6. 2 Creeping viscous flow in a semi-infinite channel 140 6. 3 Poiseuille flow in tubes of circular cross-section 144 6. 4 Motion of a Newtonian liquid between two coaxial cylinders 148 151 6. 5 Bodies in liquids 6. 6 liquid flow and intermolecular forces 154 Non-Newtonian liquids 157 6. 7 6. 8 Viscometers 160 Chapter 7 Surface effects 163 7. 1 Introduction 163 7. 2 Excess surface free energy and surface tension of liquids 163 7. 3 The total surface energy of liquids 167 7. 4 Surface tension and intermolecular forces 168 7. 5 Solid surfaces 171 7. 6 Specific surface free energy and the intermolecular potential 172 7. 7 liquid surfaces and the Laplace-Young equation 174 7. 8 liquid spreading 178 7. 9 Young's relation 181 7. 10 Capillary effects 184 7. 11 The sessile drop 187 7. 12 Vapour pressure and liquid-surface curvature 189 7. 13 The measurement of surface free energies 191 Chapter 8 High polymers and liquid crystals 197 8. 1 Introduction 197 8. 2 High polymers 197 8. 3 The mechanisms of polymerisation 198 8. 4 The size and shape of polymer molecules 199 8. 5 The structure of solid polymers 201 8. 6 The glass transition temperature 203 8. 7 Young's modulus of solid polymers 205 Stress-strain curves of polymers 8. 8 206 8. 9 Viscous flow in polymers 209 liquid crystals 8.

This investigation is an outgrowth of my doctoral dissertation at Princeton University. I am particularly grateful to Professors George F. Pinder and William G. Gray of Princeton for their advice during both my research and my writing. I believe that finite-element collocation holds promise as a numer ical scheme for modeling complicated flows in porous media. However, there seems to be a "conventional wisdom" maintaining that collocation is hopelessly beset by oscillations and is, in some way, fundamentally inappropriate for multiphase flows. I hope to dispel these objections, realizing that others will remain for further work. The U. S. National Science Foundation funded much of this study through grant number NSF-CEE-8111240. TABLE OF CONTENTS ABSTRACT ;; FOREWORD ;; ; CHAPTER ONE. THE PHYSICAL SYSTEM. 1.1 Introduction. 1 1.2 The reservoir and its contents. 5 1.3 Reservoir mechanics. 9 1.4 Supplementary constraints. 18 1.5 Governing equations. 26 CHAPTER TWO. REPRESENTING FLUID-PHASE BEHAVIOR. 39 2.1 Thermodynamics of the fluid system. 40 2.2 Standard equation-of-state methods. 45 2.3 Maxwell-set interpolation.

Applied Mathematics is the art of constructing mathematical models of observed phenomena so that both qualitative and quantitative results can be predicted by the use of analytical and numerical methods. Theoretical Mechanics is concerned with the study of those phenomena which can be ob served in everyday life in the physical world around us. It is often characterised by the macroscopic approach which allows the concept of an element or particle of material, small compared to the dimensions of the phenomena being modelled, yet large compared to the molecular size of the material. Then atomic and molecular phenomena appear only as quantities averaged over many molecules. It is therefore natural that the mathemati cal models derived are in terms of functions which are continuous and well behaved, and that the analytical and numerical methods required for their development are strongly dependent on the theory of partial and ordinary differential equations. Much pure research in Mathematics has been stimu lated by the need to develop models of real situations, and experimental observations have often led to important conjectures and theorems in Analysis. It is therefore important to present a careful account of both the physical or experimental observations and the mathematical analysis used. The authors believe that Fluid Mechanics offers a rich field for il lustrating the art of mathematical modelling, the power of mathematical analysis and the stimulus of applications to readily observed phenomena."

The scope of the present book is to offer the most efficient tools for the vectorization of serial computer programs. Here, by vectorization we understand the adaptation of computer programs to the special architecture of modern available vector computers to exploit fully their potential, which will often result in remarkable performance improvements. The book is written primarily for users working in the various fields of computational physics, for scientists as well as for programmers running their jobs on a vector computer. The text may, however, also be of value to those who are interested in numerical algorithms. Although the examples discussed in chapter 9 have been taken from Computational Fluid Dynamics, the numerical methods are well-known, and are applied in many fields of Computational Physics. The book is divided into four parts. After a short introduction which outlines the limits of conventional serial computers in contrast to the possibilities offered by the new vector machines, the second part is addressed to the discussion of some main features of existing computer architectures. We restrict ourselves to the vector computers CRAY-1S and CDC-CYBER 205, although, in the meantime, many vector and parallel computers and array processors are available such as DENELCOR's Heterogeneous Element Processor (HEP), ICL's Distributed Array Processor (DAP), SPERRY UNIVAC's Array Processing System (APS), STAR TECHNOLOGIES ST-l00, FLOATING POINT SYSTEMS' Array Processor (FPS), FUJITSU's FACOM VP-l00 and VP-200, HITACHI's Integrated Array Processor (lAP), HITACHI's S 810/10 and S 810/20 and others.

The concept of vorticity is of central importance in fluid mechanics and the change and variability of atmospheric flow is dominated by transient vortices of different time- and space scales. Of particular importance are the most in- tense vortices such as hurricanes, typhoons and tornadoes which are associated with extreme and hazardous weather events of great concern to society. In recent years the un- derstanding of these phenomena has grown due to increased and improved surveillance by satellites and aircraft as well as by numerical modelling and simulation, theoretical studies and laboratory experiments. The symposium on "Intense Atmospheric Vortices" was held at the European Centre for Medium Range Weather Forecasts (ECMWF), Reading, England, July 14-17, 1981. The subject area of the Symposium was concerned with observational work, experimental models, theoretical and numerical studies in- volving hurricanes, typhoons, tornadoes and related pheno- mena. The aim was to bring together experts on these meteo- rological processes and on the fundamental fluid-dynamic mechanisms for vorticity intensification from all parts of the world. Thirtyfour scientists participated in the Sympo- sium, including more than half of those leading world ex- perts in the field whom the organizers had invited.

The content of this book is based, largely, on the core curriculum in geophys ical fluid dynamics which land my colleagues in the Department of Geophysical Sciences at The University of Chicago have taught for the past decade. Our purpose in developing a core curriculum was to provide to advanced undergraduates and entering graduate students a coherent and systematic introduction to the theory of geophysical fluid dynamics. The curriculum and the outline of this book were devised to form a sequence of courses of roughly one and a half academic years (five academic quarters) in length. The goal of the sequence is to help the student rapidly advance to the point where independent study and research are practical expectations. It quickly became apparent that several topics (e. g., some aspects of potential theory) usually thought of as forming the foundations of a fluid-dynamics curriculum were merely classical rather than essential and could be, however sadly, dispensed with for our purposes. At the same time, the diversity of interests of our students is so great that no curriculum can truly be exhaust ive in such a curriculum period. It seems to me that the best that can be achieved as a compromise is a systematic introduction to some important segment of the total scope of geophysical fluid dynamics which is illustrative of its most fruitful methods."

Ever since airplane speeds started to approach the speed of sound, the study of compressible flow problems attracted much talent and support in the major indus trialized countries. Today, gas dynamics is a mature branch of science whose many aspects and applications are much too numerous to be mastered by a single person or to be described in a few volumes. This book commemorates the 70th birthday of a great pioneer and teacher of gas dynamics, Dr. Klaus Oswatitsch, Professor of Fluid Mechanics at the Technical University of Vienna and former Director of the Institute for Theoretical Gas Dyna mics, Deutsche Forschungs-und Versuchsanstalt fUr Luft-und Raumfahrt. Several reasons motivated us to prepare an English translation of Oswatitsch's selected sci entific papers. First, we hope that a book containing his major papers will be wel come as a valuable reference text in gas dynamics. Oswatitsch's work is frequently used in the literature in one form or another, but it is usually quite time-consuming for the English speaking reader to consult the original texts. As a result, reference to and understanding of his papers is often incomplete. For example, Oswatitsch's formulation of the equivalence rule hardly ever is quoted in recent textbooks, al though it preceded declassification of Whitcomb's results by several years. Further more, his papers contain much information, which has not yet been fully appreciated in the Anglo-American literature."

Die Neuauflage halt am bewahrten und anerkannten Konzept der Vorauflage fest: ein Grundlagenwerk zum Einsatz in der universitaren Lehre, aber vor allem ein Nachschlagewerk fur den Beruf zum tieferen Verstandnis der verfahrenstechnischen Zusammenhange. Gegenuber der Vorauflage wurde das Werk allerdings erheblich erweitert sowie durch aktuelle Forschungsergebnisse und ein Kapitel zur konzeptuellen Prozessentwicklung erganzt.

Die Grundverfahren werden auf der Basis der Thermodynamik, der Warme- und Stoffubertragung und der Fluiddynamik ubergreifend dargestellt. Damit erhalt der Praktiker erste Informationen uber die Auswahl, die Auslegung und den Betrieb von Apparaten. Nach einer komprimierten Darstellung wichtiger Grundlagen werden u.a. das Destillieren, die Rektifikation, die Absorption, die Kristallisation und die Adsorption behandelt. Es wird aufgezeigt, wie sich grundlagenorientierte Berechnungsansatze fur fluiddynamische und kinetische Vorgange in bekannten und neuen Apparaten finden lassen."

Flowing matter is all around us, from daily-life vital processes (breathing, blood circulation), to industrial, environmental, biological, and medical sciences. Complex states of flowing matter are equally present in fundamental physical processes, far remote from our direct senses, such as quantum-relativistic matter under ultra-high temperature conditions (quark-gluon plasmas). Capturing the complexities of such states of matter stands as one of the most prominent challenges of modern science, with multiple ramifications to physics, biology, mathematics, and computer science. As a result, mathematical and computational techniques capable of providing a quantitative account of the way that such complex states of flowing matter behave in space and time are becoming increasingly important. This book provides a unique description of a major technique, the Lattice Boltzmann method to accomplish this task. The Lattice Boltzmann method has gained a prominent role as an efficient computational tool for the numerical simulation of a wide variety of complex states of flowing matter across a broad range of scales; from fully-developed turbulence, to multiphase micro-flows, all the way down to nano-biofluidics and lately, even quantum-relativistic sub-nuclear fluids. After providing a self-contained introduction to the kinetic theory of fluids and a thorough account of its transcription to the lattice framework, this text provides a survey of the major developments which have led to the impressive growth of the Lattice Boltzmann across most walks of fluid dynamics and its interfaces with allied disciplines. Included are recent developments of Lattice Boltzmann methods for non-ideal fluids, micro- and nanofluidic flows with suspended bodies of assorted nature and extensions to strong non-equilibrium flows beyond the realm of continuum fluid mechanics. In the final part, it presents the extension of the Lattice Boltzmann method to quantum and relativistic matter, in an attempt to match the major surge of interest spurred by recent developments in the area of strongly interacting holographic fluids, such as electron flows in graphene.

In dem Forschungsgebiet "Insektenflug" treffen Fragestellungen der Biologie und der StrAmungsmechanik vielseitig zusammen. Der Bogen reicht von der Konstruktionsmorphologie A1/4ber die Flugbiophysik bis zur Energetik und zum Flugverhalten. Der Autor ist einer der international angesehensten Grundlagenforscher in diesem Forschungsgebiet. Das Buch stellt nicht nur einen Bericht A1/4ber die vielseitigen ForschungsansAtze von ihm und seiner Arbeitsgruppe dar; es bringt auch die allgemeinen Grundlagen und fA1/4hrt mit einer FA1/4lle von Beispielen an die Grenzen des derzeitigen Kenntnisstandes.

Fluid Physics in Geology provides an introductory treatment of the physical and dynamical behavior of fluids, considering first how fluids behave in a general way, then looking more specifically at how they are involved in certain geological processes. The book is aimed at those interested in understanding fluid behavior and motion in the context of a wide variety of geological problems. Helpful example problems following each chapter illustrate applications of the material to realistic problems involving groundwater flows, magma dynamics, open-channel flows, and thermal convection.

This book is devoted to the study of the dynamics of rotating bodies with cavities containing liquid. Two basic classes of motions are analyzed: rotation and libration. Cases of complete and partial filling of cavities with ideal liquid and complete filling with viscous liquid are treated. The volume presents a method for obtaining relations between angular velocities perpendicular to main rotation and external force momentums, which are treated as control. The developed models and methods of solving dynamical problems as well as numerical methods for solving problems of optimal control can be used for studying the dynamics of aircraft in the atmosphere and spacecraft with stores of liquid fuel, which are rotating around some axis for stabilization. The results are also applicable in the development of fast revolving rotors, centrifuges and gyroscopes, which have cavities filled with liquid. This work will be of interest to researchers at universities and laboratories specializing in problems of control for hybrid systems, as well as to under-/postgraduates with this specialization. It will also benefit researchers and practitioners in aerospace and mechanical engineering.