【正文】 High Pressure Capillary Rheometry 1 Introduction Polymers are used because: ? They are cheap to form into shape in molten state Therefore, ? We need to understand how they flow when molten also important in: food processing, pharmaceuticals, paints, inks, pastes, slurries etc... Very important in Polymer Processing But, molten polymers are plicated systems... ? Temperature dependent ? Rate dependent ? Time dependent ? Work dependent (and that’s 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 ? time ? shear rate ? ? (T, p, t, g) = g . . Shear viscosity definition g shear rate . ? shear stress ? ? = g . ? shear viscosity ?Viscosity 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 moulding machines and dies. 1 . E + 0 01 . E + 0 21 . E + 0 41 . E + 0 61 . E + 0 81 . E 0 5 1 . E 0 3 1 . E 0 1 1 . E + 0 1 1 . E + 0 3 1 . E + 0 5S he a r r a t e ( s1)Viscosity (Pa.s)Typical process shear rates Relaxation Coating Free surface Mixing Extrusion Injection moulding Why do we need a highpressure capillary rheometer? The application is important log g/s1 DMA Osc. / Rot. rheometer High pressure capillary rheometer Viscosities: (low), middle to highviscous Quantities: Shear and extensional viscosity, wall slip relaxation, PVT, Flow instabilities 101 103 Levelling 104 101 Extrusion, Injection Moulding 100 102 Mixing 103 106 Roll Coating, Spraying Viscosities: low viscous to solidlike Quantities: Shear viscosity, yield, viscoelastic properties, relaxation etc. Nondestructive Oscillarory shear ? rot. rheometer: structural/low shear measurements – highpressure capillary: processing flow behaviour ? Single point test (generates one number) MFI die ( diameter) ? Defined by standards (ISO1133) ? Simple ? Cheap ? Easy to use ? Pressure driven Melt Flow Indexer (MFI) Melt Flow Indexer (MFI) ? Single point test ? Does not generate engineering units (grams per 10 minutes) ? Mainly a shear flow measurement neglects extension ? Very low shear rate test (gapp = MFI) But, 1 . E + 0 01 . E + 0 21 . E + 0 41 . E + 0 61 . E + 0 81 . E 0 5 1 . E 0 3 1 . E 0 1 1 . E + 0 1 1 . E + 0 3 1 . E + 0 5S he a r r a t e ( s1)Viscosity (Pa.s)Typical process shear rates Relaxation Coating Free surface Mixing Extrusion Injection moulding MFI test Capillary Rheometer Measure: Pressure drop Piston Capillary die Pressure transducer Polymer melt Set: Piston speed Die Dim’s Capillary rheometry We set: Temperature, piston speed, die geometry We measure: Melt pressure (long amp。 short dies) Giving us: Shear stress (at a range or rates) Extensional stress (at a range or rates) Capillary rheometry Long die: shear Short die: extension 3 Shear viscosity ? 完全發(fā)展區(qū)剪切應(yīng)力的計算 ? 管壁處 22 rPrL ??? ???L2Pr???LPR2???3 Shear viscosity ? 不可壓縮性流體剪切速率的計算 )zv( r00rz ???? ?g?? ?2rzp11rv0rz0r????????? )rR(zp41v 220r??? ?zp8Rr d r)rR(zp21drvr2Q04220R0rR0 ????????? ???????30Nw R4Q???g ? ???L 2R 3 Shear viscosity Given quantity: piston speed ? wall shear rate Measured quantity: pressure drop ? wall shear stress Entrance pressure drop Shear pressure drop v Measured pressure drop = + P L BARREL PL Pl Pw ENTRANCE LENGTH FULLY DEVELOPED FLOW REGION 0 Z 0 L ? small ram extruder Measuring Principle Pressure drop through a capillary/slit die N o n Ne w to n ia n flu id rh e o lo g ic a l equ a tio n o f sta te :( p o w e r la w ) ? = K ( a )n ? = K . a n 1n = ? lo g ? / ? lo g aNewtonian fluid shear rate , = 4Q / ? r3 shear stress, ? = ?Pr / 2L shear viscosity, ? = ? / Shear Flow Analysis w he r e : K = co nsiste ncy i nd e x ( P n ) n = po w e r l aw ( n o n N e w t o ni an) i nd e x Q = v o l um e tr ic f l o w r ate m 3 / m i n r = capi l l ar y r adi us ( m ) L = ca pi l l ar y l e ng th ( m ) . ? P = p r e s s ur e d r o p ( P a )g . g . (g) . g . g . Calculation of Entrance Pressure Drops 1. Historical BagleyMethod according to DIN 11443 10 20 30 40 L/D Pges (L/D=0) = Entrance Pressure Drop ? ? ? ? 176。 176。 176。 176。 Principle: ? Measurement of the Full Pressure Drop at constant Shear rate and different L / D ratio ? Linear extrapolation to L / D = 0 E. B. Bagley, J. Appl. Physics 28 (1957), 624 DDnL PDLDL PDL PPDLP f u l lf u l len tf u l l ??????????? ///Calculation of Entrance Pressure Drops 2. Practical Difficulties with Historical Bagley Method 10 20 30 40 L/D negative Entrance Pressure Drop ! ? ? ? ? ?