COMPUTATIONAL ANALYSIS OF POLYMER PROCESSING COMPUTATIONAL ANALYSIS OF POLYMER PROCESSING Edited by 1. R. A. PEARSON and S. M. RICHARDSON Department of Chemical Engineering and Chemical Technology, Imperial College of Science and Technology, London, UK APPLIED SCIENCE PUBLISHERS LONDON and NEW YORK APPLIED SCIENCE PUBLISHERS LTD Ripple Road, Barking, Essex, England Sole Distributor in the USA and Canada ELSEVIER SCIENCE PUBLISHING CO., INC. 52 Vanderbilt Avenue, New York, NY 10017, USA British Library Cataloguing in Publication Data Pearson, J. R. A. Computational analysis of polymer processing. I. Polymers and polymerization-Data processing I. Title II. Richardson, S. M. 668.4'028'54 TPI120 ISBN-13: 978-94-009-6636-9 e-ISBN-13: 978-94-009-6634-5 DOl: 10.1007/978-94-009-6634-5 WITH 9 TABLES AND 97 ILLUSTRATIONS © APPLIED SCIENCE PUBLISHERS LTD 1983 Softcover reprint of the hardcover 1s t edition 1983 The selection and presentation of material and the opinions expressed in this publication are the sole responsibility of the authors concerned All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the copyright owner, Applied Science Publishers Ltd, Ripple Road, Barking, Essex, England Preface Large, fast, digital computers have been widely used in engineering practice and their use has had a large impact in many fields. Polymer processing is no exception, and there is already a substantial amount of literature describing ways in which processes can be analysed, designed or controlled using the potentialities of modern computers. The emphasis given varies with the application, and most authors tend to quote the results of their calculations rather than describing in any detail the way the calculations were undertaken or the difficulties experienced in carrying them out. We aim to give here as useful and connected an account as we can of a wide class of applications, for the benefit of scientists and engineers who find themselves working on polymer processing problems and feel the need to undertake such calculations. The major application we have in mind is the simulation of the dynamics ofthe various physical phenomena which arise in a polymer process treated as a complex engineering system. This requires that the system be reasonably well represented by a limited number of relatively simple subprocesses whose connections can be clearly identified, that the domi- nant physical effects relevant to each subprocess can be well defined in a suitable mathematical form and that the sets of equations and boundary conditions developed to describe the whole system can be successfully discretised and solved numerically. Problems arise at each of these operations, and the objective here will be to suggest general methods for overcoming these difficulties. In particular we shall concentrate on those v VI PREFACE aspects that are peculiar to polymer processing, and on those techniques that seem to hold most promise for the future, when progressively greater accuracy will be expected of computer simulations. It must be emphasised that the mathematical model chosen for any process should reflect the needs of the worker concerned and be selected to provide the information required in its most convenient form and at acceptable cost computationally. This implies that there is no universally suitable model for any polymer process, nor any universally suitable method of mathematical treatment. In some cases very crude methods will suffice, while in others even the most elaborate may prove unsuccessful. However, most direct engineering applications will seek to predict physical dimensions of items of equipment or of the product of the process, and so usually the aim is to achieve the greatest accuracy possible. To this extent, it may be assumed that few of the models described in this text are unnecessarily elaborate. In writing such a text, it is always tempting to use a very didactic approach and to present material in a very careful sequential fashion, eminently suitable for teaching engineering graduates under class con- ditions. We have opted instead for an approach that borrows much from the case study method, with each chapter covering a particular process in as self-contained a fashion as possible. This has the advantage that an occasional reader can start at one of the later chapters, only going back to one of the earlier chapters to refresh his or her mind about certain fundamental issues. This leads to a limited amount of repetition, but far less than might be expected; indeed such as there is may well prove a help to those readers trying to master the whole contents of the text. The reason for this is that each process presents its own peculiar characteristics- geometrical, kinematical or dynamical-with attention directed at dif- ferent engineering aspects, so that quite different techniques of solution may be employed. Another advantage of having essentially independent chapters is that we have been able to get an acknowledged expert to write each chapter. This has ensured that most approaches are well represented in an authoritative fashion and that there is a welcome element of variety in the presentation. Most of the authors concerned could not have found time to write a complete :text; the present arrangement has led to a more up-to-date account than anyone of them could have produced on his own. By choosing a group of authors who knew one another's work and had a common background in the subject, a strong underlying element of homogeneity is to be found in the whole work, while editorial additions PREFACE vii have introduced valuable forward and backward references between chapters. The structure of the book is explained in the introductory chapter. As outlined earlier, it is aimed at those engineers and scientists who have a background in mechanics, particularly fluid mechanics and heat transfer, and some experience of computing, wishing to tackle problems in polymer processing. We hope that they will find it helpful. J. R. A. PEARSON S. M. RICHARDSON Contents Preface v List of Contributors XI Notation XIII 1. Introduction: Polymer Melt Mechanics 1. R. A. PEARSON 2. Computational Techniques for Viscoelastic Fluid Flow 21 M. 1. CROCHET and K. WALTERS 3. Extrudate Swell 63 R. I. TANNER 4. Extrusion (Flow in Screw Extruders and Dies) 93 R. T. FENNER 5. Moulding 139 S. M. RICHARDSON 6. Fibre Spinning 179 M. M. DENN IX x CONTENTS 7. Film Blowing, Blow Moulding and Thermoforming 217 C. J. S. PETRIE 8. Coating Flows 243 S. F. KISTLER and L. E. SCRIVEN 9. Process Control 301 J. WORTBERG Index 337 List of Contributors M. J. CROCHET Unite de Mecanique Appliquee, Universite Catholique de Louvain, Biitiment Simon Stevin, Place du Levant, 2, B-1348 Louvain-la-Neuve, Belgium. M. M. DENN Department of Chemical Engineering, University of California, Berkeley, California 94720, USA. R. T. FENNER Department of Mechanical Engineering, Imperial College of Science and Technology, Exhibition Road, London SW7 2BX, UK. S. F. KISTLER Department of Chemical Engineering and Materials Science, University ofM innesota, 151 Amundson Hall, 421 Washington Avenue S.E., Minneapolis, Minnesota 55455, USA. J. R. A. PEARSON Department of Chemical Engineering and Chemical Technology, Imperial College of Science and Technology, Prince Consort Road, London SW7 2BY, UK. Xl XII LIST OF CONTRIBUTORS C. J. S. PETRIE Department of Engineering Mathematics, University of Newcastle upon Tyne, Stephenson Building, Claremont Road, Newcastle upon Tyne, NEJ 7RU, UK. S. M. RICHARDSON Department of Chemical Engineering and Chemical Technology, Imperial College of Science and Technology, Prince Consort Road, London SW7 2BY, UK. L. E. SCRIVEN Department of Chemical Engineering and Materials Science, University of Minnesota, J5 J Amundson Hall, 42 J Washington Avenue S.E., Minneapolis, Minnesota 55455, USA. R. I. TANNER Department of Mechanical Engineering, University ofS ydney, Sydney, New South Wales 2006, Australia. K. WALTERS Department of Applied Mathematics, University College of Wales, Penglais, Aberystwyth, Wales, UK. J. WORTBERG Institut fur KunststojJverarbeitung, Pontstrasse 49, D-5100 Aachen, West Germany.