Designation: D5481 − 13Standard Test Method forMeasuring Apparent Viscosity at High-Temperature andHigh-Shear Rate by Multicell Capillary Viscometer1This standard is issued under the fixed designation D5481; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.INTRODUCTIONSeveral different configurations of capillary viscometers have been successfully used for measuringthe viscosity of engine oils at the high shear rates and high temperatures that occur in engines. Thistest method covers the use of a single apparatus2at a single temperature and single shear rate toachieve greater uniformity and improved precision.1. Scope*1.1 This test method covers the laboratory determination ofhigh-temperature high-shear (HTHS) viscosity of engine oils ata temperature of 150 °C using a multicell capillary viscometercontaining pressure, temperature, and timing instrumentation.The shear rate for this test method corresponds to an apparentshear rate at the wall of 1.4 million reciprocal seconds(1.4 × 106s−1).3This shear rate has been found to decrease thediscrepancy between this test method and other high-temperature high-shear test methods3(Test Methods D4683and D4741) used for engine oil specifications. Viscosities aredetermined directly from calibrations that have been estab-lished with Newtonian oils with nominal viscosities from1.4 mPa·s to 5.0 mPa·s at 150 °C. The precision has only beendetermined for the viscosity range 1.45 mPa·s and 5.05 mPa·sat 150 °C for the materials listed in the precision section.1.2 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.2.1 The centiPoise (cP) is a non-SI metric unit of viscositythat is numerically equal to the milliPascal-second (mPa·s).1.2.2 Pounds per square inch (psi) is a non-SI unit ofpressure that is approximately equal to 6.895 kPa. These unitsare provided for information only in 6.1.1, 7.3, 9.1.2.1, and thetables.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:4D4683 Test Method for Measuring Viscosity of New andUsed Engine Oils at High Shear Rate and High Tempera-ture by Tapered Bearing Simulator Viscometer at 150 °CD4741 Test Method for Measuring Viscosity at High Tem-perature and High Shear Rate byTapered-PlugViscometerD6300 Practice for Determination of Precision and BiasData for Use in Test Methods for Petroleum Products andLubricantsD6708 Practice for Statistical Assessment and Improvementof Expected Agreement Between Two Test Methods thatPurport to Measure the Same Property of a Material3. Terminology3.1 Definitions:3.1.1 apparent viscosity, n—viscosity of a non-Newtonianliquid determined by this test method at a particular shear rateand shear stress.3.1.2 density, n—mass per unit volume of the test liquid at agiven temperature.1This test method is under the jurisdiction of ASTM Committee D02 onPetroleum Products, Liquid Fuels, and Lubricants and is the direct responsibility ofSubcommittee D02.07 on Flow Properties.Current edition approved Oct. 1, 2013. Published November 2013. Originallyapproved in 1993. Last previous edition approved in 2010 as D5481 – 10. DOI:10.1520/D5481-13.2Manning, R. E., and Lloyd, W. A., “Multicell High Temperature High-ShearCapillary Viscometer,” SAE Paper 861562. Available from Society of AutomotiveEngineers (SAE), 400 Commonwealth Dr., Warrendale, PA 15096-0001, www.sae-.org.3Girshick, F., “Non-Newtonian Fluid Dynamics in High Temperature HighShear Capillary Viscometers,” SAE Paper 922288. Available from Society ofAutomotive Engineers (SAE), 400 Commonwealth Dr., Warrendale, PA 15096-0001, www.sae.org.4For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.2.1 Discussion—In SI notation, the unit of density is thekilogram per cubic metre. However, for practical use, gram percubic centimetre is customarily used and is equivalent to103kg/m3.3.1.3 kinematic viscosity, n—the ratio of the viscosity to thedensity of the fluid.3.1.3.1 Discussion—Kinematic viscosity is a measure of afluid’s resistance to flow under the force of gravity. In the SI,the unit of kinematic viscosity is the metre squared per second(m2/s); for practical use, a submultiple (millimetre squared persecond, mm2/s) is more convenient. The centistoke (cSt) is 1mm2/s and is often used.3.1.4 Newtonian oil or liquid, n—an oil or liquid that at agiven temperature exhibits a constant viscosity at all shear ratesor shear stresses.3.1.5 non-Newtonian oil or fluid, n—an oil or liquid thatexhibits a viscosity that varies with changing shear rate orshear stress.3.1.6 shear rate—velocity gradient in liquid flow in milli-metres per second per millimetre (mm/s per mm) resultingfrom applied shear stress; the System International (SI) unit forshear rate is reciprocal seconds, s–1.3.1.6.1 Discussion—The velocity gradient in the Multi-CellCapillary Viscometer varies across the capillary annulus froma maximum at the wall of the capillary to zero at the center ofthe capillary annulus.Assuming a parabolic flow profile acrossthe capillary, the apparent shear rate at the capillary wall can becalculated as follows:Sa5 4V/πR3t (1)where:Sa= apparent shear rate (at the wall, s−1),V = volume of fluid (mm3) passed through the capillary intime t (s), andR = capillary radius (mm).Sais precise for Newtonian liquids which generate aparabolic flow profile but may be approximate for non-Newtonian liquids that do not necessarily generate a para-bolic flow profile.3.1.7 shear stress, n—force per unit area causing liquid flowover the area where viscous shear is being caused; in SI, theunit of shear stress is the Pascal (Pa).3.1.7.1 Discussion—In a capillary viscometer, the signifi-cant shear stress is at the wall of the capillary. That is, the totalforce acting on the area of the capillary annulus divided by theinside area of the capillary through which the liquid flows. Theshear stress at the wall does not depend on the nature of theliquid (that is, whether the liquid is Newtonian or non-Newtonian). The shear stress at the capillary wall may becalculated as follows:Z 5 PR/2L (2)where:Z = shear stress (Pa),P = pressure drop (in Pa),R = capillary radius, andL = capillary length (in units consistent with R).3.1.8 viscosity, n—ratio of applied shear stress and theresulting rate of shear.3.1.8.1 Discussion—It is sometimes called dynamic or ab-solute viscosity. Viscosity is a measure of the resistance to flowof the liquid at a given temperature. In SI the unit of viscosityis the Pascal second (Pa·s), often conveniently expressed asmilliPascal second (mPa·s), which has the English systemequivalent of the centiPoise (cP).3.2 Definitions of Terms Specific to This Standard:3.2.1 calibration oils—those oils used for establishing theinstrument’s reference framework of apparent viscosity versuspressure drop from which the apparent viscosities of the testoils are determined.3.2.1.1 Discussion—Calibration oils, which are Newtonianfluids, are available commercially5or can be blended by theuser.3.2.2 test oil—any oil for which the apparent viscosity is tobe determined by the test method.3.2.3 viscometric cell—that part of the viscometer compris-ing all parts which may be wet by the test sample, includingexit tube, working capillary, fill tube, pressure/exhaustconnection, plug valve, and fill reservoir.4. Summary of Test Method4.1 The viscosity of the test oil in any of the viscometriccells is obtained by determining the pressure required toachieve a flow rate corresponding to an apparent shear rate atthe wall of 1.4 × 106s−1. The calibration of each cell is used todetermine the viscosity corresponding to the measured pres-sure.4.2 Each viscometric cell is calibrated by establishing therelationship between pressure and flow rate for a series ofNewtonian oils of known viscosity.5. Significance and Use5.1 Viscosity is an important property of fluid lubricants.The viscosity of all fluids varies with temperature. Manycommon petroleum lubricants are non-Newtonian: their vis-cosity also varies with shear rate. The usefulness of theviscosity of lubricants is greatest when the viscosity is mea-sured at or near the conditions of shear rate and temperaturethat the lubricants will experience in service.5.2 The conditions of shear rate and temperature of this testmethod are thought to be representative of those in the bearingof automotive engines in severe service.5.3 Many equipment manufacturers and lubricant specifica-tions require a minimum high-temperature high-shear viscosityat 150 °C and 106s−1. The shear rate in capillary viscometersvaries across the radius of the capillary. The apparent shear rateat the wall for this test method is increased to compensate forthe variable shear rate.35The sole source of supply known to the committee at this time is CannonInstrument Co., 2139 High Tech Rd., State College, PA 16803. If you are aware ofalternative suppliers, please provide this information to ASTM InternationalHeadquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee,1which you may attend.D5481 − 1325.4 This test was evaluated in an ASTM cooperative pro-gram.66. Apparatus6.1 Multi-Cell Capillary High-Temperature High-Shear(HTHS) Viscometer,5consisting of several viscometer cells in atemperature-controlled block and including means for control-ling and measuring temperature and applied pressure and fortiming the flow of a predetermined volume of test oil. Eachviscometric cell contains a precision glass capillary and meansfor adjusting the test oil volume to the predetermined value.6.1.1 The Multi-Cell Capillary HTHS viscometer has thefollowing typical dimensions and specifications:Diameter of capillary 0.15 mmLength of capillary 15 mm to 18 mmTemperature control 150 °C ± 0.1 °CPressure range 350 kPa to 3500 kPa (~50 to 500psi)Pressure control ±1 %Sample volume 7 mL ± 1 mL6.1.2 The thermometer for measuring the temperature of theblock is a preset digital resistance thermometer. The accuracyof this thermometer may be checked by means of a specialthermowell and calibrated thermometer5whose accuracy is60.1 °C or better. See manufacturer’s recommendations forprocedure.7. Reagents and Materials7.1 Newtonian Oils,5having nominal certified viscosities of1.5 mPa·s to 7.0 mPa·s at 150 °C. See Table 1.7.2 Non-Newtonian Reference Sample,5having a certifiedviscosity at 150 °C and 106s−1.7.3 Carbon Dioxide or Nitrogen Cylinder, with reducervalve having a maximum pressure of at least 3500 kPa (~500psi).8. Sampling8.1 A representative sample of test oil, free from suspendedsolid material and water, is necessary to obtain valid results.When the sample is suspected to contain suspended material,filter with about 10-µm filter paper.9. Calibration and Standardization9.1 Calibration:9.1.1 The volume and capillary diameter of each viscomet-ric cell in the instrument is provided by the manufacturer, andthe nominal flow time, to, corresponding to an apparent shearrate at the wall of 1.4 × 106s−1is calculated by the manufac-turer using the following equation:to5 4V/1.4*106πR3(3)where symbols are defined as in 3.1.6.9.1.2 Using a minimum of four Newtonian calibration oilscovering the viscosity range from 1.5 mPa·s to 5 mPa·s at150 °C, determine the relationship between pressure and flowrate for each viscometric cell. The pressure should be adjustedfor each calibration oil such that the measured flow time iswithin 62 % of the nominal flow time, to. Make threedeterminations for each oil in each cell. Follow the instrumentsupplier’s documentation for using the software “High ShearViscosity Calculator” to record these results.9.1.2.1 The following relationship can be used to expressthe data:ηi5FC1·t·P 2C2tG·F11C3·S1 2ttoD G(4)where:ηi= intermediate viscosity, mPa·s,t = flow time, s,P = pressure, kPa, andC1,C2,C3= coefficients specific to each viscometric cell.9.1.2.2 Coefficient C1is specific to the units in whichpressure is expressed, as well as to each cell. Coefficient C2will be essentially constant over the relatively narrow range ofshear rates and viscosities of interest in measurement of thehigh-temperature viscosity of automotive engine oil. In moregeneral applications, C2may not be constant for all values ofReynolds Number.9.1.2.3 Intermediate viscosity equals viscosity for the cali-bration oils.9.1.2.4 Use the suppliers “High Shear Viscosity Calculator”software to determine the calibration coefficients for eachviscometric cell.9.1.2.5 Alternatively, Annex A1 describes the procedure fordetermining coefficients C1, C2, and C3.9.2 Stability of Viscosity Calibration—Check the stability ofthe calibration by running a calibration oil in the same manneras a test oil would be run. This shall be done no less frequentlythan before each new series of runs and every twentieth run.The non-Newtonian calibration oil should be run at leastmonthly. The calibration oil viscosity determined in this waymust not differ from the standard value by more than therepeatability of the test (see 12.1). If it is out of limits, and ifthe result is confirmed by a repeat run, look for the source ofthe trouble, rectify it, and repeat the entire calibrationprocedure, if necessary. Some possible steps to find the sourceof the trouble are to check the system thoroughly for faults,including foreign material in the capillary, verify the fidelity ofthe operating procedure, and accuracy of temperature control,and readout.6Supporting data have been filed at ASTM International Headquarters and maybe obtained by requesting Research Report RR:D02-1767.TABLE 1 Calibration OilsCalibration OilApproximateViscosity at 150 °CAApproximate Pressurefor Test Method(mPa·s) psi kPaHT22 1.5 190 1310HT39 2.0 225 1550HT75 2.7 290 2000HT150 3.7 375 2590HT240 5.0 480 3310HT390B7.0 645 4450AConsult the supplier for specific values.BConsult the supplier for use in instruments with pressure limiters of 525 psi.D5481 − 1339.3 Stability of Temperature Calibration—Check the cali-bration of the temperature sensor at least once a year using astandardized thermometer inserted in the thermowell in thealuminum block.10. Procedur