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1、High Pressure Capillary Rheometry,1 Introduction,Polymers 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 Processing
2、,But,molten polymers are complicated systems.,Temperature dependent,Rate dependent,Time dependent,Work 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 ti
3、me shear rate,Shear viscosity definition,t-shear stress,-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.,Typical proc
4、ess shear rates,Relaxation,Coating,Free surface,Mixing,Extrusion,Injection moulding,Why do we need a high-pressure capillary rheometer?,The application is important,log/s-1,Viscosities:(low-),middle-to high-viscousQuantities:Shear-and extensional viscosity,wall slip relaxation,PVT,Flow instabilities
5、,Viscosities:low viscous to solid-likeQuantities:Shear viscosity,yield,viscoelastic properties,relaxation etc.,Non-destructiveOscillarory shear,rot.rheometer:structural/low shear measurements high-pressure capillary:processing flow behaviour,2.Structure,2.16kg,Single point test(generates one number)
6、,MFI die(2.095mm 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(app
7、=2.4 MFI),But,Typical process shear rates,Relaxation,Coating,Free surface,Mixing,Extrusion,Injection moulding,MFItest,Capillary Rheometer,Measure:Pressure drop,Piston,Capillary die,Pressure transducer,Polymer melt,Set:Piston speedDie Dims,Capillary rheometry,We set:,Temperature,piston speed,die geom
8、etry,We measure:,Melt pressure(long&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,L,2R,3 Shear viscosity,Given quantity:piston
9、speed wall shear rateMeasured quantity:pressure drop wall shear stress,v,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,Newtonian fluidshear rate,=4Q/r3 shear stress,=Pr/2L shear viscosity,=/,S
10、hear Flow Analysis,Calculation of Entrance Pressure Drops,1.Historical Bagley-Method according to DIN 11443,full,10 20 30 40,High shear rate,Low shear rate,L/D,E.B.Bagley,J.Appl.Physics 28(1957),624,Calculation of Entrance Pressure Drops,2.Practical Difficulties with Historical Bagley Method,full,10
11、 20 30 40,L/D,?,Calculation of Entrance Pressure Drops,3.Reasons for the Errors in Extrapolation,full,2 4 6 8 10 12,L/D,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 Drops,4.Solutio
12、n:Double capillary system,full,5 10 15 20,L/D,The Rosand Double Capillary System with orifice die,Measure the die entrance pressure drop directly,L,2R,v,pentrance,pshear,Pfull,Pfull=Pshear+Pentrance,v,pentrance,left:Capillary dieright:Orifice die,Rabinowitsch Correction,For non-Newtonian flow profil
13、e,Rabinowitsch Correction,Corrected shear flow(polymer melts)If n=0.5,=1.25*,polyethylene 0.3 to 0.6polypropylene0.3 to 0.4PVC 0.2 to 0.5polyamide0.6 to 0.9.,Optional,but try to keep consistency!,Wall Slip correction,Wall Slip,A fundamental assumption in most rheology is velocity at the metal wall=0
14、,Slip is well known to occur in PVC,HDPE and metallocene catalysed polymers,Difficult to measure-can be approximated using capillary rheometry,Slip is affected by fillers and lubricants,Evidence of wall slip,Wall Slip Correction,Result:Dependency of wall slip velocity on shear stress(true shear rate
15、),Mooney,M.,J.Rheology 2,210(1931),Wall Slip Measurement,Slip component of flowrate,Q=R2 v,Vs mm/s w kPa,PE Vs=1.50(w/100)3.20 w 90 kPa,PVC Vs=9.5(w/100)2.28,Some typical slip velocities,Many materials only slip above a critical stress,typically 0.1 MPa,Extensional Flow Analysis,4 Extensional Flow A
16、nalysis,4 Extensional Flow Analysis,4 Extensional Flow Analysis,4 Extensional Flow Analysis,拉伸黏度是在实际纺丝过程即非稳态拉伸流中的黏度。表观拉伸黏度定义为：,采用摄影的方法，对稳态的丝条拍照，从照片量取纤维直径沿轴向的变化数据,Extensional Flow Analysis,5 melt fracture,实际成型加工及流变测量中，物料流动状态受诸多因素影响，常常出现不稳定流动情形。许多情况下，流场边界条件存在一个临界值。一旦超越该临界值，就会发生从层流到湍流，从平整到波动，从管壁无滑移到有滑移
17、的转变，破坏了事先假定的稳定流动条件。研究这类熔体流动不稳定性及壁滑现象是从“否定”意义上讨论高分子的流变性质，具有重要意义。该问题的工程学意义是，当工艺过程条件不合适，会造成制品外观、规格尺寸及材质均一性严重受损，直接影响产品的质量和产率，严重时甚至使生产无法进行。高分子流动不稳定性主要表现为挤出过程中的熔体破裂现象、拉伸过程（纤维纺丝和薄膜拉伸成型）中的拉伸共振现象及辊筒加工过程中的物料断裂现象等。熔体在管壁发生滑移与此类现象密切相关。可以肯定地说，这些现象与高分子液体的非线性粘弹行为，尤其是弹性行为有关，是高分子液体弹性湍流的表现。,熔体的挤出破裂行为：在挤出过程中，当熔体剪切速率超过某
18、一临界剪切速率时，挤出物表面开始出现畸变的现象。表现为：最初表面粗糙，而后随剪切速率（或切应力）的增大，分别出现波浪型、鲨鱼皮型、竹节型、螺旋型畸变，直至无规破裂。,从现象上分，挤出破裂行为可归为两类：一类称LDPE（低密度聚乙烯）型。破裂特征是先呈现粗糙表面，当挤出超过临界剪切速率发生熔体破裂时，呈现无规破裂状。属于此类的材料多为带支链或大侧基的聚合物，如聚苯乙烯、丁苯橡胶、支化的聚二甲基硅氧烷等。,一类称HDPE（高密度聚乙烯）型。熔体破裂的特征是先呈现粗糙表面，而后随着剪切速率的提高逐步出现有规则畸变，如竹节状、螺旋型畸变等。很高时，出现无规破裂。属于此类的材料多为线型分子聚合物，如聚丁
19、二烯、乙烯-丙烯共聚物，线型的聚二甲基硅氧烷、聚四氟乙烯等。这种分类不够严格，有些材料的熔体破裂行为不具有这种典型性,流变曲线的差别：属于LDPE型的熔体，其流变曲线上可明确标出临界剪切速率或临界剪切力 位置，曲线在临界剪切速率之前为光滑曲线，之后出现波动，但基本为一连续曲线属于HDPE型的熔体，其流变曲线在达到临界剪切速率后变得复杂。随着剪切速率的提高，流变曲线出现大幅度压力振荡或剪切速率突变，曲线不连续，有时使流变测量不能进行,造成熔体破裂现象的机理十分复杂，肯定地说，它与熔体的非线性粘弹性、与分子链在剪切流场中的取向和解取向（构象变化及分子链松弛的滞后性）、缠结和解缠结及外部工艺条件诸因
20、素有关。从形变能的观点看，高分子液体的弹性是有限的，其弹性贮能本领也是有限的。当外力作用速率很大，外界赋予液体的形变能远远超出液体可承受的极限时，多余能量将以其它形式表现出来，其中产生新表面、消耗表面能是一种形式，即发生熔体破裂。,Elongational viscosity influence,Convergence into a flat entry die,LDPE,HDPE,Also important in any convergent or divergent part of a process,Tordella的流动双折射实验对LDPE型熔体，其应力主要集中在口模入口区，且入口区
21、的流线呈典型的喇叭型收缩，在口模死角处存在环流或涡流。当剪切速率较低时，流动是稳定的，死角处的涡流也是稳定的，对挤出物不产生影响。但当剪切速率 后，入口区出现强烈的拉伸流，其造成的拉伸形变超过熔体所能承受的弹性形变极限，强烈的应力集中效应使主流道内的流线断裂，使死角区的环流或涡流乘机进入主流道而混入口模。主流线断裂后，应力局部下降，又会恢复稳定流动，然后再一次集中弹性形变能，再一次流线断裂。这样交替轮换，主流道和环流区的流体将轮番进入口模。这是两种形变历史和携带能量完全不同的流体，可以预见，它们挤出时的弹性松弛行为也完全不同，由此造成口模出口处挤出物的无规畸变。,对HDPE型熔体，其流动时的应
22、力集中效应主要不在口模入口区，而是发生在口模内壁附近，口模入口区不存在死角环流。低剪切速率时，熔体流过口模壁，在壁上无滑移，挤出过程正常。当剪切速率 增高到一定程度，由于模壁附近的应力集中效应突出，此处的流线会发生断裂（后面将说明，流线断裂的一个原因是由于分子链解缠结造成的）。又因为应力集中使熔体贮能大大增加，当能量累积到超过熔体与模壁之间的摩擦力所能承受的极限时，将造成熔体沿模壁滑移，熔体突然增速（柱塞上压力下降），同时释放出能量。释能后的熔体又会再次与模壁粘着，从而再集中能量，再发生滑移。,这种过程周而复始，将造成聚合物熔体在模壁附近“时滑时粘”，表现在挤出物上呈现出竹节状或套锥形的有规畸
23、变。当剪切速率再增大时，熔体在模壁附近会出现“全滑动”，这时反而能得到表面光滑的挤出物，即所谓第二光滑挤出区。此时应力集中效应将转到口模入口区。在极高的剪切速率下，熔体流线在入口区就发生扰乱，这时的挤出物必然呈无规破裂状。,13 影响熔体挤出破裂行为的因素一切能够影响熔体弹性的因素，都将影响聚合物熔体的挤出破裂行为。这些因素大致可分为三类：一是口模的形状和尺寸；二是挤出成型过程的工艺条件；三是挤出物料的性质。,131 口模形状、尺寸的影响口模的入口角对LDPE型熔体的挤出破裂行为影响很大。实验发现，当入口区为平口型（入口角）时，挤出破裂现象严重。而适当改造入口区，将入口角减小变为喇叭口型时，挤
24、出物外观有明显改善；且开始发生熔体破裂的临界剪切速率（或临界剪切应力）增高。口模的定型长度L对熔体破裂行为也有明显影响。对于LDPE型熔体，已知造成熔体破裂现象的根源在于入口区的流线扰动。这种扰动会因聚合物熔体的松弛行为而减轻，因而定型长度L越长，弹性能松弛越多，熔体破裂程度就越轻，对于HDPE型流体，熔体破裂现象的原因在于模壁处的应力集中效应，因而定型长度越长，挤出物外观反而不好。,132 挤出工艺条件和物料性质的影响给出低密度聚乙烯在不同挤出速度（不同剪切速率）下通过同一个口模时，测得的压力波动沿口模轴向的分布图。已知低密度聚乙烯通过口模时，其弹性形变主要发生在入口区。，挤出速度越小，材料
25、发生的弹性形变小，且形变得以松弛的时间较长，因此熔体内的压力波动幅度较小。适当升高熔体温度是另一个典型例子。熔体温度升高，粘度下降，会使松弛时间缩短，从而使挤出物外观得以改善。因此在工厂中，升高料温（特别是口模区温度）是解决熔体破裂的快速补救办法。,从材料角度看，平均分子量大的物料，最大松弛时间较长，容易发生熔体破裂。而在平均分子量相等的条件下，分子量分布较宽（较大）的物料的挤出行为较好，发生熔体破裂的临界剪切速率 较高，这可能与宽分布试样中低分子量级分的增塑作用有关。填料的作用。无论填加填充补强剂还是软化增塑剂，都有减轻熔体破裂程度的作用。这一是因为某些软化剂的增塑作用；二是填料本身无熵弹性
26、，填入后使能够发生破裂的熔体比例减少。,A deeper look inside,What happens in the entrance zone of a capillary die?,a change in cross-section leads to a entrance-pressure-drop because of:,Elastic stringing,Acceleration,secondary flow,Extensional,viscous flow,Comparison of Typical Shear Data,Comparison of Typical Extensi
27、on Data,Typical Polymer Processing Temperatures,1.Polyolefins:190C,Polyethylene(HDPE,LDPE,LLDPE)Polypropylene(PP),2.PVC:165-180,UPVC and plasticised,3.Engineering Polymers:240-300C,Nylon,PET,ABS,4.Rubbers:80-100C,Cogswell:Entrance Pressure Drop Extensional Viscosity,Shear viscosity curve,1,10,100,10
28、00,1,10,100,1000,10000,100000,Corrected shear rate 1/s,Shear viscosity Pas,sample 1,sample 2,Extensional viscosity curve,10,100,1,10,100,1000,10000,Extensional rate 1/s,Extensional viscosity kPas,Differences only in extension(Structure sensitivity),Benefits of Capillary Rheometry,Comparison of Data
29、from Capillary&Rotational Rheometers,Polypropylene Measured at 190 C,Comparison of Data from Capillary&Rotational Rheometers,Analysis of Flow Curves,Online-pressure drop homogeneity of your sample,important factor for quality(influence of Mixing,pre-shear etc.),homogeneous:,inhomogeneous:,g,.,t,Prin
30、ciple:Ramp in steps,Analysis of inhomogeneities,Pressure deviations gives approx.average length scale,mainly used for polymer blends,suspensions.,3 common corrections in capillary rheometry,1.Bagley(entrance pressure losses),2.Rabinowitsch(non-Newtonian flow),3.Wall Slip(non-zero velocity at die wal
31、l),Flow curves Measurement,Sequence of shear steps,measurement:,D,v,t,t,Step Rate,p,Apparent values-data has to be corrected.,Advantages of Capillary Rheometry,Pressure driven,Mimics the process(flow through a die/nozzle),Simple to use,Robust,Simple to interpret,Accurate drive system,Accurate temper
32、ature control,*engineers point of view,Advantages of Capillary Rheometry,Wide shear rate range,from 0.1-100,000/s,Shear and extension,Absolute Data(Bagley,Rabinowitsch,wall slip),Density,compressibility,Die swell&Elasticity,Uniaxial extension,*rheologists point of view,Range of tests on Rosand Rheom
33、eters,Test Procedure I,1.Select the type of test,2.Select the capillary die(s),3.Select the pressure transducer(s),4.Set machine temperature,5.Set machine parameters-overload limits,equilibrium determination,6.Run test,Test Procedure II,1.Charge the barrel,2.Manual compression,3.Start test,4.Pre-tes
34、t stages-compression(2)at set speed-pre-heat(2)total time:9 mins*,5.Test stages,*depend s on bore diameter,Rheometer software,Rheometer softwareresults analysis,1.Steady shear,Test:Data obtained:Uses:,Range of constant shear ratesLong die and optional short die,Shear stress and shear viscosityat a r
35、ange of shear rates,Die design,extruder design,pressure drop prediction,flow modelling,quality control,development,1.Steady Shear,1.Steady Shear,Capillary wall shear rate is only dependent upon die diameter,for a set piston speed.,Typical shear rates:*0.5mm dies:50-100,000 s-11mm dies:10-15,000 s-12
36、mm dies:1-1,500 s-1,Standard Speed machine,Steady Shear-test pressures,Steady Shear-typical results,Steady Shear-typical results,2.Extensional Viscosity,Test:Data obtained:Uses:,Range of constant shear ratesLong die and short die,Extensional stress and extensionalviscosity at a range of shear rates,
37、Die design,pressure drop prediction,flow modelling,quality control,development,film blowing,fibre spinning,2.Shear/extension-typical results,Extension-typical results,3.Melt Fracture,Test:Data obtained:Uses:,Examines areas of melt instabilityLong die and/or short die,or 2 materials,Accurate determin
38、ation of the conditionswhere instability occurs,Die design,profile extrusion,troubleshooting,injection mouldingHDPE,PVC,heavily filled,3.Melt Fracture,3.Evidence of melt fracture,4.Material degradation,Test:Data obtained:Uses:,Range of shear rates with wait stagesLong die and/or short die,Shear and
39、extension varying with timeat a range of shear rates,Time dependent materialsMoisture dependent materialsResidence time designTroubleshooting,4.Material degradation,5.Low speed degradation,Test:Data obtained:Uses:,Constant low shear rateLong die and/or short die,Shear and extension varying with time
40、at a constant shear rate,Time dependent materialsMoisture dependent materialsResidence time designTroubleshooting,5.Low speed degradation,6.Stress relaxation,Test:Data obtained:Uses:,Pressure decay from constant rateLong die and/or short die,Decay in pressure over time-indicative of elastic behaviou
41、r,Time dependent materialsHighly elastic materialsQuality controlThermoforming,6.Stress relaxation,6.Stress relaxation resultsLDPE with Mg(OH)2 filler,7.Flow/No flow,Test:Data obtained:Uses:,Constant shear rate as temperature decreases,single die,Minimum flow temperature,Process designMaterial speci
42、fication,7.Flow/No flow,8.Manual test,Test:Data obtained:Uses:,After initial heat-up,take over manualcontrol&take data points whenever,Shear/extensional data,test pressures,Initial investigationEstablish conditions before testing,9.Low level script,Test:Data obtained:Uses:,Program test yourself,What
43、ever you want,Non-standard testse.g.crosslinking,*need a detailed understanding of how the machine works,10.Wall slip,Test:Data obtained:Uses:,Steady shear using 3 dies with sameL:D ratio,different diameters,Slip velocity vs.shear stress,Die designProcess designTroubleshootingFiller effects,10.Wall
44、slip,10.Wall slip,11.PVT/Density test,Test:Data obtained:Uses:,Compresses melt Special plug die&piston tip,Melt compressibility(versus pressure)Melt density(5%),Flow simulationFiller&additive investigationMaterial specificationTroubleshooting,11.PVT/Density test,11.PVT/density test,11.PVT/density te
45、st resultsLDPE at 200C,12.Fibre spinning test,Test:Data obtained:Uses:,Special haul-off motor&scalesHaul-off speed ramped up,Force vs haul-off speedBreaking point,tensile force,Uniaxial extensionIndication of biaxial extensionEmpirical determination of tensile strength,12.Fibre spinning test,Practic
46、al measurement,Uni-axial extension(Haul Off):Extensional properties at small extension rates,Haul Off:Example,LDPE at different temperatures,Main interest is rupture force under non-isothermal conditions,Laun,Schuch.:J.Rheol.33(1989),119,13.Die Swell Test,Test:Data obtained:Uses:,Laser gauge diamete
47、r measurementof extrudate after exiting die,Extrudate diameter vs.shear rate,Indication of elasticity(high shear rates)Profile extrusion,thermoforming,shrink film etc.,13.Die Swell Test,1.Die-Swell I(Laser-Die-Swell),13.Die Swell Test,2.Die-Swell I(Video-Die-Swell),Die Swell:Example,PP1 has high-mol
48、ecular tail in MwD compared to PP2,Viscosity curves nearly identical elastic response important for profile extrusion,Laun,H.M.:Progr.Coll.Polym.Sci.75(1987),111,Summary,Standard test(shear extension),Other test using standard dies-degradation,relaxation,wall slip,flow/no flow,melt fracture,Speciali
49、st tests-manual,low-level script,Special options-PVT,fibre spinning,Instruments,Desktop and floor standing devices,RH7D&RH10D,RH2100/2200,Measurement,Example:Desktop-RH2000,RH2000(Investigation of dental composites to find optimum geometry for pumping and surface effects),Conclusion,The complete flo
50、w behaviour under processing conditions,Rosand Double Capillary System with Orifice Die:,direct measurement of the entrance pressure drop-no extrapolation needed,calculation of extensional viscosity according Cogswell method,flow curve up to very high shear end extensional rates(107 s-1),ability to
