《高分子流变学》PPT课件.ppt

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, “Rheological 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 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 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. 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 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, 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 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 flow Dimensionless groups in Newtonian fluid mechanics the Reynolds 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 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 Processing,Chapter I Non-Newtonian Flows: Phenomenology,“The mountains flowed before the Lord” From Deborahs Song, Judges, 5:5,Secondary flow,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 International 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 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 instability,Photographs 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),I.5 Secondary Flows and Instability (cont.),Taylor-Couette flow,Flow visualization of the elastic Taylor-Couette instability in Boger fluids. /sjmgrp/,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, “Rheological characterisation of polymer gels”, Prog. Polym. Sci., 23, 533 (1998).,I.6 Probing Techniques,2-1 Rheometry Shear and Shearfree Flows Flow Geometries & Viscometric Functions 2-2 Basic Vector/Tensor Manipulations Vector Operations Tensor Operations 2-3 Material Functions in Simple Shear Flows Steady Flows Unsteady Flows 2-4 Material Functions in Elongational Flows,Topics in Each Section,Two standard kinds of flows, shear and shearfree, are used to characterize polymeric liquids,2.1. Rheometry,FIG. 3.1-1. Steady simple shear flow,FIG. 3.1-2. Streamlines for elongational flow (b=0),(a) Shear,(b) Shearfree,Shear rate,Elongation rate,The Stress Tensor,x,y,z,Shear Flow,Elongational Flow,*See 2.2,Total stress tensor*,Hydrostatic pressure forces,Stress tensor,Classification of Flow Geometries,(a) Shear,(b) Elongation,Cone-and-Plate,Concentric Cylinder,Parallel Plates,Capillary,Moving Clamps,Pressure Flow:,Drag Flows:,Typical Shear/Elongation Rate Range & Concentration Regimes for Each Geometries,Homogeneous deformation:*,Nonhomogeneous deformation:,Parallel Plates,(a) Shear,(b) Elongation,Capillary,Cone-and-Plate,Concentric Cylinder,Concentrated Regime,Dilute Regime,For Melts & High-Viscosity Solutions,Moving clamps,*Stress and strain are independent of position throughout the sample,Example: Concentric Cylinder,FIG. Concentric cylinder viscometer,(From p.188 of ref 3),Viscometric Functions & Assumptions,(homogeneous),Flow Instability in a Concentric Cylinder Viscometer for a Newtonian Liquid,Laminar Secondary Turbulent,Onset of Secondary Flow,Turbulent,Taylor vortices,Ta (or Re) plays the central role!,Rod Climbing is not a subtle effect, as demonstrated on the cover by Ph.D. student Sylvana Garcia-Rodrigues from Columbia. Ms. Garcia-Rodrigues is studying rheology 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 Carlos Arango Sabogal (2006),(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 make the polymer molecules act as small “rubber bands” wanting to snap back,I. 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),P,Examples 1.3-4 & 10.2-1: Cone-and-Plate Instrument,FIG. 1.3-4. Cone-and-plate geometry,(From p.205 of ref 3),(homogeneous),Example: p.530 Uniaxial Elongational Flow,FIG. 10.3-1a. Device used to generate uniaxial elongational flows by separating Clamped ends of the sample,Exptl. data see 2.4,Supplementary Examples Capillary: Example 10.2-3: Obtaining the Non-Newtonian Viscosity from the Capillary Concentric Cylinders Problem 10B.5: Viscous Heating in a Concentric Cylinder Viscometer Parallel Plates: Example 10.2-2: Measurement of the Viscometric Functions in the Parallel-Disk Instrument Problem 1B.5: Parallel-Disk Viscometer Problem 1D.2: Viscous Heating in Oscillatory Flow,2.2. Basic Vector/Tensor Manipulations,Vector Operations (Gibbs Notation),Dot product:,Vector:,1,2,3,Cross product:,Tensor Operations,Hydrostatic pressure forces,Stress tensor or Momentum flux tensor,Tensor:,1,2,3,FIG. The stress tensor,Stresses acting on plane 1,The total momentum flux tensor for an incompressible fluid is:,Normal stresses,Example:,Some Definitions & Frequently Used Operations:,Cartesian coordinate,Cartesian coordinate,2.3. Material Functions in Simple Shear Flows,Remarks: 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 on Representative fluid behavior will also be shown by means of sample experimental data The description of the nature and diversity of material response to simple shearing and shearfree flow is given,FIG. 3.4-1. Various types of simple shear experiments used in rheology,Steady Shear Flow Material Functions,Exp a: Steady Shear Flow,FIG. 3.3-1. Non-Newtonian viscosity of a low-density polyethylene at several different temperatures,The 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 for the Low-density polyethylene melt shown in previous figure,FIG. 3.3-4. Intrinsic viscosity of polystyrene solutions, With various solvents, as a function of reduced shear rate ,Intrinsic Viscosity:,Relative Viscosity:,Unsteady Shear Flow Material Functions,Exp b: Small-Amplitude Oscillatory Shear Flow,FIG. 3.4-2. Oscillatory shear strain, shear rate, shear stress, and first normal stress difference in small-amplitude oscillatory shear flow,FIG. 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 solid curves are calculated from the generalized Maxwell model, Eqs. 5.2-13 through 15,It is customary to rewrite the above eq to display the in-phase and out-of-phase parts of the shear stress,Storage modulus,Loss modulus,Exp c: Stress Growth upon Inception of Steady Shear Flow,Transient Shear Stress:,Relaxation Modulus:*,For small shear strains,*Example 5.3-2: Stress Relaxation after a Sudden Shearing Displacement,The Lodge-Meissner Rule:,Exp e: Stress Relaxation after a Sudden Shearing Displacement (Step-Strain Stress Relaxation),2.4. Material Functions in Elongational Flows,Shearfree Flow Material Functions,The number average and weight average molecular weights of the samples:,Monodisperse, but with a tail in high M.W. (GPC results),3-1 Introduction to Rheo-Optics Method 3-1.1. Introduction & Review of Optical Phenomena 3-1.2. Characteristic Dimension & Optical Range 3-2 Typical Experimental Set-ups 3-2.1 Flow Dichroism and Birefringence Measurements for Case Study 1-2 3-2.2 Combined Rheo-Optcial Measurements (including Rheo-SALS) for Case Study 3 3-3 Information Retrieval in Individual Measurements Case Study 1: Flow Dichroism and Birefringence of Polymers Case Study 2: Dynamics of Multicomponent Polymer Melts Case Study 3: Combined Rheo-Optcial Measurements References,Topics in Each Section,3-1.1 Introduction & Review of Optical Phenomena A rheological measurement entails the measurement of: Force (related to the stress) Displacement (related to the strain) In a rheo-optical experiment, both the force and optical properties of the sample are measured,3-1. Introduction to Rheo-Optics Method,Table: 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: Transmission of Light The light can propagate through the material with no change in direction or energy, but with a change in its state of polarization Birefringence; “Dichroism”; Turbidity Scattering Radiation The 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 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 & 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 below,3-2.1. Flow Dichroism and Birefringence of Polymers in Shear Flows Basic Concepts:,3-2. Typical Experimental Set-ups,Turbidity,The Lambert-Beers Law:,Dichriosm,EX 1: Polariod Sun Glasses (A daily Eexample of dichrism resulting from absorption),EX 2: Colloids under Shear Flow,FIG. Representation of a Polaroid sheet. Light with a polarisation direction parallel to the aligned polymers is absorbed more strongly as compared to light with a polarisation direction perpendicular to the polymers,The total amount of scattered light depends on the polarisation direction due to the anisotropic nature of the microstructure under shear flow,More specifically, the polarisation direction of the light can be decomposed into a component parallel to the direction where the refractive index is large and a component parallel to the direction where the refractive index is small After having traversed the sample, there is a relative phase shift of the two field components and the sum of the two fields is generally elliptically polarised,FIG. Linear polarised light is generally transmitted as elliptically polarized light through a birefringent material,Basic Polarimeter Design:,PSG,PSA,FIG. Basic polarimeter schematic,Light source,Sample,Detector,A Polarization State Generator, PSG, defines the polarization of the light prior to transmission through the sample A Polarization State Analyzer, PSA, determines the state of polarization of the existing light, In transmission exps, one is normally concerned with the measurement of light polarization,The Stokes Vector Entering the Detector is:,The specific Mueller matrix components (optical properties) of the sample can be identified,Example: The Crossed Polarizer System,The Measured Intensity I for a Sample with Coaxial Birefringence and Dichroism oriented at an Angle is:,FIG. Birefringent and dichroic sample sandwiched between corssed polarizers,Typical Arrangement for Flow Birefringence and Dichroism Measurements:,FIG. Schematic of the experimental set-up for dichroism and birefringence measurements,A somewhat simpler set-up can be sued: Dichroism only: removal of R2, P2, and D2 Turbidity only: removal of R1, R2, P2, and D2,BS,BS: Beam splitter D1-D3: Detectors P1,P2: Polarizers R1,R2: Rotating quarter wave platelets,Optical Train Mounted on a Rheometer,http:/www.chemie.uni-hamburg.de/tmc/kulicke/rheology/rheo2.htm,FIG A combination of rheomechanical and rheo-optical measurements,FIG Experimental apparatus for determination of flow birefringence and flow dichroism,3-2.2. Combined Rheo-Optical Measurements Optical Setup for Shear-Small-Angle-Light-Scattering (SALS) Mesurements Kume et al. (1997),FIG. Schematic diagram of the experimental setup for shear-light scattering: one-dimensional detector (photodiode array), cone-and-plate type shear cell to generate Couette flow, and coordinate system used in this study,FIG. Schematic diagram of the experimental setup for shear-dichroism, shear-birefringence, and rheology: (a) Schematic diagram of the combined mechanical rheometer and optical train. (b) Shear cell and optical train,Optical Setup for Shear-Dichroism, Shear-Birefringence, and Rheological M