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Polymer Rheology( 高分子流變學 )

Instructor: Prof. Chi-Chung Hua

( 華繼中 教授 )

Complex Fluids & Molecular Rheology Laboratory, National Chung Cheng University, Chia-Yi 621, Taiwan, R.O.C.

國立中正大學　複雜流體暨分子流變實驗室

Homepage: http://www.che.ccu.edu.tw/~rheology/

TextbookR. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids. Vol I: Fluid Mechanics, 2nd edition, Wiley-Interscience (1987).

Reference1. 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 stresses arising during processing of complex fluids and, in particular, the microstructures that underlie the macroscopic observations.

This course focuses on the general concepts, analytical tools, and applications that are central to the interest of most researchers.

Rheology will not necessarily be your expertise after this course; rather, you might start loving it and, in some respect, benefit from it.

Course outline

Non-Newtonian Flows: Phenomenology Mechanical Characterizations: Measurements and

Material Functions Optical Characterizations: Flow

Birefringence/Dichroism and Light Scattering General Analyses: Scaling Laws, Time-Temperature

Superposition, Solvent Quality, and Fundamental Material Constants

Constitutive Equations and Modeling of Complex Flow Processing

Ongoing Researches and Future Perspectives

Chapter 0 Introduction of

Rheology

Terminology

What is Rheology?

normally refers to the flow and deformation of “non-classical materials” (or called Non-Newtonian Fluids in this course)

What is the “non-classical materials” ?

such as rubber, molten plastics, polymer solutions, slurries & pastes, electrorheological fluids, blood, muscle, composites, soils and paints.

[Excerpt from the website of the Institute of Non-Newtonian Fluid Mechanics (INNFM), http://innfm.swan.ac.uk/innfm_mms/index.html]

Importance of Rheological Properties

Rheological parameters acting as a “link” between monomer structure and final properties of a polymer.[Reproduce from M. Gahleitner, “Melt rheology of polyolefins”, Prog. Polym. Sci., 26, 895 (2001).]

Fluid MechanicsKinetic Theory

Rheological Circle

[Reproduced from C. Clasen and W. M. Kulicke, “Determination of viscoelastic and rheo-optical material functions of water-soluble cellulose derivatives”, Prog. Polym. Sci., 26, 1839 (2001).]

Chapter I Non-Newtonian Flows:

Phenomenology

“The mountains flowed before the Lord”

[From Deborah’s Song, Judges, 5:5]

Content of Chapter I

Viscosity Thinning/Thickening (pp. 60-61)

Normal Stress Differences and Elasticity (pp. 62-69, 72-83)

The Deborah/Weissenberg numbers (pp. 92-95)

Flow Regimes of Typical Processing

Secondary Flows and Instabilities (pp.69-72)

Length scale (or time scale) & Probing Techniques

I.1 Shear Thinning/Thickening

Dilatants(Shear thickening)

Newtonian Fluids

Pseudoplastics(Shear thinning)

Dilatants(Shear thickening)

Newtonian Fluids

Pseudoplastics(Shear thinning)

0 pleatau

(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

flow/De t

We

/Re LV

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

Secondary flow

Primary Flow

Secondary Flow

Non-Newtonian Fluids

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]

Primary Flow

Secondary Flow

Newtonian Fluids

Newtonian fluid (N):water-glycerin

Non-Newtonian fluid (P):100 ppm polyacrylamide in water-glycerin

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.)

Primary FlowSecondary Flow

Non-Newtonian Fluids

Primary FlowSecondary Flow

Newtonian Fluids

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)]

Sharkskin Melt fracture

I.5 Secondary Flows and Instability (cont.)

Taylor-Couette flow

Flow visualization of the elastic Taylor-Couetteinstability in Boger fluids.[http://www.cchem.berkeley.edu/sjmgrp/]

Taylor vortex

R1R2

[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