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Principles of non-newtonian fluid mechanics
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in sympathy with the first point and admits that a certain elegance and ease of presentation may result from the use of tensor fields rather than tensor components. He has yet to be convinced that any major result can be obtained by the tensor field method which cannot be obtained using more conventional tensor - component ideas. He therefore looks at the tensor field development given in the book as one of the many alternative tools that can be used in continuum mechanics. Having said that, it is certainly useful to have a thorough and scholarly treatment of this particular approach available in the literature. This reviewer is happy to recommend Professor Lodge’s new book to readers of the Journal of Non-Newtonian Fluid Mechanics. It is sure to become an influential contribution to the rheological literature - perhaps even more influential than his Elastic liquids. It may be confidently predicted that workers in the field will still be discovering rheological gems in its pages many years from now. K. WALTERS
Principles of Non-Newtonian Fluid Mechanics, G. Astarita and G. Marrucci, McGraw-Hill, London, 1974, ix +289 pages, S 6.45. The authors have set out to produce an exposition of non-Newtonian mechanics in a way that can be easily understood by the non-mathematician. In this they have largely succeeded. Their description of the basic principles on which the theory rests is written with clarity, and points of difficulty and debate are discussed without bias, though the authors’ position is always evident. Much of the first chapter is devoted to an attempt to formulate the rules of manipulation of vectors and tensors. It is in this description of the basic mathematics that I think the authors fail in their objective. It is, of course, very difficult in a relatively few pages to advance mathematical concepts in a way that will benefit the reader with a limited mathematical background. One example will suffice to demonstrate the point. The authors define a tensor as a linear operator on a vector, which is quite a nice way to define a “second-order tensor”. However, “third-order tensors” are introduced almost by accident in a rather unsatisfactory way later on in the chapter. Perhaps the use of the tensor product would be effective here. Chapters 2-6 on kinematics, constitutive equations and rheometry are consistently good and most enjoyable to read, despite the difficulty of the subject matter. It was pleasing to see a section on thermodynamics, though perhaps a little more space could have been devoted to the convected coordinate approach. Chapter 7, on fluid mechanics, was, in contrast, rather disappointing. Far too much material has been put into the space available, with the inevitable loss of style. Almost every section could have been expanded with advantage. This book fills a gap in the literature in providing a readable and thorough account of the principles on which the subject is based. It is written in a style that will delight both the expert and the newcomer to this field. It could be used as a textbook, particularly for those with some knowledge of tensor algebra. There are, unfo~unately,_ a number of misnrints. both in the text and in the biblio~a~hy
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R.S. JONES
in sympathy with the first point and admits that a certain elegance and ease of presentation may result from the use of tensor fields rather than tensor components. He has yet to be convinced that any major result can be obtained by the tensor field method which cannot be obtained using more conventional tensor - component ideas. He therefore looks at the tensor field development given in the book as one of the many alternative tools that can be used in continuum mechanics. Having said that, it is certainly useful to have a thorough and scholarly treatment of this particular approach available in the literature. This reviewer is happy to recommend Professor Lodge’s new book to readers of the Journal of Non-Newtonian Fluid Mechanics. It is sure to become an influential contribution to the rheological literature - perhaps even more influential than his Elastic liquids. It may be confidently predicted that workers in the field will still be discovering rheological gems in its pages many years from now. K. WALTERS
Principles of Non-Newtonian Fluid Mechanics, G. Astarita and G. Marrucci, McGraw-Hill, London, 1974, ix +289 pages, S 6.45. The authors have set out to produce an exposition of non-Newtonian mechanics in a way that can be easily understood by the non-mathematician. In this they have largely succeeded. Their description of the basic principles on which the theory rests is written with clarity, and points of difficulty and debate are discussed without bias, though the authors’ position is always evident. Much of the first chapter is devoted to an attempt to formulate the rules of manipulation of vectors and tensors. It is in this description of the basic mathematics that I think the authors fail in their objective. It is, of course, very difficult in a relatively few pages to advance mathematical concepts in a way that will benefit the reader with a limited mathematical background. One example will suffice to demonstrate the point. The authors define a tensor as a linear operator on a vector, which is quite a nice way to define a “second-order tensor”. However, “third-order tensors” are introduced almost by accident in a rather unsatisfactory way later on in the chapter. Perhaps the use of the tensor product would be effective here. Chapters 2-6 on kinematics, constitutive equations and rheometry are consistently good and most enjoyable to read, despite the difficulty of the subject matter. It was pleasing to see a section on thermodynamics, though perhaps a little more space could have been devoted to the convected coordinate approach. Chapter 7, on fluid mechanics, was, in contrast, rather disappointing. Far too much material has been put into the space available, with the inevitable loss of style. Almost every section could have been expanded with advantage. This book fills a gap in the literature in providing a readable and thorough account of the principles on which the subject is based. It is written in a style that will delight both the expert and the newcomer to this field. It could be used as a textbook, particularly for those with some knowledge of tensor algebra. There are, unfo~unately,_ a number of misnrints. both in the text and in the biblio~a~hy
.
R.S. JONES