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Complex fluids. Modeling and algorithms. (English) Zbl 1361.76001
Mathématiques & Applications (Berlin) 79. Cham: Springer (ISBN 978-3-319-44361-4/pbk; 978-3-319-44362-1/ebook). xvi, 276 p. (2016).
The present book dwells on phenomena which could not be explained on the basis of viscous fluid theory. Ample examples of such fluids exist in nature, and these fluids have various applications. The book is divided into five chapters.
The first chapter deals with the basics of the fluid flow phenomena. It introduces the formulation of general fluid flow problems. A rigorous derivation of the Navier-Stokes equations provides the required knowledge to the beginner. Some exact solutions of the Navier-Stokes equations are illustrated by the Poiseuille and Couette flows. A few approximate and numerical methods are also included in Chapter 1.
Chapter 2 introduces non-Newtonian fluids. The role of the viscosity function in the characterization of a non-Newtonian fluid is very clearly enunciated. Methods to tackle the complexity coming in the solution due to the generalized viscosity function are included. The fixed point method and Newton’s method are examined.
Chapter 3 discusses viscoplastic fluids. The physical characterization and the corresponding constitutive equations are explained. It is asserted that explicit solutions for this category of fluids are not possible. The author presents numerical algorithms for this purpose. These are used to solve illustrative examples. The chapter also includes references to the available literature in this area.
Viscoelastic fluids are included in the fourth chapter. Following the set-up in the previous chapter, the physical characteristics are discussed. Subsequently, the rheological models are derived. The classical problems of Poiseuille and Couette flows for viscoelastic fluids are explained. The global free energy estimate for viscoelastic fluids could be also useful for industrial design. References to the available work in this area are given in the text.
The last chapter discusses elastoviscoplastic fluids. These models have interesting applications in human biology as well as in various industrial processes. Obviously, these models are more complicated than viscoelastic and viscoplastic models. A framework of thermodynamics is included to provide a platform for rigorous derivation of the constitutive equations. Classical flow problems are solved as illustrative examples. References to further extensions are provided.
Several numerical algorithms are suggested in each chapter. References to the software suitable for non-Newtonian fluid flow are included. The text is a useful addition to the literature on non-Newtonian fluids. It should also act as a concise reference work in this area.

##### MSC:
 76-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics 76A05 Non-Newtonian fluids 76A10 Viscoelastic fluids 35Q35 PDEs in connection with fluid mechanics 00A79 Physics
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