《高分子流变学》PPT课件资料.ppt

高分子流变学高分子流变学PPTPPT课课件件I.1 Shear Thinning/Thickening(cont.)Tube flow and“shear thinning”.In each part,the Newtonina behavior is shown on the left(N);the behavior of a polymer on the right(P).(a)A tiny sphere falls at the same rate through each;(b)the polymer flows out faster than the Newtonian fluid.Reproduced from R.B.Bird,R.C.Armstrong and O.Hassager,Dynamics of Polymeric Liquids.Vol I:Fluid Mechanics,2nd edition,Wiley-Interscience(1987),p.61.Retrieved from the video of Non-Newtonian Fluid Mechanics(University of Wales Institute of Non-Newtonian Fluid Mechanics,2000)I.2 Normal Stress Difference and ElasticityRod-ClimbingFixed cylinder with rotating rod.(N)The Newtonian liquid,glycerin,shows a vortex;(P)the polymer solution,polyacrylamide in glycerin,climbs the rod.Reproduced from R.B.Bird,R.C.Armstrong and O.Hassager,Dynamics of Polymeric Liquids.Vol I:Fluid Mechanics,2nd edition,Wiley-Interscience(1987),p.63.Retrieved from the video of Non-Newtonian Fluid Mechanics(University of Wales Institute of Non-Newtonian Fluid Mechanics,2000)I.2 Normal Stress Difference and Elasticity(cont.)Extrudate Swell(also called“die swell”)Behavior of fluid issuing from orifices.A stream of Newtonian fluid(N,silicone fluid)shows no diameter increase upon emergence from the capillary tube;a solution of 2.44 g of polymethylmethacrylate(Mn=106 g/mol)in 100 cm3 of dimethylphthalate(P)shows an increase by a factor in diameter as it flows downward out of the tube.Reproduced from A.S.Lodge,Elastic Liquids,Academic Press,New York(1964),p.242.Retrieved from the video of Non-Newtonian Fluid Mechanics(University of Wales Institute of Non-Newtonian Fluid Mechanics,2000)Tubeless SiphonWhen the siphon tube is lifted out of the fluid,the Newtonian liquid(N)stops flowing;the macromolecular fluid(P)continues to be siphoned.Reproduced from R.B.Bird,R.C.Armstrong and O.Hassager,Dynamics of Polymeric Liquids.Vol I:Fluid Mechanics,2nd edition,Wiley-Interscience(1987),p.74.Retrieved from the video of Non-Newtonian Fluid Mechanics(University of Wales Institute of Non-Newtonian Fluid Mechanics,2000)I.2 Normal Stress Difference and Elasticity(cont.)Elastic RecoilAn aluminum soap solution,made of aluminum dilaurate in decalin and m-cresol,is(a)poured from a beaker and(b)cut in midstream.In(c),note that the liquid above the cut springs back to the breaker and only the fluid below the cut falls to the container.Reproduced from A.S.Lodge,Elastic Liquids,Academic Press,New York(1964),p.238.I.2 Normal Stress Difference and Elasticity(cont.)A solution of 2%carboxymethylcellulose(CMC 70H)in water is made to flow under a pressure gradient that is turned off just before frame 5.Reprodeced from A.G.Fredrickson,Principles and Applications of Rheology,Prentice-Hall,Englewood cliffs,NJ(1964),p.120.Dimensionless groups in Non-Newtonian fluid mechanics the Deborah number(De):the characteristic time of the fluid,tflow:the characteristic time of the flow system the Weissenberg number(We):the characteristic strain rate in the flowDimensionless groups in Newtonian fluid mechanics the Reynolds number(Re)L:the characteristic length;V,and are the velocity,the density and the viscosity of fluidI.3 The Deborah/Weissenberg Number I.3 The Deborah/Weissenberg Number(cont.)Streak photograph showing the streamlines for the flow downward through an axisymmetric sudden contraction with contraction ratio 7.675 to 1 as a function of De.(a)De=0 for a Newtonian glucose syrup.(b-e)De=0.2,1,3 and 8 respectively for a 0.057%polyacrylamide glucose solution.Reproduced from D.B.Boger and H.Nguyen,Polym.Eng.Sci.,18,1038(1978).Typical viscosity curve of a polyolefin-PP homopolymer,melt flow rate(230 C/2.16 Kg)of 8 g/10 min-at 230 C with indication of the shear rate regions of different conversion techniques.Reproduced from M.Gahleitner,“Melt rheology of polyolefins”,Prog.Polym.Sci.,26,895(2001).I.4 Flow Regimes of Typical ProcessingChapter I Non-Newtonian Flows:Phenomenology“The mountains flowed before the Lord”From Deborahs Song,Judges,5:5SecondaryflowI.5 Secondary Flows and InstabilitySecondary flow around a rotating sphere in a polyacrylamide solution.Reporduce from H.Giesekus in E.H.Lee,ed.,Proceedings of the Fourth International Congress on Rheology,Wiley-Interscience,New York(1965),Part 1,pp.249-266Newtonian fluid(N):water-glycerinNon-Newtonian fluid(P):100 ppm polyacrylamide in water-glycerinSecondaryflowSteady streaming motion produced by a long cylinder oscillating normal to its axis.The cylinder is viewed on end and the direction of oscillation is shown by the double arrow.The photographs do not show streamlines but mean particles pathlines made visible by illuminating tiny Spheres with a stroboscope synchronized with the cylinder frequency.Reproduced from C.T.Chang and W.R.Schowalter,Nature,252,686(1974).I.5 Secondary Flows and Instability(cont.)Melt instabilityPhotographs of LLDPE melt pass through a capillary tube under various shear rates.The shear rates are 37,112,750 and 2250 s-1,respectively.Reproduced from R.H.Moynihan,“The Flow at Polymer and Metal Interfaces”,Ph.D.Thesis,Department of Chemical Engineering,Virginia Tech.,Blackburg,VA,1990.Retrieved from the video of Non-Newtonian Fluid Mechanics(University of Wales Institute of Non-Newtonian Fluid Mechanics,2000)SharkskinMelt fractureI.5 Secondary Flows and Instability(cont.)Taylor-Couette flowFlow visualization of the elastic Taylor-Couetteinstability in Boger fluids.http:/www.cchem.berkeley.edu/sjmgrp/Taylor vortexR1R2S.J.Muller,E.S.G.Shaqfeh and R.G.Larson,“Experimental studies of the onset of oscillatory instability in viscoelastic Taylor-Couette flow”,J.Non-Newtonian Fluid Mech.,46,315(1993).I.5 Secondary Flows and Instability(cont.)Reproduced from G.M.Kavanagh and S.B.Ross-Murphy,“Rheological characterisation of polymer gels”,Prog.Polym.Sci.,23,533(1998).I.6 Probing Techniquesq2-1 RheometryShear and Shearfree FlowsFlow Geometries&Viscometric Functionsq2-2 Basic Vector/Tensor ManipulationsVector OperationsTensor Operationsq2-3 Material Functions in Simple Shear FlowsSteady Flows Unsteady Flowsq2-4 Material Functions in Elongational FlowsTopics in Each SectionTopics in Each SectionqTwo standard kinds of flows,shear and shearfree,are used to characterize polymeric liquids2.1.Rheometry2.1.RheometryFIG.3.1-1.Steady simple shear flowFIG.3.1-2.Streamlines for elongational flow(b=0)(a)Shear(b)ShearfreeShear rateElongationrateqThe Stress TensorxyzShear FlowElongational Flow*See 2.2Total stresstensor*Hydrostatic pressure forcesStress tensorqClassification of Flow Geometries(a)Shear(b)ElongationCone-and-PlateConcentric CylinderParallel PlatesCapillaryMoving ClampsPressure Flow:Drag Flows:qTypical Shear/Elongation Rate Range&Concentration Regimes for Each GeometriesHomogeneousdeformation:*Nonhomogeneousdeformation:Parallel Plates(a)Shear(b)ElongationCapillaryCone-and-PlateConcentric CylinderConcentrated RegimeDilute RegimeFor Melts&High-Viscosity SolutionsMoving clamps*Stress and strain are independent of position throughout the sampleExample:Concentric CylinderFIG.Concentric cylinder viscometer(From p.188 of ref 3)qViscometric Functions&Assumptions(homogeneous)Flow Instability in a Concentric Cylinder Viscometer for a Newtonian LiquidLaminar Secondary TurbulentOnset of Secondary FlowTurbulentTaylor vorticesTa(or Re)plays the central role!Rod Climbingis not a subtle effect,as demonstrated on thecover by Ph.D.student Sylvana Garcia-Rodrigues from Columbia.Ms.Garcia-Rodrigues is studyingrheology in the Mechanical Engineering Department at U.of Wisconsin-Madison,USA.The Apparatus shown was created by UWMadison Professors Emeriti John L.Schrag and Arthur S.Lodge.The fluid shown is a 2%aqueous polyacrylamide solution,and the rotational speed is nominally 0.5 Hz.Photo by C a r l o s A r a n g o S a b o g a l (2 0 0 6)(F):For the Newtonian fluids the surface near the rod is slightly depressed and acts as a sensitive manometer for the smaller pressure near the rod generated by centrifugal force(N)(P)Example 2.3-1:Interpretation of Free Surface Shapes in the Rod-Climbing Experiment(P):The Polymeric fluids exhibit an extra tension along the streamlines,that is,in the“”direction.In terms of chemical structure,this extra tension arises from the stretching and alignment of the polymer molecules along the streamlines.The thermal motions makethe polymer molecules act as small“rubber bands”wanting to snap backI.Phenomenological Interpretation:The resultant formula derived in this example is:II.Use of Equations of Change to Analyze the Distribution of the Normal Pressure(N)(P)PExamples 1.3-4&10.2-1:Cone-and-Plate InstrumentFIG.1.3-4.Cone-and-plate geometry(From p.205 of ref 3)(homogeneous)Example:p.530Uniaxial Elongational FlowFIG.10.3-1a.Device used to generate uniaxial elongational flows by separating Clamped ends of the sampleExptl.data see 2.4qSupplementary ExamplesCapillary:oExample 10.2-3:Obtaining the Non-Newtonian Viscosity from the CapillaryConcentric CylindersoProblem 10B.5:Viscous Heating in a Concentric Cylinder Viscometer Parallel Plates:oExample 10.2-2:Measurement of the Viscometric Functions in the Parallel-Disk InstrumentoProblem 1B.5:Parallel-Disk ViscometeroProblem 1D.2:Viscous Heating in Oscillatory Flow2.2.Basic Vector/Tensor Manipulations2.2.Basic Vector/Tensor ManipulationsqVector Operations(Gibbs Notation)Dot product:Vector:123Cross product:qTensor OperationsHydrostatic pressureforcesStress tensororMomentum flux tensorTensor:123FIG.The stress tensorStresses acting on plane 1The total momentum flux tensor for an incompressible fluid is:NormalstressesExample:Some Definitions&Frequently Used Operations:CartesiancoordinateCartesiancoordinate2.3.Material Functions in Simple Shear Flows2.3.Material Functions in Simple Shear FlowsqRemarks:A variety of experiments performed on a polymeric liquid will yield a host of material functions that depend on shear rate,frequency,time,and so onRepresentative fluid behavior will also be shown by means of sample experimental dataThe description of the nature and diversity of material response to simple shearing and shearfree flow is givenFIG.3.4-1.Various types of simple shear experiments used in rheologyI.Steady Shear Flow Material FunctionsExp a:Steady Shear FlowFIG.3.3-1.Non-Newtonian viscosity of a low-density polyethylene at several different temperaturesThe shear-rate dependent viscosity is defined as:The first and second normal stress coefficients are defined as follows:FIG.3.3-2.Master curves for the viscosity and first normal Stress coefficient as functions of shear rate forthe Low-density polyethylene melt shown in previousfigureFIG.3.3-4.Intrinsic viscosity of polystyrene solutions,With various solvents,as a function of reduced shearrate Intrinsic Viscosity:Relative Viscosity:II.Unsteady Shear Flow Material FunctionsExp b:Small-Amplitude Oscillatory Shear FlowFIG.3.4-2.Oscillatory shear strain,shear rate,shear stress,and first normal stress difference in small-amplitude oscillatoryshear flowFIG.3.4-3.Storage and loss moduli,G and G”,as functions of frequency at a reference temperature of T0=423 K for the low-density polyethylene melt shown in Fig.3.3-1.The solidcurves are calculated from the generalized Maxwell model,Eqs.5.2-13 through 15It is customary to rewrite the above eq to display the in-phase and out-of-phase parts of the shear stressStorage modulusLoss modulusExp c:Stress Growth upon Inception of Steady Shear FlowTransient Shear Stress:Relaxation Modulus:*For small shear strains*Example 5.3-2:Stress Relaxation after a Sudden Shearing DisplacementThe Lodge-Meissner Rule:Exp e:Stress Relaxation after a Sudden Shearing Displacement(Step-Strain Stress Relaxation)2.4.Material Functions in Elongational Flows2.4.Material Functions in Elongational FlowsqShearfree Flow Material FunctionsThe number average and weight averagemolecular weights of the samples:Monodisperse,but with atail in high M.W.(GPC results)q3-1 Introduction to Rheo-Optics Method3-1.1.Introduction&Review of Optical Phenomena3-1.2.Characteristic Dimension&Optical Rangeq3-2 Typical Experimental Set-ups3-2.1 Flow Dichroism and Birefringence Measurements for Case Study 1-23-2.2 Combined Rheo-Optcial Measurements(including Rheo-SALS)for Case Study 3q3-3 Information Retrieval in Individual MeasurementsCase Study 1:Flow Dichroism and Birefringence of PolymersCase Study 2:Dynamics of Multicomponent Polymer MeltsCase Study 3:Combined Rheo-Optcial MeasurementsReferencesTopics in Each SectionTopics in Each Section3-1.1 Introduction&Review of Optical PhenomenaA rheological measurement entails the measurement of:(a)Force(related to the stress)(b)Displacement(related to the strain)In a rheo-optical experiment,both the force and optical properties of the sample are measured3-1.Introduction to Rheo-Optics Method3-1.Introduction to Rheo-Optics MethodOpticalMechanicalMeasured QuantityMolecular orientation and shapeDissipation and/or storage of energyPolymer ContributionDominates the measured signalRelatively small for dilute solutionsSpatial ResolutionPossibleImpossibleMolecular LabelingPossibleImpossibleSensitivityGood precision-Time ScaleShorterLongerTable:A comparison of some important features in optical and mechanical measurements When incident electromagnetic radiation interacts with matter,three broad classes of phenomena are of interest:I.Transmission of LightThe light can propagate through the material with no change in direction or energy,but with a change in its state of polarizationBirefringence;“Dichroism”;TurbidityII.Scattering RadiationThe radiation can be scattered(change in direction)with either no change in energy(elastic)or a measruable change in energy(inelastic)Static Light,X-Ray,and Neutron Scattering;Dynamic Light ScatteringIII.Absorption and Emission SpectroscopiesEnergy can be absorbed with the possible subsequent emission of some or all of the energyFluorescence;Phosphorescence3-1.2 Characteristic Dimension&Optical Range Typical levels of structures in polymeric systems are listed below The general order of structural levels that can be studied by some of the different techniques is given below3-2.1.Flow Dichroism and Birefringence of Polymers in Shear FlowsBasic Concepts:3-2.Typical Experimental Set-ups3-2.Typical Experimental Set-upsTurbidityThe Lambert-Beers Law:DichriosmEX 1:Polariod Sun Glasses(A daily Eexample of dichrism resulting from absorption)EX 2:Colloids under Shear FlowFIG.Representation of a Polaroid sheet.Light with a polarisation direction parallel tothe aligned polymers is absorbed more strongly as compared to light with a polarisationdirection perpendicular to the polymersThe total amount of scattered light depends on the polarisation direction due to theanisotropic nature of the microstructure under shear flowBirefringenceMore specifically,the polarisation direction of the light can be decomposed intoa component parallel to the direction where the refractive index is large and acomponent paral