高分子流变学.ppt

1、I.1 Shear Thinning/Thickening,(a) Shear stress vs shear rate and (b) log viscosity vs log shear rate for Dilatants, Newtonian fluids and Pseudoplastics. For very high shear rates the pseudoplastic material reaches a second Newtonian pleatau. Reproduced from G. M. Kavanagh and S. B. Ross-Murphy, “Rhe

2、ological characterisation of polymer gels”, Prog. Polym. Sci., 23, 533 (1998).,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 thr

3、ough 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 (Universi

4、ty of Wales Institute of Non-Newtonian Fluid Mechanics, 2000),I.2 Normal Stress Difference and Elasticity,Rod-Climbing,Fixed 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. Bir

5、d, 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

6、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 dimet

7、hylphthalate (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 Mech

8、anics, 2000),Tubeless Siphon,When 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

9、, 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 Recoil,An aluminum soap solution, made of aluminum dilaurate in decalin an

10、d 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 D

11、ifference 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

12、.,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 flow Dimensionless groups in Newtonian fluid mechanics the Rey

13、nolds number (Re) L: the characteristic length; V, and are the velocity, the density and the viscosity of fluid,I.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 wit

14、h 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-

15、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 Processing,Chapter I Non-

16、Newtonian Flows: Phenomenology,“The mountains flowed before the Lord” From Deborahs Song, Judges, 5:5,Secondaryflow,I.5 Secondary Flows and Instability,Secondary flow around a rotating sphere in a polyacrylamide solution. Reporduce from H. Giesekus in E. H. Lee, ed., Proceedings of the Fourth Intern

17、ational Congress on Rheology, Wiley-Interscience, New York (1965), Part 1, pp. 249-266,Secondary flow,Steady 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 no

18、t 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 instability,Photographs o

19、f 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.,Retrie

20、ved from the video of Non-Newtonian Fluid Mechanics (University of Wales Institute of Non-Newtonian Fluid Mechanics, 2000),I.5 Secondary Flows and Instability (cont.),Taylor-Couette flow,Flow visualization of the elastic Taylor-Couette instability in Boger fluids. /sjmgrp

21、/,S. 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, “Rheo

22、logical characterisation of polymer gels”, Prog. Polym. Sci., 23, 533 (1998).,I.6 Probing Techniques,2-1 Rheometry Shear and Shearfree Flows Flow Geometries “Dichroism”; Turbidity Scattering Radiation The radiation can be scattered (change in direction) with either no change in energy (elastic) or a

23、 measruable change in energy (inelastic) Static Light, X-Ray, and Neutron Scattering; Dynamic Light Scattering Absorption and Emission Spectroscopies Energy can be absorbed with the possible subsequent emission of some or all of the energy Fluorescence; Phosphorescence,3-1.2 Characteristic Dimension

24、 Figs. Reproduced from Sondergaard and Lyngaae-Jorgensen (1995),Note that only data for the case of Mw=1.54 x 106 is shown in the following 3 pages,One-to-one correlation between the onset of shear thickening and the occurrence of a maximum in the dichroism, The viscosity and dichroism patterns for

25、the lowest concentration are similar to those exhibited by a lower molecular weight sample (Mw=4.3 x 105). Namely, the dichroism rises to a plateau, while viscosity undergoes a monotonic drop with shear rate to an eventual Newtonian plateau,Viscosity,Dichroism, At higher concentrations, a dramatic a

26、nd distinctive pattern emerges. One sees a shaper rise in the dichroism to an eventual maximum, while the viscosity simultaneously drops to a minimum. This is followed by a region of shear thickening in which the viscosity continuously rises, while the dichroism decreases and eventually turns negati

27、ve, This figure shows that, in this range, the orientation angle dropped to a constant near-alignment with the flow axis, Throughout the entire flow curve, the birefringence exhibits a steady monotonic increase with shear rate, These data offer strong evidence that the overall orientation of the cha

28、in segments is independent of the structuring processes, which may take place as indicated in the dichroism,CASE STUDY 2: Dynamics of Multicomponent Polymer Melts Infrared Dichroism Measurements of Molecular Relaxation in Binary Blend Melt Rheology Kornfield et al. (1989),3. The most interesting res

29、ult is that the longest relaxation time of the the shorter chains is a strongly increasing function of the volume fraction of longer chains. This contrasts with the predictions of the basic reptation model,1. Chains are identical in chemical composition, but differ in M.W. Isotopic labeling with deu

30、terium (D) can be used to distinguish one M.W. component from another 2. At 2,180 cm-1 the C-D bond absorbs but the C-H bond does not,CASE STUDY 3: Combined Rheo-Optical Measurements Rheo-Optical Studies of Shear-Induced Structures in Semidilute Polystyrene Solutions Kume et al. (1997),1. Shear-indu

31、ced structure formation in semidilute solutions of high molecular weight polystyrene was investigated using a wide range of rheo-optical techniques 2. The effects of shear on the semidilute polymer solutions could be classified into some regimes w.r.t. shear rate,FIG. A complete picture of the shear

32、-induced phase separation and structure formation from a wide range of techniques on the same polymer solutions,Shear-microscopy results,Homogeneous solution,Strong butterfly-type LS pattern,Long stringlike structures,Streaklike LS pattern,Chains weakly orient along the flow dir.,Chains in the strin

33、gs with their end-to-end vectors parallel to the flow dir.,Change of the sign,Oblate-ellipsoidal structures,Due to the stringlike structures oriented parallel to the flow dir.,Continued,Continued,Notice that the behavior of the shear viscosity is also classified into three regimes,Comparisons with M

34、echanical Characterizations:,Mechanical,References,Chapter IV General Analyses: Scaling Laws, Times-Temperature Superposition, Solvent Quality, and Fundamental Material Constants,Fig 3.3-1 (p 105) in the textbook,IV.1 Effects of Solvent Quality,Fig 3.3-4 (p 107) in the textbook, or T. Kotaka et al.,

35、 J. Chem. Phys. 45, 2770-2773 (1966).,Magnitude of intrinsic viscosity -temperature black circles: plot of (lnr)/c vs. c. (1) Zimm-Crothers viscometer (3.710-3 7.610-2 dyn/cm2); (2)Ubbelohde viscometer (8.67 dyn/cm2); (3)Ubbelohde viscometer (12.2 dyn/cm2).,cf. p109,IV.2.3 Impact of MolecularWeight

36、Distribution,H. Munstedt, J. Rheol. 24, 847-867 (1980),Linear Polymer Star Polymer Pom-Pom Polymer,IV.2.4 Molecular Architecture,polybutadiene Polyisoprene Polyisoprene,IV.3 Retrieval of Fundamental Material Constants,Fig 3.3-1 (p 105) in the textbook,IV.3 Retrieval of Fundamental Material Constants

37、,e M0 d M3,Theoretical results of (a) G(t) and (b) G() for polymer melts.,Storage modulus vs. frequency for narrow distribution polystyrene melts. Molecular weight ranges from Mw = 8.9x103 r/mol (L9) to Mw = 5.8x105 g/mol (L18).,M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford Scienc

38、e: New York (1986), pp 229-230.,IV.4 Time-Temperature Superposition,Time-temperature superposition holds for many polymer melts and solutions, as long as there are no phase transitions or other temperature-dependent structural changes in the liquid. Time-temperature shifting is extremely useful in p

39、ractical application, allows one to make prediction of time-dependent material response.,IV.4 Time-Temperature Superposition,J. D. Ferry, Viscoelastic Properties of Polymers, 3rd ed., Wiley: New York (1980).,WLF temperature shift parameters,Master curves for the viscosity and first normal Stress coe

40、fficient as functions of shear rate for the Low-density polyethylene melt,IV.4 Time-Temperature Superposition,Non-Newtonian viscosity of a low-density polyethylene melt at several different temperature.,Fig 3.3-1 and 3.3-2 (pp105-106) in the textbook.,IV.4 Time-Temperature Superposition,Fig 3.6-5 (p

41、 146) in the textbook.,A master curve of polystyrene-n-butyl benzene solutions. Molecular weights varied from 1.6x105 to 2.4x106 g/mol, concentration from 0.255 to 0.55 g/cm3, and temperature from 303 to 333 K.,Chapter V Constitutive Equations and Modeling of Complex Flow Processing,Models for Gener

42、alized Newtonian Fluids Constitutive Equations for Generalized Linear Viscoelasticity Objective Differential/Integral Constitutive Equations Simulations of complex Flow Processing Case Study,Content of Chapter V,V.1 Models for Generalized Newtonian Fluids,In many industrial problems the most importa

43、nt feature of polymeric liquids is that their viscosity decrease markedly as the shear rate increases. The generalized Newtonian model incorporates the idea of a shear-rate-dependent viscosity into the Newtonian constitute equation. This generalized Newtonian model can not describe normal stress eff

44、ects or time-dependent elastic effects.,V.1 Models for Generalized Newtonian Fluids,The Carreau-Yasuda model The power-law model n 1, shear-thickening (dilatant) fluids,V.1 Models for Generalized Newtonian Fluids,The Eyring model The Bingham model Other empirical functions in the generalized Newtoni

45、an fluid model (see Table 4.5-1, p 228 in the textbook),Goal: to introduce a equation that can describe some of the time-dependent motions of fluids under a flow with very small displacement gradients Why do we concern the linear viscoelasticity (LVE) of fluids? (1) interrelate structure with the li

46、near mechanical responses (2) proceed to the subject of nonlinear viscoelasticity How to combine the idea of viscosity and elasticity into a single constitutive equation described various interesting elastic effects? shearing motion of a Newtonian fluid the zero-shear-rate viscosity (s and p) of sol

47、vent and polymer; and the dimensionless “mobility factor”, . is associated with anisotropic Brownian motion and/or anisotropic hydrodynamic drag on the polymer molecules.,V.3 Objective Differential/Integral Constitutive Equations,Nonlinear integral model The factorized K-BKZ model The factorized Riv

48、lin-Sawyers model,V.3 Objective Differential/Integral Constitutive Equations,Advantage of nonlinear integral model (1) they include the general linear viscoelastic fluid completely (2) they provide a framework of constitutive equations with molecular and empirical origin (3) it is possible to use th

49、ese constitutive equations to interrelate material functions Disadvantage of nonlinear integral model (1) the models generally predict too much recoil in elastic recoil experiments (2) these models have been omitted for the cases of memory-strain coupling,V.3 Objective Differential/Integral Constitu

50、tive Equations,V.4 Simulations of Complex Flow Processing,Polymer properties Governing equations (balance equations of mass, momentum and energy) Power-law constitutive equation Finite element method,A. Makradi et al, J. Appl. Polym. Sci. 100, 2259-2266 (2006).,V.4 Simulations of Complex Flow Proces

51、sing,1D Post Draw model for IPP Spinning,Polymer properties,CAEFF (Center for Advanced Engineering Fibers and Films) software,Roller 2,Roller 1,Roller 3,V.4 Simulations of Complex Flow Processing,Model properties,Heat capacity parameters,Roller parameters,V.4 Simulations of Complex Flow Processing,V

52、elocity of Roller 2 = 160 m/s,Velocity of Roller 2 = 80 m/s,Chapter VI Ongoing Researches and Future Perspectives,Course outline,Major Fields of Ongoing Researches Celebrated Rheological Puzzles A Few Words on the Future Perspectives: Need for Interdisciplinary Collaboration,Polymer Rheology,Textboo

53、k R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids. Vol I: Fluid Mechanics, 2nd edition, Wiley-Interscience (1987). Reference 1. R. G. Larson, The Structure and Rheology of Complex Fluids, Oxford University Press (1998). 2. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford Science: New York (1986). 3. C. W. Macosko, Rheology-Principles, Measurements, and Applications, Wiley-VCH (1994). 4. G. G. Fuller, Optical Rheometry of Complex Fluids, Oxford University Press (1995).,Scope and Goal,Rheology is a science that concerns, in general, the mechanical