Techniques in Rheological Measurement

345 Pages·1993·7.11 MB·English

by  A. A. Collyer (eds.), D. M. Binding (auth.)

TECHNIQUES IN RHEOLOGICAL MEASUREMENT
TECHNIQUES IN
RHEOLOGICAL
MEASUREMENT
Edited by
A.A.COLLYER
Division of Applied Physics,
School of Science,
Sheffield Hal/am University, UK
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
First edition 1993
© 1993 Springer Science+Business Media Dordrecht
Originally published by Chapman & Hali in 1993
Softcover reprint of the hardcover 1 st edition 1993
Typeset in Times 10/12pt by J.W. Arrowsmith Ltd
ISBN 978-94-010-4937-5 ISBN 978-94-011-2114-9 (eBook)
DOI 10.1007/978-94-011-2114-9
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Preface
In an earlier book, Rheological Measurement (A. A. Collyer & D. W.
Clegg, Elsevier Applied Science, 1988), the basic rheological methods
of measurement presently used were discussed in the light of the basic
underlying principles and current theories. The same approach is adopted
in this companion book, which is concerned with some newer or more
sophisticated techniques that have resulted from a fresh understanding of
the subject, or as a result of improvement in computer control, data
acquisition and computational power, or more simply from an industrial
need, particularly with regard to process control.
The first two chapters deal with the extensional flow properties of
fluids and their measurement. This inclusion is in response to a greater
awareness in industry of the importance of these flows. Chapter 3 intro-
duces and develops the subject of surface rheology and the measurement
of its properties, again a subject of increasing significance. The methods
of measurement of the dynamic mechanical properties of fluids and the
calculation of the resulting rheological parameters are discussed in Chap-
ters 4-7 inclusive. The subject areas covered are: large-amplitude oscilla-
tory shear, a model for viscoelastic fluids and solids, a new method of
measuring dynamic mechanical properties, particularly for curing sys-
tems, and the use of complex waveforms in dynamic mechanical analysis.
Rheological measurements on small samples, typical of those obtained
from biological systems or from new chemical syntheses, are described in
Chapter 8. The last two chapters are of relevance to the measurement of
rheological parameters during processing. The topics discussed are speed-
or stress-controlled rheometry and rheometry for process control.
It is hoped that this book will be a suitable introduction to those rapidly
changing areas in rheological measurement, and make readers more aware
of the greater variety of techniques that can be used to assist in the
understanding of the way in which their fluids are behaving during pro-
cessing or in quality control, be they polymer melts, biological materials,
slurries, or food materials. Where mathematics is used, the reader need
have no further knowledge than 'A' level or a pre-university level.
v
vi Preface
This work is of importance to all establishments in which rheological
work is carried out. Material scientists, engineers, or technologists in
industry, research laboratories, and academia should find this book
invaluable in updating their information and understanding of the wide-
ranging area that is rheology.
A.A.COLLYER
Contents
Preface .................................................. v
List of Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX
1. Contraction Flows and New Theories for Estimating Exten-
sional Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
D. BINDING
2. A Critical Appraisal of Available Methods for the Measurement
of Extensional Properties of Mobile Systems .............. 33
D. F. JAMES and K. WALTERS
3. Surface Rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
B. WARBURTON
4. Large-Amplitude Oscillatory Shear ...................... 99
A. J. GIACOMIN and J. M. DEALY
5. A Parsimonious Model for Viscoelastic Liquids and Solids .. 123
H. H. WINTER, M. BAUMGARTEL and P. R. SOSKEY
6. Rheological Studies Using a Vibrating Probe Method ...... 161
R. A. PETHRICK
7. Dynamic Mechanical Analysis Using Complex Waveforms .. 197
B. I. NELSON and J. M. DEALY
8. Rheological Measurements on Small Samples .... . . . . . . . . .. 225
M. E. MACKAY
9. Rate- or Stress-Controlled Rheometry .................... 259
W. GLEIBLE
10. Rheometry for Process Control .......................... 285
J. M. DEALY and T. O. BROADHEAD
Index.. . . . .. . .. . . . . . . ... . . ... . . . .. . . . .. . .. . ... . . . . ... . . .. 333
VlI
List of Contributors
M. BAUMGARTEL
Department of Chemical Engineering, University of Massachusetts, 159
Goessmann Laboratory, Amherst, Massachusetts 01003, USA
D. BINDING
Department of Mathematics, UCW, Penglais, Aberystwyth, Dyfed, SY23
3BZ UK
T.O.BROADHEAD
Department of Chemical Engineering, McGill University, 3480 University
St., Montreal, Quebec, Canada H3A 2A7
J. M. DEALY
Department of Chemical Engineering, McGill University, 3480 University
St., Montreal, Quebec, Canada H3A 2A7
A. J. GIACOMIN
Department of Mechanical Engineering, Texas A&M University, College
Station, Texas 77843-3123, USA
w. GLEIBLE
Institut fur Mechanische Verfahrenstechnik und Mechanik, Universitiit
Karlsruhe (TH), Kaiserstrasse 12, D-7500 Karlsruhe, Germany
D. F. JAMES
Department of Mechanical Engineering, University of Toronto, Toronto,
Ontario, Canada, M5S lAL
M. E. MACKAY
Department of Chemical Engineering, University of Queensland, St. Lucia,
Brisbane, Queensland, Australia 4072
B. I. NELSON
Department of Chemical Engineering, McGill University, 3480 University
St., Montreal, Quebec, Canada H3A 2A7
IX
x List of contributors
R. A. PETHRICK
Department of Pure and Applied Chemistry, University of Strathclyde,
Thomas Graham Building, 295 Cathedral St., Glasgow, UK, Gl lXL
P. R. SOSKEY
ENICHEM Americas Inc., 2000 Princeton Park, Corporate Center, Mon-
mouth Junction, New Jersey 08852, USA
K. WALTERS
Department of Mathematics, UCw, Penglais, Aberystwyth, Dyfed, SY23
3BZ UK
B. WARBURTON
School of Pharmacy, University of London, 29/39 Brunswick Square,
London, UK, WClN lAX
H. H. WINTER
Department of Chemical Engineering, University of Massachusetts, 159
Goessmann Laboratory, Amherst, Massachusetts OJ003, USA
Chapter 1
Contraction Flows and New Theories for Estimating
Extensional Viscosity
D. M. BINDING
Department of Mathematics, University of Wales, Aberystwyth, UK
1.1. Introduction 1
1.2. The Contraction Flow Problem 3
1.3. Experiment 5
1.3.1. Experimental technique 5
1.3.2. The flow field 7
1.3.3. The stress field 9
1.3.4. Numerical simulation 9
1.3.5. Discussion II
1.4. Analysis 13
1.4.1. General consideration 13
1.4.2. Approximating the stress field 16
1.4.3. Quasi-radial flow 19
1.4.4. Funnel flow 23
1.4.5. Discussion of analytical results 26
1.5. Estimating Extensional Viscosity 27
1.6. Concluding Remarks 29
References 30
1.1. INTRODUCTION
A knowledge of the extensional viscosity of a fluid, or at least a quantity
that reflects its extensional properties, is crucial to the overall understand-
ing of how a fluid will respond in different flow situations. The extensional
viscosities, for example, can be several orders of magnitude higher than
the corresponding shear viscosities, and this can have a dramatic influence
on the flow field in a complex process.
2 D. M. Binding
The measurement of extensional viscosity, however, is not a straight-
forward task, particularly for mobile fluid systems. This fact arises prin-
cipally because of the difficulty encountered in generating a well-defined
extensional flow field in the fluid. Experimentally, it is simply not possible
to apply to a fluid the relevant boundary conditions necessary to sustain
such a flow. Chapter 2 of this book refers to many of the problems
involved. Invariably one has to resort to studying flows that are known
to contain a substantial component of extension in order to extract from
them the required information. Contraction flows are an example that
satisfies that need.
The contraction flow problem is a fundamentally important one in the
field of rheology. With the exception of shear flow it has probably received
more attention from researchers than any other flow and is the subject of
J
regular reviews (recent ones include those by White et a/. and Boger2).
Such devotion to one particular flow is easy to understand. Analytically
the problem is insoluble even for the simplest of materials such as Newton-
ian fluids. As a consequence, therefore, many techniques such as simple
approximations to the velocity field, boundary-layer analysis, variational
methods, asymptotic expansions, etc., have been used to provide useful
information about various aspects of the flow.
Experimentally the problem is, at least in principle, quite straight-
forward because of the geometric simplicity involved, and measurements
of quantities such as excess entry pressure are now fairly routine. Determi-
nation of velocity and stress fields is more difficult, however, and reliable
data are not plentiful in the literature. On the other hand, flow visualisa-
tion studies have unfolded a situation that is as complex as is likely to be
encountered in any flow problem. Observations of vortex enhancement
and, more recently, of the generation of 'lip' vortices as well as several
other unusual flow features have provided further impetus to studies of
entry flows.
This diversity of intriguing flow behaviours has provided the
numerical analysts with a geometrically simple problem of considerable
kinematic complexity, on which to test a multitude of numerical
schemes. For good measure the problem provides singular points in
the flow field that require particular attention. Unfortunately, the
difficulties are such that they have detracted somewhat from one of the
important aims of numerical simulation studies, that of differentiating
between the many viable constitutive relations used to model the fluids'
responses. Very recently, however, significant advances have been
made.