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**Fundamentals of two-fluid dynamics. Part II: Lubricated transport, drops and miscible liquids.**
*(English)*
Zbl 0784.76003

Interdisciplinary Applied Mathematics. 4. New York: Springer-Verlag. xv, 445 p. (1993).

Part II (with 306 illustrations, 30 in color) of the present treatise on the fundamentals of two-fluid dynamics by Joseph and Renardy deals with lubricated transport, drops and miscible liquids. The topics treated are arranged in six chapters: (V) introduction to lubricated pipelining, (VI) lubricated pipelining: linear stability analysis, (VII) core-annular flow in vertical pipes, (VIII) nonlinear stability of core-annular flow, (IX) vortex rings of one fluid in another in free fall, and (X) miscible liquids. Like Part I [see the foregoing entry], the book is impressive in its scholary approach. The most beautiful of the lubricated flows are the rollers discussed in chapter II of Part I, while the most useful of these flows are the water-lubricated pipelines which are investigated in chapters V through VIII of the second put. The last two chapters of the book are completely independent of the others. Chapter IX is a description of the immiscible vortex rings which develop in free fall. In chapter X the authors develop a new theory of binary mixtures of incompressible liquids based on the observation that the velocity of a fluid particle in such a mixture cannot be solenoidal when diffusion is active. It explores the idea that gradients of composition can induce direct stresses which will mimic the effects of a transient interfacial tension when the gradients are large.

The book summarizes the research effects of the authors and their coworkes since the early 1980’s. The beautiful color inserts in both parts deserve special mention. This reviewer considers the book to be without competition as a general reference for the fundamentals of two- fluid dynamics for many years to come. It requires a certain sophistication on the part of the readers for which the reader, however, is amply rewarded.

The book summarizes the research effects of the authors and their coworkes since the early 1980’s. The beautiful color inserts in both parts deserve special mention. This reviewer considers the book to be without competition as a general reference for the fundamentals of two- fluid dynamics for many years to come. It requires a certain sophistication on the part of the readers for which the reader, however, is amply rewarded.

Reviewer: J.Siekmann (Essen)

### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76T99 | Multiphase and multicomponent flows |

76D08 | Lubrication theory |

76E05 | Parallel shear flows in hydrodynamic stability |

76E30 | Nonlinear effects in hydrodynamic stability |