An Introduction to Rheology.pdf

AN INTRODUCTION TO

RHEOLOGY

H.A.Barnes

Senior Scientist and Subject Specialist in Rheology and Fluid Mechanics,

Unilever Research, Port Sunlight Laboratory, Wirral, K.

Formerly: Principal Scientist and Leader of Tribology Group, Shell Research

Ltd., Ellesmere Port, K.

and

K. Walters R.S.

Professor of Mathematics, University College of Wales, Aberystwyth, K.

Amsterdam - London - New York-Tokyo

SCIENCE PUBLISHERSB.V.

Sara Burgerhartstraat 25

P.O. Box 211,1000 AE Amsterdam, The Netherlands

First edition 1989

Second impression 1991

Third impression 1993

ISBN 0-444-87140-3 (Hardbound)

ISBN 0-444-87469-0 (Paperback)

1989

No part of this publication may be reproduced, stored in a retrieval system ortransmitted in any

form or by any means, electronic, mechanical, photocopying, recording or otherwise, without

the prior written permission of the publisher, Science Publishers

Sciences Engineering Division, P.O. Box 521,1000 AM Amsterdam, The Netherlands.

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any methods, products, instructions or ideas contained in the material herein.

Printed in The Netherlands

PREFACE

Rheology, defined as the science of deformation is now recognised as an

important field of scientific study. A knowledge of the subject is essential for

scientists employed in many industries, including those involving plastics, paints,

printing inks, detergents, oils, etc. Rheology is also a respectable scientific discipline

in its own right and may be studied by academics for their own esoteric reasons,

with no major industrial motivation or input whatsoever.

The growing awareness of the importance of rheology has spawned a plethora of

books on the subject, many of them of the highest class. It is therefore necessary at

the outset to justify the need for yet another book.

Rheology is by common consent a difficult subject, and some of the necessary

theoretical components are often viewed as being of prohibitive complexity by

scientists without a strong mathematical background. There are also the difficuities

inherent in any multidisciplinary science, like rheology, for those with a specific

training in chemistry. Therefore, newcomers to the field are sometimes discour-

aged and for them the existing texts on the subject, some of are outstanding,

are of limited assistance on account of their depth of detail and highly mathematical

nature.

For these reasons, it is our considered judgment after many years of experience in

industry and academia, that there still exists a need for a modern text

on the subject; one which will provide an overview and at the same time ease

readers into the necessary complexities of the field, pointing them at the same time

to the more detailed texts on specific aspects of the subject.

In keeping with our overall objective, we have purposely (and with some

difficulty) minimised the mathematical content of the earlier chapters and relegated

the highly mathematical chapter on Theoretical Rheology to the end of the book. A

glossary and bibliography are included.

A major component of the anticipated readership will therefore be made up of

newcomers to the field, with at least a first degree or the equivalent in some branch

of science or engineering (mathematics, physics, chemistry, chemical or mechanical

engineering, materials science). For such, the present book can be viewed as an

important (first) stepping stone on the journey towards a detailed appreciation of

the subject with Chapters 1-5 covering foundational aspects of the subject and

Chapters 6-8 more specialized topics. We certainly do not see ourselves in competi-

tion with existing books on rheology, and if this is not the impression gained on

reading the present book we have failed in our purpose. We shall judge the success

or otherwise of our venture by the response of newcomers to the field, especially

those without a strong mathematical background. We shall not be unduly disturbed

if long-standing rheologists find the book superficial, although we shall be deeply

concerned if it is concluded that the book is unsound.

We express our sincere thanks to all our colleagues and friends who read earlier

drafts of various parts of the text and made useful suggestions for improvement.

Mr Robin Evans is to be thanked for his assistance in preparing the figures and

Mrs Pat Evans for her tireless assistance in typing the final manuscript.

H.A. Barnes

J.F.

K. Walters

CONTENTS

PREFACE

1 . INTRODUCTION

1.1 What is rheology?

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2 Historical perspective

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3 The importance of non-linearity

1.4 Solids and liquids

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.5

is a difficult subject

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.6 Components of

research

1.6.1

1.6.2 Constitutive equations

Complex flows of elastic liquids

2 . VISCOSITY

2.1 Introduction

2.2 Practical ranges of variables which affect viscosity

2.2.1 Variation with shear rate

2.2.2 Variation with temperature

1 2

Variation with pressure

2.3 The shear-dependent viscosity of non-Newtonian liquids

2.3.1 Definition of Newtonian behaviour

2.3.2 The shear-thinning non-Newtonian liquid

The shear-thickening non-Newtonian liquid

Time effects in

liquids

2.3.5 Temperature effects in two-phase non-Newtonian liquids

2.4

for measuring shear viscosity

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.1 Generalconsiderations

2.4.2 Industrial shop-floor instruments

2.4.3 Rotational instruments; general comments

2.4.4 The narrow-gap concentric-cylinder viscometer

2.4.5 The wide-gap concentric-cylinder viscometer

2.4.6 Cylinder rotating in a large volume of liquid

2.4.7 The cone-and-plate viscometer

2.4.8 The parallel-plate viscometer

2.4.9 Capillary viscometer

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.10 Slit viscometer

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.11 On-line measurements

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 . LINEAR VISCOELASTICITY

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 The meaning and consequences of linearity

vii

3.1 Introduction

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