Journal of Non-Newtonian Fluid Mechanics, 30 (1988) 93-95 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

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Book review

Dynamics of Polymeric liquids: Volume 1. Fluid Mechanics (2nd ed)

by R.B. Bird, R.C. Armstrong and 0. Hassager, Wiley-Interscience, New York, NY, 1987, 649 + xxi pages, ISBN 0-471-80245-X (V.l), price US$ 69.95

Perhaps the most useful task of the reviewer of a second edition such as this is to highlight the differences from the first edition in order to make clear why an individual or a library ought to purchase this second edition.

Those who have not encountered the first edition, published in 1977, can be assured that the appearance of a second edition does signify that the book (and its companion volume 2 on kinetic theory) is probably the most important text book on polymer fluid dynamics that has been published to date. The text book description should be noted; the book has a wealth of examples (with detailed solutions) and problems (without solutions) for the reader.

The volume is organised into five parts. The introductory section entitled Newtonian versus non-Newtonian behaviour provides background material on Newtonian fluid mechanics and on the flow behaviour of polymeric liquids. The second part consists of chapters on the “Generalized Newto- nian Fluid” and the general linear viscoelastic fluid and the third part deals with nonlinear viscoelastic constitutive equations in solving fluid dynamical problems. The fourth part covers some fundamental continuum mechanical ideas and also experimental methods of measuring rheological properties. The fifth part of the volume is a set of appendices (covering over seventy pages) which provides an introduction to vector and tensor notation and expressions for useful tensors and equations, both for general flows and for the special cases of shearing and shearfree flows. (This reviewer still prefers the term extensional flow to shearfree flow, but there seem to be a good enough reasons for either usage.)

A glance at the chapter titles and subtitles reveals that the second half of this volume has been changed substantially. The discussions of nonlinear viscoelastic models has both been restructured to follow a line less peculiar to the authors than that pursued in the first edition and has been brought up to date. The corotational model, which occupied two chapters and 24 lines in the index in 1977, now is found in only 2 lines in the index. This is not to say that the model is out of date, (which it is not) or even out of fashion (which may be true), but that the authors have rightly given priority to models which are regarded as being more useful or less problematic. A further reason which the authors give, in their introductory comments on this volume, is that the codeformational formalism, and the convected

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derivative to which it leads, seems to arise more naturally from molecular theories.

If the reviewer expresses regret at the disappearance of the “Questions for Discussion” at the end of each chapter, which are described in the first edition as “occasionally provocative”, it has to be admitted that some were cryptic and few were satisfying to a solitary reader. There are, in any case, enough statements in the text to provoke plenty of discussions and even argument with the authors. The only ctiticism one might offer is that some items this reviewer finds mildly provocative are presented as authoritative statements-as in the discussion on the elongational viscosity of the eight- constant Oldroyd model. The authors are kind enough to cite one of this reviewer’s published papers but unfortunately seem to miss one of its more basic points-that an elongational viscosity function may be both well behaved (finite for all finite extension rates) and meaningless (because the “transients” do not decay). However, this is a quibble about one small point in a book whose scope is extraordinary wide. The reviewer in any case must express pleasure at the increased attention given to elongational flows.

One example where the authors have missed a didactic opportunity is on flow in a circular die with viscous heating. It took the reviewer a few minutes to track down the reason for the different scales for the graphs of tempera- ture rise against radius in example 4.4-3 of this edition and the almost identical 5.4-5 of the first edition. The diagrams look so similar, and the dimensionless variables are the same but for some unexplained reason the polymer melt is given a thermal conductivity of 0.25 W/mK instead of of 0.04184 W/mK. Hence we have a good illustration of the effect of the change of this one parameter-provided we have both editions of the book.

A minor criticism-on a matter of opinion-is that the typography and layout and the quality of the reproduction of photographs are superior in the first edition. This was noticed, for example, in the spacing of subheadings for example 4.4-4 (5.4-6 in the first edition). One suspects computerised typesetting with one parameter chosen without enough care. The setting of derivatives both as

au, a auj

ay andGUj rather thanz 1 was mildly irritating, but the reason for the more awkward choice may be inferred from a discussion of the notation VU. It is also irritating to have text and cited figures separated sometimes by four or five pages.

The section on retarded motion expansions nearly evoked a groan from the reviewer, at the prospect of another rewriting of the classic results, but here the discussion is careful, there is a wealth of useful information and the limitations of the approach are clearly stated. The comment on the applica- tion of a law of diminishing returns to this is well worth noting. The effort

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of obtaining a third order solution is far greater than that for a second order solution and the usefulness of the information obtained is generally much smaller. The following chapters on nonlinear differential and integral models are full of information and generally as well up to date as any book can be. Of course there are omissions, but the treatment will give an intelligent newcomer an excellent feeling for what is likely to be of interest currently in the application of rheology to solving problems in fluid mechanics.

One matter which is not mentioned in the book at all is that of errata or corrigenda. The authors do invite readers to inform them of errors, and indeed there are a few but what is useful, if known, is that computer mail aficionados may obtain an ever-growing list of corrigenda from the authors. This reviewer is on a mailing list maintained in Wisconsin by the senior author. The electronic mail address to which to send a request for this list is “ bird@chewi.che.wisc.edu” on the educational partition of INTERNET (formerly ARPANET). From the UK it may be necessary to use “birdSedu.wisc.che.chewi@eam-relay (from the Joint Academic NETwork -JANET).

One of the neat things a list of corrigenda allows is a change as in problem 8C.2 from “verify that . . . predicts” to “verify that . . . does not predict”. It is not appropriate here to list other errata known to the authors or found by the reviewer-the latter are few in number. However, one piece of carelessness which has been introduced since the first edition should be mentioned. On page 14 the example of flow in an inclined circular tube is discussed with the aid of a “modified pressure”, 9=p - pgz cos x

( = pressure - gravitational head), but the boundary conditions used for this 9 are that “the pressures at the tube ends . . . are g0 and gL” which taken literally leads to the conclusion that there would be no flow down an inclined tube if the pressure is the same at each end. It is probably fair to describe this as another quibble; any self-respecting reader will know exactly what the authors meant to write, and it is quite hard to trip up the authors even in this way.

A final note to readers concerns the change in the cryptic dedication of this volume. U.S.A. Bicentennial is succeeded by one of the preeminent rheologists of this century, whose spirit has clearly influenced the new edition of this book. It is truly a book on non-Newtonian fluid mechanics and conveys the spirit of our discipline with clarity and enthusiasm. It is not an easy book, but then ours is not an easy subject and oversimplification is liable to be deceptive and even dishonest. This is a book for every rheologi- cal library whether it already has the first edition or not and many individual rheologists will find it invaluable.

CHRIS PETRIE Newcastle upon Tyne