Non-Newtonian flow and rheology are subjects which are essentially interdisciplinary in their nature and which are also wide in their areas of application. Indeed non-Newtonian fluid behaviour is encountered in almost all the chemical and allied processing industries. The factors which determine the rheological characteristics of a material are highly complex, and their full understanding necessitates a contribution from physicists, chemists and applied mathematicians, amongst others, few of whom may have regarded the subject as central to their disciplines. Furthermore, the areas of application are also extremely broad and diverse, and require an important input from engineers with a wide range of backgrounds, though chemical and process engineers, by virtue of their role in the handling and processing of complex materials (such as foams, slurries, emulsions, polymer melts and solutions, etc.), have a dominant interest. Furthermore, the subject is of interest both to highly theoretical mathematicians and scientists and to practicing engineers with very different cultural backgrounds.

Owing to this inter-disciplinary nature of the subject, communication across subject boundaries has been poor and continues to pose difficulties, and therefore, much of the literature, including books, is directed to a relatively narrow readership with the result that the engineer faced with the problem of processing such rheological complex fluids, or of designing a material with rheological properties appropriate to its end use, is not well served by the available literature. Nor does he have access to information presented in a form which is readily intelligible to the non-specialist. This book is intended to bridge this gap but, at the same time, is written in such a way as to provide an entree to the specialist literature for the benefit of scientists and engineers with a wide range of backgrounds. Non-Newtonian flow and rheology is an area with many pitfalls for the unwary, and it is hoped that this book will not only forewarn readers but will also equip them to avoid some of the hazards.

Coverage of topics is extensive and this book offers an unique selection of material. There are eight chapters in all.

The introductory material, Chapter 1, introduces the reader to the range of non-Newtonian characteristics displayed by materials encountered in every day life as well as in technology. A selection of simple fluid models which are used extensively in process design calculations is included here.

xii Preface

Chapter 2 deals with the characterization of materials and the measurement of their rheological properties using a range of commercially available instruments. The importance of adequate rheological characterization of a material under conditions as close as possible to that in the envisaged application cannot be overemphasized here. Stress is laid on the dangers of extrapolation beyond the range of variables covered in the experimental characterization. Dr. P.R. Williams (Reader, Department of Chemical Biological Process Engineering, Swansea, University of Wales, U.K.) who has contributed this chapter is in the forefront of the development of novel instrumentations in the field.

The flow of non-Newtonian fluids in circular and non-circular ducts encompassing both laminar and turbulent regimes is presented in Chapter 3. Issues relating to the transition from laminar to turbulent flow, minor losses in fittings and flow in pumps, as well as metering of flow, are also discussed in this chapter.

Chapter 4 deals with the highly complex but industrially important topic of multiphase systems - gas/non-Newtonian liquid and solid/non-Newtonian liquids - in pipes.

A thorough treatment of particulate systems ranging from the behaviour of particles and drops in non-Newtonian liquids to the flow in packed and fluidised beds is presented in Chapter 5.

The heating or cooling of process streams is frequently required. Chapter 6 discusses the fundamentals of convective heat transfer to non-Newtonian fluids in circular and non-circular tubes under a range of boundary and flow conditions. Limited information on heat transfer from variously shaped objects - plates, cylinders and spheres - immersed in non-Newtonian fluids is also included here.

The basics of the boundary layer flow are introduced in Chapter 7. Heat and mass transfer in boundary layers, and practical correlations for the estimation of transfer coefficients are included.

The final Chapter 8 deals with the mixing of highly viscous and/or non-Newtonian substances, with particular emphasis on the estimation of power consumption and mixing time, and on equipment selection.

A each stage, considerable effort has been made to present the most reliable and generally accepted methods for calculations, as the contemporary literature is inundated with conflicting information. This applies especially in regard to the estimation of pressure gradients for turbulent flow in pipes. In addition, a list of specialist and/or advanced sources of information has been provided in each chapter as "Further Reading".

In each chapter a number of worked examples has been presented, which, we believe, are essential to a proper understanding of the methods of treatment given in the text. It is desirable for both a student and a practicing engineer to understand an appropriate illustrative example before tackling fresh practical problems himself. Engineering problems require a numerical answer and it is problems himself. Engineering problems require a numerical answer and it is thus essential for the reader to become familiar with the various techniques so that the most appropriate answer can be obtained by systematic methods rather than by intuition. Further exercises which the reader may wish to tackle are given at the end of the book.

Incompressibility of the fluid has generally been assumed throughout the book, albeit this is not always stated explicitly. This is a satisfactory approximation for most non-Newtonian substances, notable exceptions being the cases of foams and froths. Likewise, the assumption of isotropy is also reasonable in most cases except perhaps for liquid crystals and for fibre filled polymer matrices. Finally, although the slip effects are known to be important in some multiphase systems (suspensions, emulsions, etc.) and in narrow channels, the usual no-slip boundary condition is regarded as a good approximation in the type of engineering flow situations dealt with in this book.

In part, the writing of this book was inspired by the work of W.L. Wilkinson: Non-Newtonian Fluids, published by Pergamon Press in 1960 and J.M. Smith's contribution to early editions of Chemical Engineering, Volume 3. Both of these works are now long out-of-print, and it is hoped that readers will find this present book to be a welcome successor.

R.P. Chhabra J.F. Richardson

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