流变学基础及应用

流变学基础及应用 S MZ HU HH Welcome 使用牙膏时挤出要容易 挤出后要求挺括 在牙刷上不能下陷 刷牙时又要轻松 这就是要求牙膏遇剪切时粘度迅速下降 而静止时又要具备一定的屈服应力 以保持坚挺 牙膏 一个典型的流变学问题 提纲 I 流变学基础1 流变学定义及发展历史2 粘度计及流变仪简介3 稳态流变学4 动态流变学4 1弹性行为及剪切模量4 2粘弹性行为4 3蠕变测试4 4弛豫测试4 5振荡测试II PhysicaMCR300流变仪简介III PhysicaMCR300流变仪应用演示 I 流变学基础 Thepersoninthepicture ThomasG Mezger RheologistofAnton Paar 1流变学及其发展历史 什么是流变学 流变学 研究物质流动和变形的科学 Rheology thescienceofdeformationandflowofmatter SocietyOfRheology SOR 希腊语 rheos toflow 流动 流动行为 www physica de 变形行为 古代 万物皆流 1676虎克定律 弹性固体 形变与受力成正比 1687牛顿定律 粘性液体 流动阻力与流动速度成正比 1905爱因斯坦 悬浮液粘度方程 h hs 1 2 5f 1920宾汉 Bingham 提出 流变学 概念1945首台旋转粘度计面世 Brookfield 1951首台旋转流变仪Rheogoniometer Weissenberg 自1970年开始 流动曲线测试代替以前的单点测试自1980年开始 大规模使用数控和计算机 流变学得到较大发展 流变学的发展历史 中国的流变学 我国流变学的应用研究起步较晚 20世纪60年代还只有个别自发研究 目前的应用研究领域较少 甚至连流变学赖以发展的聚合物加工行业也知之不多 以塑料制品为例 塑料厂引进的模具 吃 进口的聚合物粒子时 制品光滑 美观 可以和国外的同类产品相媲美 而一旦换成国产原料粒子时 产品质量就下降 这是因为所使用的模具是按国外原料的流变性能设计的 而国产原料的流变性与进口原料并不完全相同 所以制品质量下降 尽管生产厂对模具进行完善修改 但也只是凭经验做机械上的改动 并未考虑到粒子的流变性 江体乾 流变学的研究内容 流变学的研究范围及方法 物质状态 性能表现 依据原理 研究方法 稳态流变学 动态流变学 SimpleTestMethods 铲刀试验 troweltest 高粘流体 稠 低粘流体 稀 手指试验 fingertest 粘稠 长 稀薄 短 2流变行为的研究工具 粘度计及流变仪 定性 简单测试 Bostwick稠度计 Consistometer 1samplecontainer max 100ml2gate tobeopenedbyaspring3scaledflowpath 测定流体 如番茄酱等 在一定时间内流过的长度 schematicpresentationofaBOSTWICK constistometer 粘度计 Falling BallViscometers DIN53015ISO12058 measuringtubeincludingtheball stand thermometer jacket fortemp control 落球粘度计 HAAKE GENEQ e g forpastesandpaste likeprintinginks weight printingink fallingrod fallingrodviscometer Laray Falling RodViscometers 落杆粘度计 accordingtoASTMD803andD1545 checkmark Gasbubblerisesafterturningthetube Viscosityevaluationbycomparisontoasetoftubes 气泡粘度计 BubbleViscometers Water Clock Kleps dra fortimemeasurementssince3500yearsinEgypte g 5lcorrespondsto6minflowtime 流杯 FlowCups measurementoftheflowtimedeterminationofthekinematicviscosity 流杯 FlowCups ISODINFord ASTM ZahnEnglerShell DINISO 流杯 CapillaryViscometers 玻璃毛细管粘度计 Stormer粘度计 Preset constanttorque shearstress appliedbyafreefallingweight ingrams Result rotationalspeedofthemeasuringsystem Krebsmeasuringsystem Paddle asarelativemeasuringsystemdesignationinKrebsUnits KU Brookfield粘度计 spindlesasrelativemeasuringsystems cylindersdiskspinsT bar 旋转流变仪 绝对测量系统 圆筒状转子 Cylinder notrecommendedforpastes airbubbles 锥板转子 Cone Plate withdispersionsonlyusefulforparticlesunder5 m 平行板 Parallel plates usefulforgelsandpastes 旋转及振荡流变仪 rotationalandoscillatoryrheometers accordingtoDIN53019andISO3219 HAAKE旋转流变仪 HAAKEExtenCaBer1 HAAKERheoScope HAAKERheoStress1 HAAKERheoStress600 HAAKERotoVisco1 TA旋转流变仪 AR500 AR1000 AR2000 ARES ARES 1s ARES rda ARES rfs Bohlin旋转流变仪 BohlinCVO BohlinC VOR BohlinGemini BohlinV88 Physica旋转流变仪 RheolabMC1 SmartPave MCR300 500 MCR301 501 ACS16 32 毛细管流变仪 Poiseuille Hagen定律 毛细管流变学的基础 DP 2R 毛细管流变仪 HAAKERheoCapS20 HAAKERheoCapT1000 RH7D RH10D RH2100 2200 毛细管流变仪的功能 在聚合物工业中 无论旋转流变仪还是毛细管流变仪 其作用都是 模仿聚合物加工过程中的流动和变形行为 log s 1 DMAOsc Rot rheometer Highpressurecapillaryrheometer Viscosities low middle tohigh viscousQuantities Shear andextensionalviscosity wallsliprelaxation PVT Flowinstabilities 10 1 10 3 Levelling 104 101 Extrusion InjectionMoulding 100 102 Mixing 103 106 RollCoating Spraying Viscosities lowviscoustosolid likeQuantities Shearviscosity yield viscoelasticproperties relaxationetc Non destructiveOscillaroryshear rot rheometer structural lowshearmeasurementshigh pressurecapillary processingflowbehaviour 聚合物加工过程对应的剪切速率 3稳态流变学 流动行为 基本概念 剪切应力 剪切速率 粘度 牛顿流体的流动行为非牛顿流体 剪切依赖型 的流动行为 剪切稀释 剪切增稠 屈服值 时间依赖型 触变性 震凝性温度依赖型 Shearstress Shearrate 剪切应力及剪切速率 剪切应力 单位面积所受的作用力 剪切速率 1 s s 1 m s m h v D g Strain 应变 单位长度的伸长 constant m m h v g dg dt 单位时间的应变 也称为 剪切梯度 速度梯度 应变率 变形率 TypicalShearRateRanges Application SedimentationofDispersions inthebeginning herbsinsaladdressing after15min Application LevellingandSaggingofaCoating 200 m 0 5m s Calculationoftheshearrate Application Coating Painting Brushing Application AutomotiveCoatings a Plastisols seamsealing underbodyspraying cavityconservationb Primerc Coatings filler basecoat topcoat clearcoat Application OffsetPrintingInks inkcontainer platecylinder rubbercylinder rubbercylinder 1ductor2filmroller3transferroller4rubber5cylindertoapplythepaint67clammyductor8clammyrubber9 paperweb 剪切 粘度 shear viscosity 1Pa s 1000mPa s1MPa s 1000kPa s 1Mio Pa s以前所用单位 厘泊1cP 1mPa s 1643 1727 粘度的定义 Pa s 1 s Pa 牛顿流体 NewtonianFluid 粘度不受剪切速率的影响 为恒定值 如 水 矿物油等非牛顿流体 Non NewtonianFluid 粘度随时间的变化而变化 如 聚合物溶液等 ViscosityValues PresettingsforFlowCurves shearraterampCSR controlledshearrate受控剪切速率 shearstressrampCSS controlledshearstress受控剪切应力 理想粘性流动行为 IdealviscousFlowBehavior 或称 Newtonian流动行为 牛顿流体 flowcurves 流动曲线 viscositycurves 粘度曲线 RawDataandRheologicalParameters Summary MeasuringParameters PhysicalParametersrawdata dependentonthemeasuringsystem RheologicalParameterscalculatedvalues independentofthemeasuringsystem shearstressshearratesheardeformation viscosityshearmodulus FlowBehavior linearscales flowcurves viscositycurves yieldpoint 1idealviscous Newtonian 牛顿流体 2shear thinning pseudoplastic 非牛顿流体 剪切稀释型 3shear thickening dilatant 非牛顿流体 胀凝型 4withoutyieldpoint 非牛顿流体 不具有屈服值 5withyieldpoint 非牛顿流体 具有屈服值 FlowBehavior log scales 1idealviscous Newtonian 2shear thinning pseudoplastic 3shear thickening dilatant 4withzero shearviscosity5withoutzero shearviscosity flowcurves viscositycurves zero shearviscosity yieldpoint IdealviscousFlowBehavior IdealviscousFlowBehavior IdealviscousFlowBehavior ComparisonofIdealviscousandShear ThinningFlowBehavior shear thinning 剪切稀释 pseudoplastic 假塑性 剪切稀释 Shear Thinning 流动行为 flowcurve viscositycurve Shear ThinningFlowBehavior polymermolecules stateatrest coiled entangled stateunderhighshearload deformationinsheardirectiondisentangled consequence shear thinningflowbehavior Shear ThinningFlowBehavior MaterialAtRest DuringShearing HighViscosityDecreaseinViscosity Suspensionwithneedle shapedorplatelet shapedparticles TheparticlesareTheparticlesaresuspendedrandomlyorientated iftherearenointeractionforces AgglomeratedParticles ThesmallprimaryTheagglomeratesareparticlesformdisintegratedintoprimaryagglomerates intheparticles Thedispersionformoflargersecondaryliquidisnolongerboundparticles Theyalsoandagainfreetoflow surroundapartofthedispersionliquidandimmobilizeit Shear ThinningFlowBehavior MaterialAtRest DuringShearing HighViscosityDecreaseinViscosity Shear thinningFlowBehavior Emulsion ThedisperseddropletsThedropletsaredeformedshowtheshapeofandtakeontheshapeofspheres ellipses MaterialAtRest DuringShearing HighViscosityDecreaseinViscosity Shear ThinningFlowBehavior Shear ThinningFlowBehavior Shear ThinningFlowBehavior Allthreesampleshavethesamepigmentconcentrationandshowthesameflowcuptime Shear ThinningFlowBehavior h0 Shear thinning 1 Orientationofthemacromoleculesundershearload disentanglements here the valuedecreases2 Re coilingsduetoviscoelasticbehavior re entanglements here the valueincreases ExplanationoftheZero ShearViscosity 零剪切粘度 ofPolymers Superpositionoftwoprocesses Result Inthelow shearrangethereisnochangeinthetotalviscosityvalue whichisreferredtoasthevalue ViscosityFunctionofPolymers low shearrange flowrange high shearrange withshear thinningzero shearviscosity flowbehavior infinite shearviscosity Shear ThinningFlowBehavior Dependenceofviscosityonconcentrationwithdiluted cc Zero ShearViscosity lowshearviscosity Zero ShearViscosity viscosityincreaseofpolymersolutionswithincreasingmolarmass increasingmolarmassofapolymer atlowshearload athighshearload therodinclinessolidificationoftheslowlyliquidduetoshear thickeningflowbehavior 剪切增稠 Shear Thichening 流动行为 Shear ThickeningFlowBehavior flowcurveviscositycurve shear thickening 剪切增稠 dilatant 胀凝型 Shear ThickeningFlowBehavior Suspension c solidconcentrationshear thickeningofhighlyconcentratedsuspensionsunderhighshearload c Shear ThickeningFlowBehavior Shear ThickeningFlowBehavior comparisonofaqueouschalkstonesuspensions 1 cube shapedparticles 2 sphericalparticlesWithbothsuspensionshavingthesamesolidconcentrationfor 2 shear thickeningflowbehavioroccursathighershearrates Shear ThickeningFlowBehavior linearscaleslogarithmicscales yieldpointaslimitingvalueoftheshearstress 屈服值 YieldValue 也称 屈服点 Yieldpoint 屈服应力 Yieldstress FlowcurvewithYieldPoint lin lin 0 500 1000 1500 2000 2500 3000 Pa t 0 200 400 600 1 000 1 s ShearRate g ketchup t ShearStress FlowcurvewithYieldPoint log log FlowcurveswithYieldPoint lin lin analysisusinganapproximationfunctionforflowcurves FlowandViscosityCurves log log ViscosityCurves log log FlowandViscosityCurves 1 idealviscous Newtonian 2 shear thinning pseudoplastic 3 shear thickening dilatant Summary FlowandViscositycurves 4 withoutyieldpoint5 withyieldpoint Summary viscosityfunctionofpolymers1 rangeofthezero shearviscosity2 flowrange shear thinning 3 rangeoftheinfinite shearviscosity Sometimescatsareverycurious Sometimescatsareverystupid 时间依赖流动行为 Time DependentFlowBehavior StepTest Thixotropy 触变性 presetting measuringresult asrotationaltestwith3intervals low shearconditionshigh shearconditionslow shearconditions stateofreststructuredecompositionstructureregeneration 触变性用来描述材料的结构的破坏与恢复的过程 testconditions 1 interval 0 11 s2 interval 1001 s3 interval 0 11 s Time DependentStructureDecompositionandRegeneration lin log Time DependentFlowBehavior presetting shearrateprofile testin3intervals upwardramp holdtime downwardrampanalysis hysteresisareadisadvantages testinginanon stationarystate nomeasurementofthestructureregeneration evaluationofthehysteresisareainbetweentheflowcurvesasameasureofthestructuredecompositionduringtheholdingtime ThixotropyTest conventional softeningandmelting orsolidificationandcrystallization presetting constantshearconditions shearrateorshearstress result viscosity temperature curvewithsteadilydecreasingorincreasingviscosity respectively gelformationandcuringpresetting constantshearconditions shearrateorshearstress result viscosity temperature curveshowingaviscosityminimum 温度依赖流动行为 Temperature DependentFlowBehavior TemperatureCurve TemperatureCurveandAnalysisaccordingtoArrhenius TemperatureCurveandAnalysisaccordingtoArrhenius 1 T TemperatureCurve Temperature DependentViscosityCurves 3D 3 dimensionaldiagram 4动态流变学 变形行为 4 1弹性行为 Elasticbehavior 剪切形变 ShearDeformation 或应变 ShearStrain ShearStress ShearDeformationorShearStrain RobertHooke 1635to1703 Shearmodulus 1GPa 1000MPa 106kPa 109Pa EmodulusorYoung smodulus ForTensileTestsapplies s tensilestresse elongation withPoisson sratio 弹性行为及剪切模量 Elasticbehavior Shearmodulus 剪切模量及刚性模量 TensileTest TensileTestatthebeginningandaftertheelongation l l l0 TensileStress ElongationDiagramofsteel yieldstress Sandyieldstrength S breakingstress Bandelongationatbreak B Poisson sratio l lengthofthespecimend thicknessofthespecimen clamp specimen forceF linearelasticdeformation E plasticdeformation latticedislocationofcrystals TensileTest TensileTestofamorphous unlinkedorsparselycross linkedpolymersorcoatingfilms Tg glasstransitiontemperature brittlefractureatT Tg coldflowatTg 30 CtoTg rubber elasticatT Tg DefinitionofShearRate a shearrateastime dependentrateofdeformationorstrainrate b shearrateasvelocitygradient explanation 4 2粘弹性行为 Viscoelasticbehavior tack showinglongstrings e g mouthsensationstirringprocess Weissenbergeffect rodclimbingeffect poormixingresultextrusion extrudateswellinge g dimensionstability result Inmanycasesthemeasurementofviscosityonlyisnotsufficientbecauseelasticeffectsareoccuring resultinginviscoelasticbehavior 粘弹性行为 Viscoelasticbehavior ViscoelasticBehaviorofPolyisobutylene PIB dieswellwhenflowingoutWeissenbergeffectduringaofacapillarystirringprocess ViscoelasticBehavior extrusionofapolystyrene viscoelasticbehavior extrudateswelling andmeltfracturetesttemperatureT 190 CdiegeometryL R 24 R 1mm YieldPoint Diagram testwithpresettingoftheshearstress yieldpointaslimitingvalueoftheshearstress determinationoftheyieldpoint yusingthetangentintheelasticdeformationrange determinationoftheyieldpoint yusingthetangentcrossovermethod Thesamplestartstoflownotbeforetheexternalforcesareexceedingtheinternalforcesofthestructure BelowtheyieldpointThereiselasticdeformation YieldPoint Diagram ComparisonoftwoKetchups YieldPoint FlowCurve ComparisonoftwoCoatings linearscales logarithmicscales YieldPoint Diagram ComparisonoftwoCoatings ViscoelasticSolidKelvin VoigtModelparallelconnectionofspringanddashpot ViscoelasticLiquidMaxwellModelserialconnectionofspringanddashpot 粘弹性模型 MaxwellModelforViscoelasticLiquids afteraloadcycle thesampleremainspartlydeformed Kelvin VoigtModelforViscoelasticSolids afteraloadcycle thesampleshowsdelayedbutcompletere formation 法向应力 NormalStress 粘弹性材料运动或形变时 不仅在其形变方向产生应力 而且通常会出现三维形变 可用三维张量描述 X方向 txx txy txzY方向 tyx tyy tyzZ方向 tzx tzy tzz 第一法向应力差 N1 Pa txx tyy 是剪切速率的函数 N1 g 第二法向应力差 N2 Pa tyy tzz 是剪切速率的函数 N2 g 第一法向应力系数 Y1 Pa s2 N1 g2 是剪切速率的函数 Y1 g 利用第一零法向应力系数Y1 0 Pa s2 lim g 0 Y1 g 常数 在双对数坐标上可以发现一个平台值 ViscoelasticBehaviorDifferentialEquations idealviscosbehavior viscositylawofNewton idealelasticbehavior elasticitylawofHooke behaviorofaviscoelasticsolid Kelvin Voigtmodel thetotalshearstressisdistributedonbothmodelcomponents behaviorofaviscoelasticliquid Maxwellmodel thedeformationsorshearrates resp areoccuringforeachindividualmodelcomponent shearstressstepwith creepintimeintervalt0tot2creeprecoveryintimeintervalt2tot4elasticreformationremainingdeformation viscousportion 4 3蠕变实验 CreepTest CreepTest Analysis Burgersmodel CreepTest Analysis a intheLVErangeb outsideoftheLVErange creepcompliance CreepTest CreepCompliance CreepTest shearstrainstep sheardeformationstep withstressrelaxationintimeintervalt2tot3 4 4弛豫实验 RelaxationTest RelaxationTest Analysis relaxationmoduluswiththeplateauvalueG0 RelaxationTimeSpectrumandRetardationTimeSpectrum generalizedgeneralizedMaxwellmodelKelvin Voigtmodel relaxationtimespectrummolarmassdistribution MMD 1 narrowMMD 2 wideMMD w rel amountM g mol molarmass RelaxationTest RelaxationTest RelaxationModulus RelaxationTimeSpectrum RelaxationTimeSpectrum MolarMassDistribution OscillatoryTests Basics 1 Two Plate ModelIdealelasticBehaviorofatotallystiffsample e g stone orsteel noshiftbetweenthesinecurvesofshearstressandsheardeformation thecurvesof and areinphase 4 5振荡实验 OscillatoryTest OscillatoryTests Basics 2 Presetting constantfrequencyandconstantamplitude here withthestrain deformation amplitudeResult Inmostcasesthesamplesshowviscoelasticbehaviorwiththephaseshift betweenthesinecurvesofpresettingandresult physically G forthestroredandG forthelost dissipated deformationenergytand 1 G G dampingorlossfactor 衰减或损耗因子 asquotientoftheviscousandelasticportions OscillatoryTests Basics 3 VectordiagramG Pa complexshearmodulus复 数 剪切模量elasticitylawofHooke foroscillation G Pa storagemodulus elasticportion储能模量弹性模量G Pa lossmodulus viscousportion耗能模量粘性模量oftheviscoelasticbehavior OscillatoryTests Basics 4 Vectordiagramh Pa s complexshearviscosity复 数 剪切粘度h Pa s G w tA sind gA w h Pa s G w tA cosd gA w h h h d RawDataandRheologicalParameters 振幅扫描 AmplitudeSweep Presetting Result constantfrequencyandStorageModulusG elasticbehavior variablestrain deformation LossModulusG viscousbehavior limitingvalueotthelinearviscoelastic LVE range limitingvalueoftheviscoelasticrange AmplitudeSweep AmplitudeSweep 101 sT 25 C AmplitudeSweep 101 sT 25 C coat1 G G coat2 G G comparisonoftwospraycoatings AmplitudeSweep comparisonoftwocoatings AmplitudeSweep 101 s temperaturedependenceofbutter AmplitudeSweep 101 sT 23 C comparisonoftwostarchgels AmplitudeSweep 101 sT 23 C comparisonoffourstarchgels 频率扫描 FrequencySweep Presetting constantamplitude withintheLVErange andvariablefrequency FrequencySweepofanUnlinkedPolymer g 10 T 23 C FrequencySweep UnlinkedPolymers Maxwellliquidthepositionofthecrossoverpoint basedonasingleofG andG isdependingontheMaxwellmodel molarmassM here M1 M2 FrequencySweep g 10 T 180 C comparisonoftwoPEmelts FrequencySweep g 1 T 170 C crosslinkedPE G G unlinkedPE G G comparisonofunlinkedandcross linkedpolymers FrequencySweep Cross linkedPolymers Gels Dispersions polymerswithdifferent 1 polymerwithunlinkedmoleculesdegreesofcross linkingandanarrowMMD 2 polymerwithunlinkedmoleculesandawideMMD 3 sparselycross linkedpolymer flexiblegelordispersionwithlowstructuralstrengthatrest 4 denselycross linkedpolymer rigidgelordispersionwithhighstructuralstrengthatrest FrequencySweep g 1 T 23 C stabledispersion gelcharacterwithG G atlowfrequenciesinstabledispersion liquidcharacterwithG G atlowfrequencies comparisonoftwocoatings FrequencySweep g 1 T 23 C stabledispersion noh0plateauinstabledispersion withh0plateau comparisonottwocoatings FrequencySweep g 0 3 T 20 C stabledispersion gelcharacterwithG G atlowfrequenciesinstabledispersion liquidcharacterwithG G atlowfrequencies comparisonoftwocosmeticlotions 步进实验 触变性 StepTest Thixotropy low shearconditionshigh shearconditionslow shearconditions stateofreststructuredecompositionstructureregeneration asoscillatorytestwith3intervals Time DependentStructureDecompositionandRegeneration g1 g3 0 2 g2 100 101 sT 23 C 3xoscillation Whatareyoudoing Waitingforketchup Time DependentStructureDecompositionandRegeneration g1 g3 0 3 101 sdg dt 1001 sT 23 C Osc Rot Osc Application AutomotiveCoatings a Plastisols seamsealing underbodyspraying cavityconservationb Primerc Coatings filler basecoat topcoat clearcoat Time DependentStructureRegeneration g1 g3 0 2 dg dt2 150001 s 101 sT 23 C comparisonof3spraycoatings StepTest DecompositionandRegenerationoftheStructure ThixotropicBehavior a rotationaltests 3intervals result time dependentviscosity onlyviscousbehavior b oscillatorytests 3intervals result twotime dependentfunctionsG viscous andG elastic viscoelasticbehavior Temperature DependentSofteningandMelting g 1 101 smeltingtemperatureTm 215 C TemperatureCurve 1 0 1 forT35 C 101 s polymermodifiedbitumen PMB TemperatureCurvesofPolymers amorphouspartiallycrystallinecross linkedTg glasstransitiontemperatureTm meltingtemperature TemperatureCurve 0 1 1 10 101 sglasstransitiontemperature Tg 62 C G max Tg 39 C tandmax polymermeltwithG G athightemperatures unlinkedpartiallycrystallinepol