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1、High Pressure Capillary Rheometry1 IntroductionPolymers are used because:They are cheap to form into shape in molten stateTherefore,We need to understand how they flow when moltenalso important in: food processing, pharmaceuticals, paints, inks, pastes, slurries etc. Very important in Polymer Proces
2、singBut, molten polymers are complicated systems.Temperature dependentRate dependentTime dependentWork dependent(and thats before we add lubricants, fillers, plasticisers, foaming agents etc!)In between a liquid and a solid Influences on Viscosity molecular structure of sample temperature pressure t
3、ime shear rate (T,p, t, ) = .Shear viscosity definition - -shear rate. - -shear stress = . - -shear viscosityViscosity is a measure of resistance of a fluid against the applied shear force.Shear viscosity is only one part of Rheology. It is the dominant effect for pressure in extruders, injection mo
4、ulding machines and dies.Typical process shear ratesRelaxationCoatingFree surfaceMixingExtrusion Injection moulding Why do we need a high-pressure capillary rheometer?The application is importantThe application is importantlog log /s/s-1-1DMA Osc.DMA Osc. / Rot. rheometer / Rot. rheometerHigh pressu
5、re capillary rheometerHigh pressure capillary rheometerViscosities: (low-), middle- to high-viscousViscosities: (low-), middle- to high-viscousQuantities: Shear- and extensional viscosity, wall slip Quantities: Shear- and extensional viscosity, wall slip relaxation, PVT, Flow instabilities relaxatio
6、n, PVT, Flow instabilities1010-1-11010-3-3LevellingLevelling10104 410101 1Extrusion, Injection MouldingExtrusion, Injection Moulding10100 010102 2MixingMixing10103 310106 6Roll Coating, SprayingRoll Coating, SprayingViscosities: low viscous to solid-likeViscosities: low viscous to solid-likeQuantiti
7、es: Shear viscosity, yield, viscoelastic properties, relaxation etc.Quantities: Shear viscosity, yield, viscoelastic properties, relaxation etc.Non-destructiveNon-destructiveOscillarory shearOscillarory shear rot. rot. rheometerrheometer: : structuralstructural/ /low shear measurements low shear mea
8、surements high- high-pressure capillarypressure capillary: : processing flow behaviourprocessing flow behaviour Single point test (generates one number)MFI die (2.095mm diameter) Defined by standards (ISO1133) Simple Cheap Easy to use Pressure drivenMelt Flow Indexer (MFI)Melt Flow Indexer (MFI) Sin
9、gle point test Does not generate engineering units - (grams per 10 minutes) Mainly a shear flow measurement- neglects extension Very low shear rate test( app = 2.4 MFI)But,Typical process shear ratesRelaxationCoatingFree surfaceMixingExtrusion Injection mouldingMFItestCapillary RheometerMeasure:Pres
10、sure dropPiston Capillary die Pressure transducer Polymer melt Set:Piston speedDie DimsCapillary rheometryWe set:Temperature, piston speed, die geometryWe measure:Melt pressure (long & short dies)Giving us:Shear stress (at a range or rates)Extensional stress (at a range or rates)Capillary rheometryL
11、ong die: shearShort die: extension3 Shear viscosity完全发展区剪切应力的计算管壁处3 Shear viscosity不可压缩性流体剪切速率的计算L2R3 Shear viscosityGiven quantity: piston speed wall shear rateMeasured quantity: pressure drop wall shear stressEntrance pressure dropEntrance pressure dropShear pressure dropShear pressure dropvMeasur
12、ed pressure Measured pressure dropdrop=+PLBARRELPLPlPwENTRANCELENGTH FULLY DEVELOPEDFLOW REGION0Z0L small ram extrudersmall ram extruderMeasuring PrinciplePressure drop through a capillary/slit dieNewtonian fluidshear rate , = 4Q / r3 shear stress, = Pr / 2L shear viscosity, = /Shear Flow Analysis .
13、 .()(). . .Calculation of Entrance Pressure Drops1. Historical Bagley-Method according to DIN 11443 full 10 20 30 40High shear rateLow shear rateL/DPges (L/D=0) = Entrance Pressure Drop Principle: Measurement of the Full Pressure Drop at constant Shear rate and different L / D ratio Linear extrapola
14、tion to L / D = 0E. B. Bagley, J. Appl. Physics 28 (1957), 624 Calculation of Entrance Pressure Drops2. Practical Difficulties with Historical Bagley Method2. Practical Difficulties with Historical Bagley Methodfull10 20 30 40L/Dnegative Entrance Pressure Drop !negative Entrance Pressure Drop ! ?Pro
15、blems:Problems: linear linear extrapolation extrapolation can leadcan lead to to physically impossible physically impossible resultsresults Extrapolation Extrapolation shows very large standard deviationshows very large standard deviationCalculation of Entrance Pressure Drops3. Reasons for the Error
16、s in ExtrapolationReasons: at small L/D -values non-linearities occur for all samples at the moment there is no theoretical approach at high L/D-values non-linearities due to wall slip, compressibility . (theoretical prediction) )full 2 4 6 8 10 12L/DNon-linearities at small L / DHistorical BagleyTrue curve Kelly, Coates, Dobbie, Fleming, Plastics, Rubber and Composites Processing and Applications1996, vol.25, No.7, 313. Datas not true to scale. .Calculation of Entrance Pressure Drops4. Solution
