) at 313.15 K: Tammann−Tait (−), modified Tait63−65 (···), Dowson and Higginson37 (−·−), Zhu and Wen38 (− −), and Jacobson and Vinet39 (−··−) equations. Gray and black lines represent the prediction and correlation EoSs for MIN-G02 and BIO-G02, respectively.

Figure 5. Isothermal compressibility values, κT (a and b), as a function of the pressure at T = 313.15 K and (c) as a function of the temperature at 40 MPa.

as the pressure increases for the EoS of Dowson and Higginson37 and Zhu and Wen.38 We have found curves similar to those obtained for other lubricants by the abovementioned authors.14,63,71 All of the equations predict similar density values up to 0.3 GPa, whereas at high pressures, the values predicted by means of the Jacobson and Vinet EoS39 are higher than those obtained through the other EoSs. The predictions of the Tammann−Tait and modified Tait methods are very similar to each other, and the same applies to the Zhu and Wen38 and Dowson and Higginson37 equations. The Dowson and Higginson37 and Zhu and Wen38 EoSs provide the lowest density values from 1.1 to 4 GPa. 3.3. Compressibilities and Thermal Expansion Coefficient. We have calculated the density-derived property isothermal compressibility (κT) by differentiation from the Tammann−Tait equation, taking into account the following equation:

In Figure 5a, we present the pressure dependence of the compressibility values at 313.15 K of the vegetable-based lubricants. It can be observed that κT values and its pressure dependence are very similar for the three oils. The following sequence is observed for temperatures lower or equal to 350 K in Figure 5b: BIO-G01 > BIO-G02 > BIO-G00. However, at the highest temperatures, the trend found is BIO-G02 > BIOG00 > BIO-G01. Therefore, it is not possible to establish a relationship between the high oleic sunflower oil (HOSO) content in these lubricants and their compressibility. The compressibilities of the three developed vegetable oils are very similar, with their maximum difference in this property being 0.6 × 10−4 MPa−1 (5%). In Figure 5c, we have plotted the compressibility values of the reference mineral lubricants along with those of the vegetable-based lubricant BIO-G01 and the synthetic-based lubricant SYN-G01, in order to perform a comparison between 4505



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the behavior of a biodegradable vegetable oil, the biodegradable synthetic lubricant, and the reference lubricants. It can be observed that the compressibility of MIN-G01 is slightly higher than those of the other lubricants (up to 4.7% at this temperature). Thus, MIN-G01, because of its higher compressibility, could form thinner films by a few percent in the highpressure regions. Compressibility values have also been calculated from differentiation from the modified Tait equation63−65 according to the following expression: ⎧ ⎛ ⎡ ⎪ p 1 ⎜1 − κT = ⎨ ln⎢1 + ⎪⎜ 1 + K 0′ ⎢⎣ K 00 exp( −βK T ) ⎩⎝ −1 ⎫ ⎤⎞ ⎪ (1 + K 0′)⎥⎟⎟(K 00 exp(−βK T ) + p(1 + K 0′))⎬ ⎪ ⎥⎦⎠ ⎭

Figure 6. Compressibility values of MIN-G02 at 313.15 K predicted through modified Tait63−65 (− −) and Dowson and Higginson37 (−·−) EoSs. (11)

between the surfaces decreases in the direction of motion (the geometric wedge) or the density of the fluid decreases in the same direction (the thermal wedge).78 For these reasons, we have calculated the thermal expansion coefficient (αp) by differentiation from the Tammann−Tait fits of the density with temperature. The uncertainty of the αp values was estimated to be 4%. Thermal expansion coefficient values are depicted in Figure 7 as a function of the pressure at different temperatures for the studied lubricants. This property decreases when the pressure increases, whereas a crossover is found between the isotherms for all of the lubricants except for BIO-G01. This is likely due to the different compositions of the base oil and additives of this last lubricant. The fact that the crossover does not happen in the experimental temperature and pressure conditions has been previously found for other liquids.29,31,79 This crossing point is related to a minimum of the isobaric heat capacity.80

A global AAD % among the compressibility values obtained from the Tammann−Tait equation and those obtained through the modified Tait63−65 equation of 0.8% was found. Compressibility values of the studied oils were also predicted by means of differentiation from the Dowson and Higginson37 and Zhu and Wen38 EoSs. It is important to notice that the compressibility values are fluid-independent. κT =

0.6 1 + 4p + 3.91p2

(12)

κT = 0.6 (1 + 4p + 3.91p ) − 0.65 × 10−3(T − TR )(1 + 1.7p)2 2

(13)

At T equal to TR, eqs 12 and 13 are equal. At pressures up to 4 GPa in the whole studied temperature range, the maximum difference between the compressibility prediction given by these last two equations is 4.2 × 10−3 MPa−1 (5.5%) and occurs at 398.15 K and 4 GPa. At these conditions, the predicted compressibilities are 7.56 × 10−2 and 7.97 × 10−2 MPa−1 for the Dowson and Higginson and Zhu and Wen EoSs, respectively. In the temperature and pressure ranges of our measurements, AAD % between the κT values obtained by the modified Tait correlation and by eqs 12 and 13 are 46 and 45%, respectively. The compressibility predictions from Dowson and Higginson37 along with the values obtained from the modified Tait63−65 equations for MIN-G02 are depicted in Figure 6 at 313.15 K. It can be observed that, at the highest and lowest pressures (p < 0.02 GPa and p > 0.5 GPa), the compressibility values predicted by means of the Dowson and Higginson EoS are lower than those obtained through the modified Tait63−65 equations. The contrary occurs at intermediate pressures. A similar behavior is found for the other five lubricants at low and intermediate temperatures, whereas at the highest temperatures (373.15 and 398.15 K), the Dowson and Higginson and Zhu and Wen EoSs predict lower compressibilities than the Tammann−Tait and modified Tait EoSs in the whole pressure range. The thermal wedge is a pressure generation action brought about by changes in the density and viscosity due to a temperature rise in a bearing film.77 Besides, it is shown that film lubrication is possible if, and only if, either the distance

4. CONCLUSIONS The viscosity data of new biodegradable developed oils and reference mineral oils for wind turbine and tractor transmission are reported. The new formulated oils present the highest VIs and the lowest viscosity data at low temperatures; therefore, they become the most suitable for machinery cold starts. Regarding pρT data, at a given temperature and pressure, it was found that the highest values are those of the synthetic lubricant, whereas the lowest values are those of the mineral lubricants. Among the vegetable-based oils, the density decreases with the HOSO content. Several empirical EoSs were used to evaluate the pρT curves. Thus, the Dowson and Higginson37 and Zhu and Wen38 EoSs predict density values with AAD % ≤ 0.4%, and the method from Jacobson and Vinet39 predicts pressure values with AAD % < 29% (which corresponds to AAD % for densities lower than 0.6%). The Tammann−Tait and modified Tait63−65 equations correlate experimental density values with AAD % of 0.02 and 0.06%, respectively. Moreover, when using all of these equations for the prediction of density values in the pressure range of 1−4 GPa, the lowest values are those of Dowson and Higginson37 and Zhu and Wen,38 whereas the highest values are those of Jacobson and Vinet.39 The studied lubricants have similar compressibilities, with the highest differences being below 5%. Thus, with regard to this property, the developed vegetable-based lubricants are suitable for use as gear lubricants. The mineral lubricant MIN-G01 4506



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Figure 7. Thermal expansion coefficient values (αp) as a function of the pressure for different temperatures: 298.15 K (◇); 313.15 K (□); 323.15 K (△); 333.15 K (○); 348.15 K (×); 373.15 K (*). (a) MIN-G01, (b) MIN-G02, (c) SYN-G01, (d) BIO-G01, (e) BIO-G00, and (f) BIO-G02.

where ϕexp is the experimental value of the measured property in this work density or viscosity, ϕexp is its correlated value, and n is the number of experimental points. The standard deviation (σ) is given by

presents the highest compressibility and therefore, according to this property, could form thinner films by a few percent in the high-pressure regions. The Dowson and Higginson and Zhu and Wen EoSs do not predict well the κT values of the six oils in the pressure and temperature ranges of the measurements. At the highest temperatures (373.15 and 398.15 K), the Dowson and Higginson and Zhu and Wen EoSs predict lower compressibilities than the Tammann−Tait and modified Tait EoSs in the whole pressure range. However, for the lowest temperatures, the compressibility curves predicted by these models present crossovers at one or two points, but for pressures higher than 0.5 MPa, the Dowson and Higginson and Zhu and Wen EoSs always predict lower compressibility values. On the other hand, the values obtained for the thermal expansion coefficients using the Tammann−Tait correlations are quite similar for the six oils.

■

σ=

■

n

⎛ |ϕ

∑ ⎜⎜ i=1

⎝

exp

− ϕcor| ϕexp

⎞ × 100⎟⎟ ⎠

i=1

(16)

AUTHOR INFORMATION

Corresponding Author

*Phone: +34881814046. Fax: + 34881814112. E-mail: josefa. [email protected]. Present Addresses †

T.R.: Center for Energy Resources Engineering, Department of Chemistry, Technical University of Denmark, DK 2800 Kgs. Lyngby, Denmark. ‡ L.L.: Departamento de Fı ́sica Aplicada, Facultad de Ciencias, Edificio de Ciencias Experimentales, Universidade de Vigo, E36310 Vigo, Spain.

The definition of the absolute average deviation (AAD %) employed in this work is as follows: 1 n

n

∑ (ϕexp − ϕcor)2

where N is the number of parameters.

APPENDIX

AAD (%) =

1 n−N

Notes

The authors declare no competing financial interest.

(15) 4507



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(18) Bamgbade, B. A.; Wu, Y.; Burgess, W. A.; McHugh, M. A. Experimental density and PC-SAFT modeling of Krytox (perfluoropolyether) at pressures to 275 MPa and temperatures to 533 K. Fluid Phase Equilib. 2012, 332, 159−164. (19) Acosta, G. M.; Smith, R. L.; Arai, K. High-Pressure PVT Behavior of Natural Fats and Oils, Trilaurin, Triolein, and n-Tridecane from 303 to 353 K from Atmospheric Pressure to 150 MPa. J. Chem. Eng. Data 1996, 41 (5), 961−969. (20) Freitas, S. V. D.; Silva, F. A.; Pastoriza-Gallego, M. J.; Piñeiro, M. M.; Lima, Á . S.; Coutinho, J. A. P. Measurement and Prediction of Densities of Vegetable Oils at Pressures up to 45 MPa. J. Chem. Eng. Data 2013, 58 (11), 3046−3053. (21) Guignon, B.; Aparicio, C.; Sanz, P. D. Volumetric properties of sunflower and olive oils at temperatures between 15 and 55 °C under pressures up to 350 MPa. High Pressure Res. 2009, 29 (1), 38−45. (22) Guignon, B.; Aparicio, C.; Sanz, P. D. Volumetric Properties of Pressure-Transmitting Fluids up to 350 MPa: Water, Ethanol, Ethylene Glycol, Propylene Glycol, Castor Oil, Silicon Oil, and Some of Their Binary Mixture. J. Chem. Eng. Data 2010, 55 (9), 3017−3023. (23) Grandelli, H. E.; Dickmann, J. S.; Devlin, M. T.; Hassler, J. C.; Kiran, E. Volumetric Properties and Internal Pressure of Poly(αolefin) Base Oils. Ind. Eng. Chem. Res. 2013, 52 (50), 17725−17734. (24) Sagdeev, D. I.; Fomina, M. G.; Mukhamedzyanov, G. K.; Abdulagatov, I. M. Experimental study of the density and viscosity of polyethylene glycols and their mixtures at temperatures from 293 to 465 K and at high pressures up to 245 MPa. Fluid Phase Equilib. 2012, 315, 64−76. (25) Bair, S. High-pressure rheology for quantitative elastohydrodynamics; Elsevier: Amsterdam, The Netherlands, 2007. (26) Kleinschmidt, R. V.; Bradbury, D.; Mark, M. Viscosity and Density of Over Forty Lubricating Fluids of Known Composition at Pressures to 150,000 psi and Temperatures to 425 F; ASME: New York, 1953. (27) Fandiño, O.; Comuñas, M. J. P.; Lugo, L.; López, E. R.; Fernández, J. Density measurements under pressure for mixtures of pentaerythritol ester lubricants. Analysis of a density−viscosity relationship. J. Chem. Eng. Data 2007, 52 (4), 1429−1436. (28) Fandiño, O.; García, J.; Comuñas, M. J. P.; López, E. R.; Fernández, J. PρT Measurements and Equation of State (EoS) Predictions of Ester Lubricants up to 45 MPa. Ind. Eng. Chem. Res. 2006, 45 (3), 1172−1182. (29) Fandiño, O.; López, E. R.; Lugo, L.; Fernández, J. Compressed liquid densities of two dipentaerythritol esters. Fluid Phase Equilib. 2010, 296 (1), 30−36. (30) Fandiño, O.; Lugo, L.; Comuñas, M. J. P.; López, E. R.; Fernández, J. Temperature and pressure dependences of volumetric properties of two poly(propylene glycol) dimethyl ether lubricants. J. Chem. Thermodyn. 2010, 42 (1), 84−89. (31) Fandiño, O.; Pensado, A. S.; Lugo, L.; Comuñas, M. J. P.; Fernán dez, J. Compressed liquid densities of squalane and pentaerythritol tetra(2-ethylhexanoate). J. Chem. Eng. Data 2005, 50 (3), 939−946. (32) Fandiño, O.; Pensado, A. S.; Lugo, L.; López, E. R.; Fernández, J. Volumetric behaviour of the environmentally compatible lubricants pentaerythritol tetraheptanoate and pentaerythritol tetranonanoate at high pressures. Green Chem. 2005, 7, 775−783. (33) Paredes, X.; Fandiño, O.; Comuñas, M. J. P.; Pensado, A. S.; Fernández, J. Study of the effects of pressure on the viscosity and density of diisodecyl phthalate. J. Chem. Thermodyn. 2009, 41 (9), 1007−1015. (34) Paredes, X.; Fandiño, O.; Pensado, A. S.; Comuñas, M. J. P.; Fernández, J. Experimental density and viscosity measurements of di(2ethylhexyl)sebacate at high pressure. J. Chem. Thermodyn. 2012, 44 (1), 38−43. (35) Regueira, T.; Lugo, L.; Fandiño, O.; López, E. R.; Fernández, J. Compressibilities and viscosities of reference and vegetable oils for their use as hydraulic fluids and lubricants. Green Chem. 2011, 13 (5), 1293−1302.

ACKNOWLEDGMENTS This work was carried out within the framework of the strategic and singular project “Biolubricants based on vegetable oils and their synthetic derivatives”, which is funded by Spanish Science and Innovation Ministry and the EU FEDER program (Grants PSE-320100-2006-1 and PSE-420000-2008-4). We are very grateful to the BIOVESIN partners for their excellent advice and for providing us the samples of the products. L.L and T.R. acknowledge financial support under the Ramon y Cajal Program and the FPU program, respectively.

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NOTE ADDED AFTER ASAP PUBLICATION This paper was originally published ASAP on March 5, 2014, with an error in equation 11. The corrected version was reposted on March 6, 2014.

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Compressibilities and Viscosities of Reference, Vegetable, and

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