Polymer RheologyLI Xiang-GangHunan University of TechnologyPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com¾剪切应力及剪切速率剪切应力Shear stressτ=F⎡N⎢⎤A⎣m2⎥⎦=[Pa]单位面积所受的作用力应变Strainγ=S⎡h⎢m⎤⎣m⎥⎦=constant单位长度的伸长剪切速率Shearrate&γ=(D=)v=dγ⎡dt⎢m⎤⎡1⎤−1h⎣×sm⎥⎦=⎢⎣s⎥⎦=[s]单位时间的应变，也称为“剪切梯度”、“速度梯度”、“应变率”、“变形率”）Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comViscosity ValuesMaterialsShearviscosity ηGases / air0.01to 0.02/ 0.018mPaxsWaterat 20°C / at 0°C / at 40°C1.00/ 1.79/ 0.65mPaxsMilk, coffeecream2 to 10 mPaxsOlive oilapprox. 100 mPaxsGlycerine1480 mPaxsPolymer melts(T=+100 to +200°C 10 to 10 000 Paxsand at shear ratesof 10 to 1000 1/s)Polymer melts(zero-shearviscosity)1 kPas to 1MPaxsBitumen (T = +80 / +60 / +40 / 200 Paxs/ 1kPaxs/ 20 kPaxs/ +20 / +0°C)0.5MPaxs/ 1 MPaxsPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com3.1 基本概念platemovingwithFN=σ⋅A=const.constantvelocityFT=τ⋅A=const.solid body→equilibrium after finite deformation provoked by FNand FTfluid→deformation arbitrarily largecombined behaviour(solid body / fluid)→behaviourof a solid body up to a critical stress τ0→behaviourof a fluid after exceeding the critical stress τPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com0¾粘度的定义（剪切）粘度（(shear) viscosity）：η=τ⎡⎢Pa⎤γ&⎣1/s⎥⎦=[Pax]s1 Paxs= 1000 mPaxs1 MPaxs= 1000 kPaxs= 1 Mio. Paxs以前所用单位：厘泊(1643 –1727)1 cP = 1mPaxs•牛顿流体（Newtonian Fluid）: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-Newtonian Fluid）：粘度随时间的变化而变化。如，聚合物溶液等Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comThe Idealized Flow Curve1) Sedimentation2) Leveling, Saggingη3) Draining under gravityg4) Chewing and swallowingo5) Dip coatingl6) Mixing and stirring7) Pipe flow8) Spraying and brushing9) Rubbing10) Milling pigments in fluid base11) High Speed coating45689123710111.00E-51.00E-41.00E-30.01000.1001.0010.00100.001000.001.00E41.00E51.00E6shear rate (1/s)Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com1ϕ¾运动粘度kinematic viscosity: ν=ηρ⎡⎢mm2⎤⎡m2⎢⎣s⎥⎥=⎢10−6⎤⎥⎦⎢⎣s⎥⎦previouslyusedunit(沲):21cSt=1mmsunitof density: ρ=1gcm3=1000kgm3The kinematic viscosity ever then ismeasured, if gravity is the driving force(weight of the sample).e.g. using: flow cups andcapillary viscometersPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com¾理想粘性流动行为（IdealviscousFlow Behavior）或称：Newtonian流动行为（牛顿流体）flowcurves（流动曲线）viscositycurves（粘度曲线）Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com¾Summary: MeasuringParametersPhysical ParametersRheologicalParametersraw data, calculatedvalues,dependenton themeasuringsystemindependent of the measuring systemtorque M [Nm]shearstress τ=CSS⋅M[Pa]rotational speed n [1/min]shearrate &=deflectionangle[°], [rad]shear deformation γγCSR⋅n[1/s]=CSD⋅ϕ[1or%]viscosity η=τ/&γ⎡⎢⎣η⎤⎥⎦=Passhear modulusG=τ/γ⎡⎤⎢⎢⎣G⎥⎦⎥=PaPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comPresettings for Flow Curvesshear rate rampshear stress rampCSR: controlled shear rateCSS: controlled shear stress受控剪切速率受控剪切应力Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comRaw Dataand Rheological ParametersRotation CSRTest presettingResultraw dataspeedn [1/min]torqueM [mNm]rheologicalparametersshearrate [1/s]&γshear stress τ[Pa]Rotation CSSTest settingResultrawdatatorqueM [mNm]speedn [1/min]rheologicalparametersshear stress τ[Pa]shearrate [1/s]&γPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com2Summary of Types of ‘Flow’flowτ Bingham (Newtonian with yield stress),sserBingham PlastictS(shear-thinning with yield stress) raehShear Thinning (Pseudoplastic)SτNewtonianyShear Thickening (Dilatant)deformationShear Rate, γ•Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comFlow Behavior0(log. scales)flow curvesviscosity curveszero-shearviscosityyieldpoint1 idealviscous(Newtonian)2 shear-thinning (pseudoplastic)3 shear-thickening (dilatant)4 withzero-shearviscosity5 without zero-shear viscosity Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comFlow Behavior(linear scales)flow curves viscosity curvesyieldpoint1 idealviscous(Newtonian)（牛顿流体）2 shear-thinning (pseudoplastic)（非牛顿流体：剪切稀释型）3 shear-thickening (dilatant)（非牛顿流体：胀凝型）4 withoutyield point（非牛顿流体：不具有屈服值）5 withyieldpoint（非牛顿流体：具有屈服值）Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comFlow and Viscosity CurvesSummary1: idealviscous(Newtonian)2: shear-thinning (pseudoplastic)3: shear-thickening (dilatant)Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com3Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com3.2 tensor basisPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com4Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com第一法向应力差一般都为正，而且当切变速率很高时，在数值上可能大于切应力。第一法向应力差为正，说明分子取向引起的拉伸力与流线平行。第二法向应力差一般为负值，其绝对值也很小，通常约为第一法向应力差的1／10。有些学者认为第二法向应力差既可能为零也可能为正值。Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com3.3 高分子液体流动中的弹性效应高分子液体流动时，表现出形形色色的奇异弹性行为。主要有挤出过程中的挤出胀大现象，不稳定流动和熔体破裂现象，“爬杆”现象（Weissenberg效应），拉伸流动等。高分子液体的弹性属于熵弹性。在流动过程中，材料的粘性行为和弹性行为交织在一起，使流变性十分复杂。研究高分子液体的弹性规律性对高分子材料加工也十分重要。实验发现，几种粘度相近、分子量分布大致相同的聚乙烯熔体，其加工行为却有很大差异，分析得知，这些差异主要因为不同熔体的弹性行为（拉伸粘度和法向应力差）不同引起的。Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.comPolymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com法向应力差在牛顿流体中为0，它是非牛顿聚合物流体的特点。法向应力是聚合物材料弹性的主要体现；弹性是由于链段的取向造成的，而大分子之间的缠结又大大有利于形变时链段的弹性回复。沿着与剪切力垂直的方向上发生膨胀, 使平行板发生分离Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com（一）挤出胀大现象挤出胀大现象又称口型膨胀效应或Barus效应，是指高分子熔体被强迫挤出口模时，挤出物尺寸大于口模尺寸，截面形状也发生变化的现象（图6-12）。对园型口模，挤出胀大比B定义为：B=di/D(6-10)式中D 为口模直径，di为完全松弛的挤出物直径。Polymer Rheology,LiXiang-Gang,Hunan图6-12 挤出胀大现象及其说明University of Technology,lixiangfm@163.com5讨论（1）挤出胀大现象是高分子液体具有弹性的典型表现。从弹性形变角度看，熔体在进入口模前的入口区受到强烈拉伸作用，发生弹性形变。这种形变虽然在口模内部流动时得到部分松弛，但由于高分子材料的松弛时间一般较长，直到口模出口处仍有部分保留，于是在挤出口模失去约束后，发生弹性恢复，使挤出物胀大。（2）从熵弹性角度考虑，无规线团状的大分子链在口模入口区被强烈拉伸，构象发生改变，构象熵减少。同样这种构象变化在口模内部部分得到松弛，但仍有部分直到挤出口模后才回复。挤出后的分子链回复到新的无规线团构象，使熵值升高而胀大。（3）实验表明，一切影响高分子熔体弹性的因素都对挤出胀大行为有影响。如挤出温度升高，或挤出速度下降，或体系中加入填料而导致高分子熔体弹性形变减少时，挤出胀大现象明显减轻。Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com讨论（1）虽然关于发生不稳定流动的机理目前尚无统一认识，但各种假定都认为，这也是高分子液体弹性行为的表现。（2）就熔体破裂现象而言，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素有关。（3）从形变能的观点看，高分子液体的弹性贮能本领是有限的。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，多余的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。Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com爬杆现象是一种有趣的高分子液体弹性行为。出现这一现象的原因仍然追寻到高分子液体的粘弹性。分析得知，在所有流线弯曲的剪切流场中高分子流体元除受到剪切应力外（表现为粘性），还存在法向应力差效应（表现为弹性）。图6-15 流体元上的应力分布状态Polymer Rheology,LiXiang-Gang,HunanUniversity of Technology,lixiangfm@163.com（二）不稳定流动和熔体破裂现象实验表明，高分子熔体从口模挤出时，当挤出速率（或剪切应力）超过某一临界剪切速率γ&力），容易出现弹性湍流，导致流动不稳定，挤出物表面c（或临界剪切应σc粗糙。随挤出速率的增大，可能先后出现波浪形、鲨鱼皮形、竹节形、螺旋形畸变，最后导致完全无规则的熔体破裂Polymer Rheology,Li图6-13 Xiang-Gang,Hunan不稳定流动的挤出物外观示意图University of Technology,lixiangfm@163.com（三）“爬杆”现象（Weissenberg效应）与牛顿型流体不同，盛在容器中的高分子液体，当插入其中的圆棒旋转时，没有因惯性作用而甩向容器壁附近，反而环绕在旋转棒附近，出现沿棒向上爬的“爬杆”现象。这种现象称Weissenberg效应，又称“包轴”现象。牛顿型流体高分子液体pA>pBpA