*(English)*Zbl 0612.76032

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

##### MSC:

76D05 | Navier-Stokes equations (fluid dynamics) |

76-02 | Research monographs (fluid mechanics) |

76D07 | Stokes and related (Oseen, etc.) flows |

76D08 | Lubrication theory |

76D10 | Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids) |

76A05 | Non-Newtonian fluids |

35Q30 | Stokes and Navier-Stokes equations |

76S05 | Flows in porous media; filtration; seepage |

76T99 | Two-phase and multiphase flows |