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Zbl 0612.76032
Happel, John; Brenner, Howard
Low Reynolds number hydrodynamics with special applications to particulate media. 2nd rev. ed., 4th printing. (English)
[B] Mechanics of Fluids and Transport Processes, 1. Dordrecht/Boston/Lancaster: Martinus Nijhoff Publishers, a member of the Kluwer Academic Publishers Group. XI, 553 p. Dfl. 75.00; {\$} 29.50; \sterling 19.00 (1986).

The topic of this publication - low Reynolds number hydrodynamics, with special application to particulate media is of interest to research workers in diverse areas of science and technology such as physical (rheology), biological and Earth sciences, and chemical, civil, mining and mechanical engineering. The sustained interest of researchers in these diverse areas has lead to the development of the subject at the present level. \par The publication of the book in second edition and fourth printing itself suggests its utility amongst research workers and teachers alike. It fulfills the need of providing the hydrodynamic view point which leads to a clearer correlation of existing theoretical and experimental literature. In the words of the authors the aim of the book is "...... an attempt to bridge this gap by providing at least the beginnings of a rational approach to fluid - particle dynamics, based on first principles." While explaining the development of the subject a host of new problems awaiting solution have also been indicated. \par The book is divided into nine chapters with two appendices on orthogonal curvilinear coordinate system and polyadic algebra, respectively. A familiarity with these techniques is basic to understand the text. The treatment is based almost entirely on the linearised form of the equations. Each chapter ends with an extensive bibliography. \par Chapter I gives a historial survey of the development of the subject. It describes various applications of low Reynolds number flow in different areas of science and technology. The list is not exhaustive, but still interests the readers. \par Chapter II contains the development of the equations of motion starting from the fundamentals of fluid dynamics. It concludes some exact solutions of the equations of motion for viscous fluid and simplications of the Navier-Stokes equations for slow motion. Whitehead's paradox and Oseen's method for resolving this have also been included. Molecular effects in fluid dynamics and non-Newtonian flows also find mention in this chapter. \par Chapter III presents general solutions of Navier-Stokes equations for creeping flows. The reduction of the governing equations to Laplace equations or biharmonic equation and subsequent application of classical methods to obtain the solution have been clearly explained. \par Chapter IV explains the concept of stream function from physical and mathematical point of view. Its applications to various axisymmetric flows cover a wide range of interesting problems. \par Chapter V deals with the motion of a rigid particle of arbitrary shape in an unbounded fluid. The equations of creeping motion takes into account the three fundamental second rank tensors, i.e. translation tensor, rotation tensor and coupling tensor. The examples have been included at all appropriate places. \par Chapter VI deals with the creeping flow past two or more particles. The interaction between two spheres and two spheroids has been treated extensively. Correlation with experimental data increases it's utility. \par Chapter VII describes the motion of wall effects on the motion of a single particle. The analysis of the motion of a sphere near a plane, spheroid near a plane, spheroid between two planes, sphere in a circular cylinder are quite interesting. \par Chapter VIII is devoted to the study of flow relative to the assemblages of particles. It is in the form of survey of practical problems like sedimentation of suspensions, sludge flow, flow through porous media and fluidisation. \par The last chapter includes the viscosity of particular systems. It gives the derivation of Einstein's formulae for the viscosity of a dilute suspension of spherical particles by including the first order effects of interaction. A discussion of the conditions under which the entire suspension could be classified as a Newtonian or non-Newtonian phenomenon has also been made. Non-Newtonian fluids and lubrication deserved a better deal in the text. The good features of the book are, in one source, all that is to be known in low Reynolds number hydrodynamics is logically and succinctly presented. The treatment is cogent without any ambiguity. The book will continue to serve the community for which it is meant. The book is already so popular that is does not need any recommendation.
[S.C.Rajvanishi]

MSC 2000:: *76D05 Navier-Stokes equations (fluid dynamics)
76-02 Research monographs (fluid mechanics)
76D07 Stokes flows
76D08 Lubrication theory
76D10 Boundary-layer theory (incompressible fluids)
76A05 Non-Newtonian fluids
35Q30 Stokes and Navier-Stokes equations
76S05 Flows in porous media
76T99 None of the above, but in this section

Keywords: low Reynolds number hydrodynamics; rheology; polyadic algebra; linearised form; exact solutions; Navier-Stokes equations; slow motion; Whitehead's paradox; Oseen's method; Molecular effects; non-Newtonian flows; creeping flows; Laplace equations; biharmonic equation; stream function; axisymmetric flows; motion of a rigid particle; unbounded fluid; sedimentation; sludge flow; flow through porous media; fluidisation; Einstein's formulae for the viscosity; dilute suspension; spherical particles; lubrication

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