P HYSICAL P ROPERTIES OF L UBRICANTS 15 log 10 (υ + a) = log 10 b + 1/T c (2.6) It has also been found that if ‘υ’ is in [cS] then ‘a’ is approximately equal to 0.6. After substituting this into the equation, the logs were taken again in the manner shown below: log 10 log 10 (υ cS + 0.6) = a' − clog 10 T (2.7) where: a', c are constants. Although equation (2.7) forms successful bases for the ASTM viscosity-temperature chart, where the ordinate is log 10 log 10 (υ cS + 0.6) and the abscissa is log 10 T, from the mathematical view point the above derivation is incorrect. This is because when taking logs, equation (2.6) should be in the form: log 10 log 10 (υ cS + 0.6) = log 10 (log 10 b + 1/T c ) consequently, a' − clog 10 T ≠ log 10 (log 10 b + 1/T c ) Despite this the ASTM chart is quite successful and works very well for mineral and synthetic oils under normal conditions. It is so well standardized that the viscosity- temperature characteristics are sometimes specified as ‘ASTM slope’. 2.4 VISCOSITY INDEX Different oils may have different ASTM slopes as shown in Figure 2.2. As early as 1920 it was known that Pennsylvania crude oils were better than the Gulf Coast (Texan) crude oils. Pennsylvania crude had the best viscosity temperature characteristics while the Gulf Coast crude had the worst since its viscosity varied much more with temperature. From the engineering viewpoint there was a need for a parameter which would accurately describe the viscosity-temperature characteristics of the oils. In 1929 a ‘Viscosity Index’ was developed by Dean and Davis [1,2]. The viscosity index is an entirely empirical parameter which compares the kinematic viscosity of the oil of interest to the viscosities of two reference oils which have a considerable difference in sensitivity of viscosity to temperature. The reference oils have been selected in such a way that one of them has the viscosity index equal to zero (VI=0) and the other has the viscosity index equal to one hundred (VI=100) at 100°F (37.8°C) but they both have the same viscosity as the oil of interest at 210°F (98.89°C), as illustrated in Figure 2.3. Since Pennsylvania and Gulf Coast oils have the same viscosity at 210°F (98.9°C) they were initially selected as reference oils. Oils made from Pennsylvania crude were assigned the viscosity index of 100 whereas oils made from the Gulf Coast crude the viscosity index of 0. The viscosity index can be calculated from the following formula: VI = (L − U) / (L − H) × 100 (2.8) Firstly the kinematic viscosity of the oil of interest is measured at 40°C (‘U’) and at 100°C. Then from Table 2.2 [3] (ASTM D2270), looking at the viscosity at 100°C of the oil of interest, the corresponding values of the reference oils, ‘L’ and ‘H’ are read. Substituting the obtained values of ‘U’, ‘L’ and ‘H’ into the above equation yields the viscosity index. Note that the viscosity index is an inverse measure of the decline in oil viscosity with temperature. High values indicate that the oil shows less relative decline in viscosity with TEAM LRN 16 E NGINEERING T RIBOLOGY temperature. The viscosity index of most of the refined mineral oils available on the market is about 100, whereas multigrade and synthetic oils have higher viscosity indices of about 150. Mineral Oil 20 VI Mineral Oil 100 VI Mineral Oil 150 VI -40 -20 0 20 40 60 80 100 120 140 160 Di-ester 140 VI Chlorinated Silicone 185 VI 100 000 10 000 5 000 1 000 500 200 100 50 20 10 8.0 6.0 4.0 3.0 2.0 1.5 Temperature [°C] Kinematic Viscosity [cS] Silicone 240 VI SAE 30W 100 VI Mineral Oil 160 VI ° F IGURE 2.2 Viscosity-temperature characteristics of selected oils (adapted from [29 and 22]). EXAMPLE Find the viscosity index of an oil which has a kinematic viscosity at 40°C of υ 40 = 135 [cS] and at 100°C of υ 100 = 17 [cS]. From Table 2.2 for υ 100 = 17 [cS], L = 369.4 and H = 180.2 can be found. Substituting into the viscosity index equation yields: VI = (369.4 − 135) / (369.4 − 180.2) × 100 = 123.9 2.5 VISCOSITY PRESSURE RELATIONSHIP Lubricant viscosity increases with pressure. For most lubricants this effect is considerably larger than the effect of temperature or shear when the pressure is significantly above atmospheric. This is of particular importance in the lubrication of heavily loaded concentrated contacts which can be found, for example, in rolling contact bearings and gears. The pressures encountered in these contacts can be so high and the rate of pressure rise so rapid that the lubricant behaves like a solid rather than a liquid. The phenomenon of viscosity increasing with pressure and the possibility of lubricant failure by fracture rather than viscous shear is often observed but not always recognized. For example, when asphalt or pitch is hit with a hammer it will shatter, on the other hand when placed on an incline it will slowly flow. TEAM LRN P HYSICAL P ROPERTIES OF L UBRICANTS 17 Kinematic Viscosity [cS] υ L υ U υ H L U H 100 VI 0 VI 37.8 98.9 Temperature [°C]° F IGURE 2.3 Evaluation of viscosity index [23]. A number of attempts have been made to develop a formula describing the relationship between pressure and viscosity of lubricants. Some have been quite satisfactory, especially at low pressures, while others have been quite complex and not easily applicable in practice. The best known equation to calculate the viscosity of a lubricant at moderate pressures (close to atmospheric) is the Barus equation [4,5]. The application of this equation to pressures above 0.5 [GPa] can, however, lead to serious errors [6]. The equation becomes even more unreliable if the ambient temperature is high. The Barus equation is of the form: η p = η 0 e αp (2.9) where: η p is the viscosity at pressure ‘p’ [Pas]; η 0 is the atmospheric viscosity [Pas]; α is the pressure-viscosity coefficient [m 2 /N], which can be obtained by plotting the natural logarithm of dynamic viscosity ‘η’ versus pressure ‘p’. The slope of the graph is ‘α’; p is the pressure of concern [Pa]. For higher pressures Chu et al. [7] suggested that the following formula can be used: η p = η 0 (1 + C × p) n (2.10) where: C, n are constants, ‘n’ is approximately 16 for most cases and ‘C’ can be obtained from the diagram shown in Figure 2.4 [7,8]. The pressure-viscosity coefficient is a function of the molecular structure of the lubricant and its physical characteristics such as molecular interlocking, molecular packing and rigidity and viscosity-temperature characteristics. There are various formulae available to calculate the pressure-viscosity coefficient. One of the early ones was derived by Wooster [5]: α = (0.6 + 0.965log 10 η 0 ) × 10 −8 (2.11) where: α is the pressure-viscosity coefficient [m 2 /N]; TEAM LRN 18 E NGINEERING T RIBOLOGY η 0 is the atmospheric viscosity [cP], i.e. 1[cP] = 10 -3 [Pas]. T ABLE 2.2 Data for the evaluation of viscosity index [3]. 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00 5.10 5.20 5.30 5.40 5.50 5.60 5.70 5.80 5.90 6.00 6.10 6.20 6.30 6.40 6.50 6.60 6.70 6.80 6.90 7.00 7.10 7.20 7.30 7.40 7.50 7.60 7.70 7.80 7.90 8.00 8.10 8.20 7.994 8.640 9.309 10.00 10.71 11.45 12.21 13.00 13.80 14.63 15.49 16.36 17.26 18.18 19.12 20.09 21.08 22.09 23.13 24.19 25.32 26.50 27.75 29.07 30.48 31.96 33.52 35.13 36.79 38.50 40.23 41.99 43.76 45.53 47.31 49.09 50.87 52.64 54.42 56.20 57.97 59.74 61.52 63.32 65.18 67.12 69.16 71.29 73.48 75.72 78.00 80.25 82.39 84.53 86.66 88.85 91.04 93.20 95.43 97.72 100.0 102.3 104.6 6.394 6.894 7.410 7.944 8.496 9.063 9.647 10.25 10.87 11.50 12.15 12.82 13.51 14.21 14.93 15.66 16.42 17.19 17.97 18.77 19.56 20.37 21.21 22.05 22.92 23.81 24.71 25.63 26.57 27.53 28.49 29.46 30.43 31.40 32.37 33.34 34.32 35.29 36.26 37.23 38.19 39.17 40.15 41.13 42.14 43.18 44.24 45.33 46.44 47.51 48.57 49.61 50.69 51.78 52.88 53.98 55.09 56.20 57.31 58.45 59.60 60.74 61.89 8.30 8.40 8.50 8.60 8.70 8.80 8.90 9.00 9.10 9.20 9.30 9.40 9.50 9.60 9.70 9.80 9.90 10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11.0 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12.0 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 13.0 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 14.0 14.1 14.2 14.3 14.4 14.5 106.9 109.2 111.5 113.9 116.2 118.5 120.9 123.3 125.7 128.0 130.4 132.8 135.3 137.7 140.1 142.7 145.2 147.7 150.3 152.9 155.4 158.0 160.6 163.2 165.8 168.5 171.2 173.9 176.6 179.4 182.1 184.9 187.6 190.4 193.3 196.2 199.0 201.9 204.8 207.8 210.7 213.6 216.6 219.6 222.6 225.7 228.8 231.9 235.0 238.1 241.2 244.3 247.4 250.6 253.8 257.0 260.1 263.3 266.6 269.8 273.0 276.3 279.6 63.05 64.18 65.32 66.48 67.64 68.79 69.94 71.10 72.27 73.42 74.57 75.73 76.91 78.08 79.27 80.46 81.67 82.87 84.08 85.30 86.51 87.72 88.95 90.19 91.40 92.65 93.92 95.19 96.45 97.71 98.97 100.2 101.5 102.8 104.1 105.4 106.7 108.0 109.4 110.7 112.0 113.3 114.7 116.0 117.4 118.7 120.1 121.5 122.9 124.2 125.6 127.0 128.4 129.8 131.2 132.6 134.0 135.4 136.8 138.2 139.6 141.0 142.4 14.6 14.7 14.8 14.9 15.0 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16.0 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 17.0 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 18.0 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 19.0 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 20.0 20.2 20.4 20.6 20.8 21.0 21.2 21.4 21.6 283.0 286.4 289.7 293.0 296.5 300.0 303.4 306.9 310.3 313.9 317.5 321.1 324.6 328.3 331.9 335.5 339.2 342.9 346.6 350.3 354.1 358.0 361.7 365.6 369.4 373.3 377.1 381.0 384.9 388.9 392.7 396.7 400.7 404.6 408.6 412.6 416.7 420.7 424.9 429.0 433.2 437.3 441.5 445.7 449.9 454.2 458.4 462.7 467.0 471.3 475.7 479.7 483.9 488.6 493.2 501.5 510.8 519.9 528.8 538.4 547.5 556.7 566.4 143.9 145.3 146.8 148.2 149.7 151.2 152.6 154.1 155.6 157.0 158.6 160.1 161.6 163.1 164.6 166.1 167.7 169.2 170.7 172.3 173.8 175.4 177.0 178.6 180.2 181.7 183.3 184.9 186.5 188.1 189.7 191.3 192.9 194.6 196.2 197.8 199.4 201.0 202.6 204.3 205.9 207.6 209.3 211.0 212.7 214.4 216.1 217.7 219.4 221.1 222.8 224.5 226.2 227.7 229.5 233.0 236.4 240.1 243.5 247.1 250.7 254.2 257.8 21.8 22.0 22.2 22.4 22.6 22.8 23.0 23.2 23.4 23.6 23.8 24.0 24.2 24.4 24.6 24.8 25.0 25.2 25.4 25.6 25.8 26.0 26.2 26.4 26.6 26.8 27.0 27.2 27.4 27.6 27.8 28.0 28.2 28.4 28.6 28.8 23.0 29.2 29.4 29.6 29.8 30.0 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 40.0 40.5 575.6 585.2 595.0 604.3 614.2 624.1 633.6 643.4 653.8 663.3 673.7 683.9 694.5 704.2 714.9 725.7 736.5 747.2 758.2 769.3 779.7 790.4 801.6 812.8 824.1 835.5 847.0 857.5 869.0 880.6 892.3 904.1 915.8 927.6 938.6 951.2 963.4 975.4 987.1 998.9 1011 1023 1055 1086 1119 1151 1184 1217 1251 1286 1321 1356 1391 1427 1464 1501 1538 1575 1613 1651 1691 1730 1770 261.5 264.9 268.6 272.3 275.8 279.6 283.3 286.8 290.5 294.4 297.9 301.8 305.6 309.4 313.0 317.0 320.9 324.9 328.8 332.7 336.7 340.5 344.4 348.4 352.3 356.4 360.5 364.6 368.3 372.3 376.4 380.6 384.6 388.8 393.0 396.6 401.1 405.3 409.5 413.5 417.6 421.7 432.4 443.2 454.0 464.9 475.9 487.0 498.1 509.6 521.1 532.5 544.0 555.6 567.1 579.3 591.3 603.1 615.0 627.1 639.2 651.8 664.2 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0 50.5 51.0 51.5 52.0 52.5 53.0 53.5 54.0 54.5 55.0 55.5 56.0 56.5 57.0 57.5 58.0 58.5 59.0 59.5 60.0 60.5 61.0 61.5 62.0 62.5 63.0 63.5 64.0 64.5 65.0 65.5 66.0 66.5 67.0 67.5 68.0 68.5 69.0 69.5 70.0 1810 1851 1892 1935 1978 2021 2064 2108 2152 2197 2243 2288 2333 2380 2426 2473 2521 2570 2618 2667 2717 2767 2817 2867 2918 2969 3020 3073 3126 3180 3233 3286 3340 3396 3452 3507 3563 3619 3676 3734 3792 3850 3908 3966 4026 4087 4147 4207 4268 4329 4392 4455 4517 4580 4645 4709 4773 4839 4905 676.6 689.1 701.9 714.9 728.2 741.3 754.4 767.6 780.9 794.5 808.2 821.9 835.5 849.2 863.0 876.9 890.9 905.3 919.6 933.6 948.2 962.9 977.5 992.1 1007 1021 1036 1051 1066 1082 1097 1112 1127 1143 1159 1175 1190 1206 1222 1238 1254 1270 1286 1303 1319 1336 1352 1369 1386 1402 1419 1436 1454 1471 1488 1506 1523 1541 1558 υ 100 LH υ 100 LH υ 100 LH υ 100 LH υ 100 LH υ 100 is the kinematic viscosity of the oil of interest at 100°C in [cS]. Although this exponential law fits most lubricants it is not particularly accurate. There are also other equations for the calculation of the pressure-viscosity coefficient available in the literature. It is often reported that some of these equations are accurate for certain fluids but TEAM LRN P HYSICAL P ROPERTIES OF L UBRICANTS 19 unsuitable for others. One of the best formulae for the analytical determination of the pressure-viscosity coefficient is the empirical expression developed by So and Klaus [9]. A combination of linear and nonlinear regression analyses with atmospheric viscosity, density and the viscosity temperature property (modified ASTM slope) was applied to obtain the following expression: α = 1.216+4.143 × (log 10 υ 0 ) 3.0627 +2.848 × 10 −4 × b 5.1903 (log 10 υ 0 ) 1 .5976 −3.999 × (log 10 υ 0 ) 3.0975 ρ 0.1162 (2.12) where: α is the pressure-viscosity coefficient [ × 10 -8 m 2 /N]; υ 0 is the kinematic viscosity at the temperature of interest [cS]; b is the ASTM slope of a lubricant divided by 0.2; ρ is the atmospheric density at the temperature of interest in [g/cm 3 ]. 1000 500 200 100 50 20 10 5 2 1 [ 10 Pa ] × -9 -1 C 0123 Viscosity [cP] η 0 0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2 0.5 1 10243852 65 79 93 107 121 149 177 204 Viscosity [Pas] η 0 Oil temperature [ o C] F IGURE 2.4 Graph for the determination of the constant ‘C’ (adapted from [8]). One of the problems associated with available formulae is that they only allow the accurate calculation of pressure-viscosity coefficients at low shear rates. In many engineering applications, especially in the heavily loaded concentrated contacts however, the lubricant operates under very high shear rates and the precise values of the pressure-viscosity coefficient are needed for the evaluation of the minimum film thickness. An accurate value of this coefficient can be determined experimentally and this problem is discussed later. If an accurate analytical formula could be developed it would certainly be useful. It could provide a relationship between the fundamental parameters of the lubricant and the pressure-viscosity coefficient as opposed to being a strictly empirical equation. This would open up the possibilities of modifying the chemical make up of the lubricant in order to achieve the desired pressure-viscosity coefficient for specific applications. A limited attempt to find such a relationship was reported by Johnston [15]. TEAM LRN 20 E NGINEERING T RIBOLOGY The rise in viscosity with pressure varies between oils, and there is a considerable difference between paraffinic and naphthenic oils. The pressure-viscosity coefficient of the Barus equation or ‘alpha value’ has a value between 1.5 - 2.4 × 10 -8 [m 2 /N] for paraffinic oils, and a value between 2.5 - 3.5 × 10 -8 [m 2 /N] for aromatic oils according to Klamann [16]. For aromatic extracts of oil, the pressure-viscosity coefficient is much higher, but this is of limited practical significance. The value of the pressure-viscosity coefficient is in general reduced at higher temperatures, with naphthenic oils being the most severely affected. In some cases even at 80°C there is a substantial reduction in the pressure-viscosity coefficient. This effect is not so pronounced in paraffinic oils, thus they usually generate more stable lubricating films over the wide temperature range, from ambient to typical bearing and gear temperatures. Water, by contrast shows only a small rise, almost negligible, in viscosity with pressure. More interestingly, at temperatures close to its freezing point it shows a decline in viscosity with pressure [17,18]. Obviously, water is not a particularly good lubricant, although it can function surprisingly well in some applications. There are many other formulae for viscosity-pressure relationships. A short review of some of the empirical formulae for the viscosity-pressure relationships is given in [9,10]. These formulae allow for the calculations of viscosity changes with pressure under various conditions and to various degrees of accuracy. An expression which is suitable for computing was initially proposed by Roelands [11,12] and developed further by Houpert [12,13]. To calculate lubricant viscosity at a specific pressure a particular form of the Barus equation was proposed: η R = η 0 e α*p (2.13) where: η R is the viscosity at pressure ‘p’ and temperature ‘θ’ [Pas]; η 0 is the atmospheric viscosity [Pas]; α* is the Roelands pressure-viscosity coefficient which is a function of both ‘p’ and ‘θ’ [m 2 /N]; p is the pressure of interest [Pa]. The Roelands pressure-viscosity coefficient ‘α*’ can be calculated from the formula: α p = [ln η {( (1 + 5.1 × 10 p) − 1 ∗ 0 + 9.67] ( θ − 138 θ − 138 0 − S 0 − 9Z { (2.14) where: θ 0 is a reference or ambient temperature [K]; η 0 is the atmospheric viscosity [Pas]; Z, S 0 are constants, characteristic for a specific oil, independent of temperature and pressure. These constants can be calculated from the following formulae [12]: α 0 − 9 Z= 5.1 × 10 η+ 9.67] β(θ − 138) 0 S = lnη+ 9.67 0 0 [ln TEAM LRN P HYSICAL P ROPERTIES OF L UBRICANTS 21 where: α is the pressure-viscosity coefficient [m 2 /N]; β is given by the following expression [12,13]: β= [ln η [ 0 + 9.67] [ S (θ − 138) 0 [1 + 5.1 × 10 p] − 9Z 0 The above formula appears to be more comprehensive than the others since it takes into account the simultaneous effects of temperature and pressure. The ‘α’ values and dynamic viscosity ‘η 0 ’ for some commonly used lubricants are given in Table 2.3 [12,14]. T ABLE 2.3 Dynamic viscosity and pressure-viscosity coefficients of some commonly used lubricants (adapted from [12]). Dynamic viscosity  η Pressure-viscosity measured at coefficient atmospheric pressure [ × 10 -9 m/N] [ ×10 -3 Pas] 30°C 60°C 100°C 30°C 60°C 100°C Light machine oil 38 12.1 5.3 - 18.4 13.4 Heavy machine oil 153 34 9.1 23.7 20.5 15.8 Heavy machine oil 250 50.5 12.6 25.0 21.3 17.6 Cylinder oil 810 135 26.8 34 28 22 Spindle oil 18.6 6.3 2.4 20 16 13 Light machine oil 45 12 3.9 28 20 16 Medicinal white oil 107 23.3 6.4 29.6 22.8 17.8 Heavy machine oil 122 26.3 7.3 27.0 21.6 17.5 Heavy machine oil 171 31 7.5 28 23 18 Spindle oil 30.7 8.6 3.1 25.7 20.3 15.4 Heavy machine oil 165 30.0 6.8 33.0 23.8 16.0 Heavy machine oil 310 44.2 9.4 34.6 26.3 19.5 Cylinder oil 2000 180 24 41.5 29.4 25.0 Water 0.80 0.47 0.28 0 0 0 Ethylene oxide- propylene oxide copolymer 204 62.5 22.5 17.6 14.3 12.2 Castor oil 360 80 18.0 15.9 14.4 12.3 Di(2-ethylhexyl) phthalate 43.5 11.6 4.05 20.8 16.6 13.5 Glycerol (glycerine) 535 73 13.9 5.9 5.5 3.6 Polypropylene glycol 750 82.3 - - 17.8 - - Polypropylene glycol 1500 177 - - 17.4 - - Tri-arylphosphate ester 25.5 - - 31.6 - - Lubricants High VI oils Medium VI oils Low VI oils Other fluids and lubricants α 2 0 TEAM LRN 22 E NGINEERING T RIBOLOGY 2.6 VISCOSITY-SHEAR RATE RELATIONSHIP From the engineering view point, it is essential to know the value of the lubricant viscosity at a specific shear rate. For simplicity it is usually assumed that the fluids are Newtonian, i.e. their viscosity is proportional to shear rate as shown in Figure 2.5. τ Shear stress Shear rates α tan α = η u/h F IGURE 2.5 Shear stress - shear rate characteristic of a Newtonian fluid. For pure mineral oils this is usually true up to relatively large shear rates of 10 5 - 10 6 [s -1 ] [31], but at the higher shear rates frequently encountered in engineering applications this proportionality is lost and the lubricant begins to behave as a non-Newtonian fluid. In these fluids the viscosity depends on shear rate, that is the fluids do not have a single value of viscosity over the range of shear rates. Non-Newtonian behaviour is, in general, a function of the structural complexity of a fluid. For example, liquids like water, benzene and light oils are Newtonian. These fluids have a loose molecular structure which is not affected by shearing action. On the other hand the fluids in which the suspended molecules form a structure which interferes with the shearing of the suspension medium are considered to be non-Newtonian. Typical examples of such fluids are water-oil emulsions, polymer thickened oils and, in extreme cases, greases. The non-Newtonian behaviour of some selected fluids is shown in Figure 2.6. υ Kinematic viscosity Grease Newtonian Dilatant Pseudoplastic (i.e. mineral oil with polymer additive) Shear rates u/h F IGURE 2.6 Viscosity - shear rate characteristics for some non-Newtonian fluids. There are two types of non-Newtonian behaviour which are important from the engineering viewpoint: pseudoplastic and thixotropic behaviour. Pseudoplastic Behaviour Pseudoplastic behaviour is also known in the literature as shear thinning and is associated with the thinning of the fluid as the shear rate increases. This is illustrated in Figure 2.7. TEAM LRN P HYSICAL P ROPERTIES OF L UBRICANTS 23 During the process of shearing in polymer fluids, long molecules which are randomly orientated and with no connected structure, tend to align giving a reduction in apparent viscosity. In emulsions a drop in viscosity is due to orientation and deformation of the emulsion particles. The process is usually reversible. Multigrade oils are particularly susceptible to this type of behaviour; they shear thin with increased shear rates, as shown in Figure 2.8 [38]. τ Shear stress Shear rates u/h F IGURE 2.7 Pseudoplastic behaviour. The opposite phenomenon to pseudoplastic behaviour, i.e. thickening of the fluid when shear rate is increased, is dilatancy. Dilatant fluids are usually suspensions with a high solid content. The increase in viscosity with the shear rates is attributed to the rearranging of the particles suspended in the fluid, resulting in the dilation of voids between the particles. This behaviour can be related to the arrangement of the fluid molecules. The theory is that in the non-shear condition molecules adopt a close packed formation which gives the minimum volume of voids. When the shear is applied the molecules move to an open pack formation dilating the voids. As a result, there is an insufficient amount of fluid to fill the voids giving an increased resistance to flow. An analogy to such fluids can be found when walking on wet sand where footprints are always dry. υ Kinematic viscosity 100 200 500 1 000 2 000 10 100 1 000 10 000 100 000 350 cS silicone SAE 30 SAE 20W/50 1000 cS silicone Shear rates -1 [cS] [s ] u/h F IGURE 2.8 Pseudoplastic behaviour of lubricating oils [38]. TEAM LRN 24 E NGINEERING T RIBOLOGY Thixotropic Behaviour Thixotropic behaviour, also known in the literature as shear duration thinning, is shown in Figure 2.9. It is associated with a loss of consistency of the fluid as the duration of shear increases. During the process of shearing, it is thought that the thixotropic fluids have a structure which is being broken down. The destruction of the fluid structure progresses with time, giving a reduction in apparent viscosity, until a certain balance is reached where the structure rebuilds itself at the same rate as it is destroyed. At this stage the apparent viscosity attains a steady value. In some cases the process is reversible, i.e. viscosity returns to its original value when shear is removed, but permanent viscosity loss is also possible. υ Apparent viscosity Time a t Low Medium High } shear rates F IGURE 2.9 Thixotropic behaviour. A converse effect to thixotropic behaviour, i.e. thickening of the fluid with the duration of shearing, can also occur with some fluids. This phenomenon is known in the literature as inverse thixotropy or rheopectic behaviour [19]. An example of a fluid with such properties is synovial fluid, a natural lubricant found in human and animal joints. It was found that the viscosity of synovial fluid increases with the duration of shearing [20,39]. It seems that the longer the duration of shearing the better the lubricating film which is generated by the body. 2.7 VISCOSITY MEASUREMENTS Various viscosity measurement techniques and instruments have been developed over the years. The most commonly used in engineering applications are capillary and rotational viscometers. In general, capillary viscometers are suitable for fluids with negligible non- Newtonian effects and rotational viscometers are suitable for fluids with significant non- Newtonian effects. Some of the viscometers have a special heating bath built-in, in order to control and measure the temperature, so that the viscosity-temperature characteristics can be obtained. In most cases water is used in the heating bath. Water is suitable for the temperature range between 0° to 99°C. For higher temperatures mineral oils are used and for low temperatures down to -54°C, ethyl alcohol or acetone is used. Capillary Viscometers Capillary viscometers are based on the principle that a specific volume of fluid will flow through the capillary (ASTM D445, ASTM D2161). The time necessary for this volume of fluid to flow gives the ‘kinematic viscosity’. Flow through the capillary must be laminar and the deductions are based on Poiseuille’s law for steady viscous flow in a pipe. There is a number of such viscometers available and some of them are shown in Figure 2.10. Assuming that the fluids are Newtonian, and neglecting end effects, the kinematic viscosity can be calculated from the formula: TEAM LRN . had the worst since its viscosity varied much more with temperature. From the engineering viewpoint there was a need for a parameter which would accurately. calculation of pressure-viscosity coefficients at low shear rates. In many engineering applications, especially in the heavily loaded concentrated contacts