Hydrodynamics Advanced Topics Part 1 docx

HYDRODYNAMICS – ADVANCED TOPICS Edited by Harry Edmar Schulz, André Luiz Andrade Simões and Raquel Jahara Lobosco... Hydrodynamics – Advanced Topics Edited by Harry Edmar Schulz, André L

HYDRODYNAMICS – ADVANCED TOPICS

Edited by Harry Edmar Schulz, André Luiz Andrade Simões and Raquel Jahara Lobosco

Hydrodynamics – Advanced Topics

Edited by Harry Edmar Schulz, André Luiz Andrade Simões and Raquel Jahara Lobosco

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First published December, 2011

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Hydrodynamics – Advanced Topics,

Edited by Harry Edmar Schulz, André Luiz Andrade Simões and Raquel Jahara Lobosco

p cm

ISBN 978-953-307-596-9

free online editions of InTech

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Contents

Preface IX Part 1 Mathematical Models in Fluid Mechanics 1

Chapter 1 One Dimensional Turbulent

Transfer Using Random Square Waves – Scalar/Velocity and Velocity/Velocity Interactions 3

H E Schulz, G B Lopes Júnior,

A L A Simões and R J Lobosco Chapter 2 Generalized Variational Principle

for Dissipative Hydrodynamics:

Shear Viscosity from Angular Momentum Relaxation in the Hydrodynamical Description of Continuum Mechanics 35

German A Maximov Chapter 3 Nonautonomous Solitons:

Applications from Nonlinear Optics

to BEC and Hydrodynamics 51

T L Belyaevaand V N Serkin Chapter 4 Planar Stokes Flows with Free Boundary 77

Sergey Chivilikhin and Alexey Amosov

Part 2 Biological Applications and Biohydrodynamics 93

Chapter 5 Laser-Induced Hydrodynamics in

Water and Biotissues Nearby Optical Fiber Tip 95

V I Yusupov, V M Chudnovskii and V N Bagratashvili Chapter 6 Endocrine Delivery System of NK4, an

HGF-Antagonist and Anti-Angiogenic Regulator, for Inhibitions of Tumor Growth, Invasion and Metastasis 119

Shinya Mizuno and Toshikazu Nakamura

VI Contents

Part 3 Detailed Experimental Analyses of Fluids and Flows 143

Chapter 7 Microrheology of Complex Fluids 145

Laura J Bonales,Armando Maestro, Ramón G Rubio and Francisco Ortega Chapter 8 Hydrodynamics Influence on

Particles Formation Using SAS Process 169

A Montes, A Tenorio, M D Gordillo,

C Pereyra and E J Martinez de la Ossa Chapter 9 Rotational Dynamics of Nonpolar

and Dipolar Molecules in Polar and Binary Solvent Mixtures 185

Sanjeev R Inamdar Chapter 10 Flow Instabilities in

Mechanically Agitated Stirred Vessels 227

Chiara Galletti and Elisabetta Brunazzi Chapter 11 Hydrodynamic Properties of

Aggregates with Complex Structure 251

Lech Gmachowski

Part 4 Radiation-, Electro-,

Magnetohydrodynamics and Magnetorheology 267

Chapter 12 Electro-Hydrodynamics of

Micro-Discharges in Gases

at Atmospheric Pressure 269

O Eichwald, M Yousfi, O Ducasse,

N Merbahi, J.P Sarrette, M Meziane and M Benhenni Chapter 13 An IMEX Method for the Euler Equations that

Posses Strong Non-Linear Heat Conduction and Stiff Source Terms (Radiation Hydrodynamics) 293

Samet Y Kadiogluand Dana A Knoll Chapter 14 Hydrodynamics on Charged Superparamagnetic

Microparticles in Water Suspension:

Effects of Low-Confinement Conditions and Electrostatics Interactions 319

P Domínguez-Garcíaand M.A Rubio Chapter 15 Magnetohydrodynamics of Metallic Foil

Electrical Explosion and Magnetically Driven Quasi-Isentropic Compression 347

Guiji Wang, Jianheng Zhao, Binqiang Luo and Jihao Jiang

Part 5 Special Topics on Simulations and Experimental Data 379

Chapter 16 Hydrodynamics of a Droplet in Space 381

Hitoshi Miura Chapter 17 Flow Evolution Mechanisms of Lid-Driven Cavities 411

José Rafael Toro and Sergio Pedraza R

Chapter 18 Elasto-Hydrodynamics of

Quasicrystals and Its Applications 429

Tian You Fan and Zhi Yi Tang

Preface

“Water is the beginning of everything” (Tales of Mile to)

“Air is the beginning of everything” (Anaxagoras of Mile to)

Introduction

Why is it important to study Hydrodynamics? The answer may be strictly technical, but it may also involve some kind of human feeling about our environment and our (eventual) limitations to deal with its fluidic constituents

As teachers, when talking to our students about the importance of quantifying fluids,

we (authors) go to the blackboard and draw, in blue color, a small circumference in the center of the board, and add the obvious name 'Earth' Some words are then said, in the sense that Hydrodynamics is important, because we are beings strictly adapted to live immersed in a fluidic environment (air), and because we are beings composed basically by simple fluidic solutions (water solutions), encapsulated in fine carbon membranes Then, with a red chalk, we draw two crosses: one inside and the other outside the circumference, explaining: “our environment is very limited We can only survive in the space covered by the blue line No one of us can survive in the inner part of this sphere, or in the outer space Despite all films, games, and books about contacts with aliens, and endless journeys across the universe, our present knowledge only allows to suggest that it is most probable that the human being will extinct while

in this fine fluid membrane, than to create sustainable artificial environments in the cosmos”

Sometimes, to add some drama, we project the known image of the earth on a wall (the image of the blue sphere), and then we blow a soap bubble explaining that the image gives the false impression that the entire sphere is our home But our “home” is better represented by the liquid film of the soap bubble (only the film) and then we touch the bubble, exploding it, showing its fragility

In the sequence, we explain that a first reason to understand fluids would be, then, to guarantee the maintenance of the fluidic environment (the film) so that we could also guarantee our survival as much as possible Further, as we move ourselves and produce our things immersed in fluid, it is interesting to optimize such operations in order to facilitate our survival Still further, because our organisms interchange heat

X Preface

and mass in cellular and corporal scales between different fluids, the understanding of these transports permits us to understand the spreading of diseases, the delivering of medicines to cells, and the use of physical properties of fluids in internal treatments Thus, understanding these transports allows us to improve our quality of life Finally, the observation of the inner part of the sphere, the outer space and its constituents, shows that many “highly energetic” phenomena behave like the fluids around us It gives us the hope that the knowledge of fluids can help, in the future, to quantify, reproduce, control and use energy sources similar to those of the stars, allowing us to

“move through the cosmos”, to create sustainable artificial environments and to leave this “limited film” when necessary Of course, this “speech” may be viewed as a sort

of escapism, related to a fiction of the future In fact, the day-by-day activities show that we are spending our time with “more important” things, like fighting among us for the dividends of the next fashion wave (or the next technical wave), the hierarchy among nations, or the hierarchy of the cultures of the different nations So, fighters, warriors, or generals still seem to be the agents that write our history But global survival, or, in other words, the guarantee of any future history, will need other agents, devoted to other activities The hope lies on the generation of knowledge, in which the knowledge about fluids is vital

Context of the present book “Hydrodynamics - Advanced Topics”

A quick search in virtual book stores may result in more than one hundred titles involving the word “Hydrodynamics” Considering the superposition existing with Fluid Mechanics, the number of titles grows much more Considering all these titles, why try to organize another book on Hydrodynamics? One answer could be that the researchers always try new points of view to understand and treat the problems related to Hydrodynamics Even a much known phenomenon may be re-explained from a point of view that introduces different tools (conceptual, numerical or practical) into the discussion of fluids And eventually, a detail shows to be useful, or even very relevant So, it is necessary to give the opportunity for the different authors to expose their points of view

Among the historically relevant books on Hydrodynamics, some should be mentioned here For example, the volumes “Hydrodynamics” and “Hydraulics”, by Daniel Bernoulli (1738) and his father, Johann Bernoulli (1743) present many interesting sketches and the analyses that converged to the so called “Bernoulli equation”, later deduced more properly by Leonhard Euler Although there are unpleasant questions about the authorship of the main ideas, as pointed out by Rouse (1967) and Calero (2008), both books are placed in a “prominent position” in history, because of their significant contributions The volume written by Sir Horace Lamb (1879), now named

“Hydrodynamics”, considers the basic equations, the vortex motion, and tidal waves, among other interesting topics Considering the classical equations and procedures followed to study fluid motion, the books “Fundamentals of Hydro and Aerodynamics“ and “Applied Hydro and Aerodynamics“ by Prandtl and Tietjens (1934) present the theory and its practical applications in a comprehensive way,

influencing the experimental procedures for several decades For over fifty years, the classical volume of Landau and Lifschitz (1959) remains an extremely valuable work for researchers in fluid mechanics

In addition to the usual themes, like the basic equations and turbulence, this book also covers themes like the relativistic fluid dynamics and the dynamics of superfluids Each

of the major topics considered in the studies of fluid mechanics can be widely discussed, generating specific texts and books An example is the theory of boundary layers, in which the book of Schlichting (1951) has been considered an indispensable reference, because it condenses most of the basic concepts on this subject Further, still considering specific topics, Stoker (1957) and Lighthill (1978) wrote about waves in fluids, while Chandrasekhar (1961) and Drazin and Reid (1981) considered hydrodynamic and hydromagnetic stability It is also necessary to mention the books of Batchelor (1953), Hinze (1958), and Monin and Yaglom (1965), which are notable examples of texts on turbulence and statistical fluid mechanics, showing basic concepts and comparative studies between theory and experimental data A more recent example may be the volume written by Kundu e Cohen (2008), which furnishes a chapter on “biofluid mechanics” The list of the “relevant books” is obviously not complete, and grows continuously, because new ideas are continuously added to the existing knowledge The present book is one of the results of a project that generated three volumes, in which recent studies on Hydrodynamics are described The remaining two titles are

“Hydrodynamics - Natural Water Bodies”, and “Hydrodynamics - Optimizing Methods and Tools” Along the chapters of the present volume, the authors show the application of concepts of Hydrodynamics in different fields, using different points of view and methods The editors thank all authors for their efforts in presenting their chapters and conclusions, and hope that this effort will be welcomed by the professionals working with Hydrodynamics

The book “Hydrodynamics - Advanced Topics” is organized in the following manner: Part 1: Mathematical Models in Fluid Mechanics

Part 2: Biological Applications and Biohydrodynamics

Part 3: Detailed Experimental Analyses of Fluids and Flows

Part 4: Radiation-, Electro-, Magnetohydrodynamics and Magnetorheology

Part 5: Special Topics on Simulations and Experimental Data

Hydrodynamics is a very rich area of study, involving some of the most intriguing theoretical problems, considering our present level of knowledge General nonlinear solutions, closed statistical equations, explanation of sudden changes, for example, are wanted in different areas of research, being also a matter of study in Hydromechanics Further, any solution in this field depends on many factors, or many “boundary conditions” The changing of the boundary conditions is one of the ways through which the human being affects its fluidic environment Changes in a specific site can impose catastrophic consequences in a whole region For example, the permanent leakage of petroleum in one point in the ocean may affect the life along the entire

XII Preface

region covered by the marine currents that transport this oil Gases or liquids, the changes in the quality of the fluids in which we live, certainly affect our quality of life The knowledge about fluids, their movements, and their ability to transport physical properties and compounds is thus recognized as important for life As a consequence, thinking about new solutions for general or specific problems in Hydromechanics may help to attain a sustainable relationship with our environment Re-contextualizing the classical discussion about the truth, in which it was suggested that the “thinking” is the guarantee of our “existence” (St Augustine, 386a, b, 400), we can say that we agree that thinking guarantees the human existence, and that there are too many warriors, and too few thinkers Following this re-contextualized sense, it was also said that the man is a bridge between the “animal” and “something beyond the man” (Nietzsche, 1883) This is an interesting metaphor, because bridges are built crossing fluids (even abysms are filled with fluids) Considering all possible interpretations of this phrase, let us study and understand the fluids, and let us help to build the bridge

Dr Harry Edmar Schulz

Nucleus of Thermal Engineering and Fluids, Department of Hydraulics and Sanitary Engineering,

School of engineering at Sao Carlos,

University of Sao Paulo,

Brazil

Dr Andre Luiz Andrade Simoes

Laboratory of Turbulence and Rheology, Department of Hydraulics and Sanitary Engineering,

School of engineering at Sao Carlos,

University of Sao Paulo,

Brazil

Dr Raquel Jahara Lobosco Laboratory of Turbulence and Rheology,

Department of Hydraulics and Sanitary Engineering,

School of engineering at Sao Carlos,

University of Sao Paulo,

Brazil

References

Batchelor, G.K (1953), The theory of homogeneous turbulence First published in the

Cambridge Monographs on Mechanics and Applied Mathematics series 1953 Reissued in the Cambridge Science Classics series 1982 (ISBN: 0 521 04117 1) Bernoulli, D (1738), Hydrodynamics Dover Publications, Inc., Mineola, New York,

1968 (first publication) and reissued in 2005, ISBN-10: 0486441857

Hydrodynamica, by Daniel Bernoulli, as published by Johann Reinhold Dulsecker at Strassburg in 1738

Bernoulli, J (1743), Hydraulics Dover Publications, Inc., Mineola, New York, 1968

(first publication) and reissued in 2005, ISBN-10: 0486441857 Hydraulica, by Johann Bernoulli, as published by Marc-Michel Bousquet et Cie at Lausanne and Geneva in 1743

Calero, J.S (2008), The genesis of fluid mechanics (1640-1780) Springer, ISBN

978-1-4020-6413-5 Original title: La génesis de la Mecánica de los Fluidos (1640–1780), UNED, Madrid, 1996

Chandrasekhar, S (1961), Hydrodynamic and Hydromagnetic Stability Clarendon

Press edition, 1961 Dover edition, first published in 1981 (ISBN: X)

0-486-64071-Drazin, P.G & Reid, W.H (1981), Hydrodynamic stability Cambridge University

Press (second edition 2004) (ISBN: 0 521 52541 1)

Hinze, J.O (1959), Turbulence McGraw-Hill, Inc second edition, 1975

(ISBN:0-07-029037-7)

Kundu, P.K & Cohen, I.M (2008), Fluid Mechanics 4th ed With contributions by P.S

Ayyaswamy and H.H Hu Elsevier/Academic Press (ISBN 9)

978-0-12-373735-Lamb, H (1879), Hydrodynamics (Regarded as the sixth edition of a Treatise on the

Mathematical Theory of the Motion of Fluids, published in 1879) Dover

Publications, New York., sixth edition, 1993 (ISBN-10: 0486602567)

Landau, L.D.; Lifschitz, E.M (1959), Fluid Mechanics Course of theoretical Physics,

Volume 6 Second edition 1987 (Reprint with corrections 2006) Elsevier (ISBN-10: 0750627670)

Lighthill, J (1978), Waves in Fluids Cambridge University Press, Reissued in the

Cambridge Mathematical Library series 2001, Third printing 2005 (ISBN-10: 0521010454)

Monin, A.S & Yaglom, A.M (1965), Statistical fluid mechanics: mechanics of

turbulence Originally published in 1965 by Nauka Press, Moscow, under the title Statisticheskaya Gidromekhanika-Mekhanika Turbulentnosti Dover edition, first published in 2007 Volume 1 and Volume 2

St Augustine (386a), Contra Academicos, in Abbagnano, N (2007), Dictionary of

Philosophy, “Cogito”, Martins Fontes, Brasil (Text in Portuguese)

St Augustine (386b), Soliloquia, in Abbagnano, N (2007), Dictionary of Philosophy,

“Cogito”, Martins Fontes, Brasil (Text in Portuguese)

St Augustine (400-416), De Trinitate, in Abbagnano, N (2007), Dictionary of

Philosophy, “Cogito”, Martins Fontes, Brasil (Text in Portuguese)

Nietzsche, F (1883), Also sprach Zarathustra, Publicações Europa-América, Portugal

(Text in Portuguese, Ed 1978)

Rouse, H (1967) Preface to the english translation of the books Hydrodynamics and

Hydraulics, already mentioned in this list Dover Publications, Inc

Prandtl, L & Tietjens, O.G (1934) Fundamentals of Hydro & Aeromechanics, Dover

Publications, Inc Ed 1957

XIV Preface

Prandtl, L & Tietjens, O.G (1934) Applied Hydro & Aeromechanics, Dover

Publications, Inc Ed 1957

Schlichting, H (1951), Grenzschicht-Theorie Karlsruhe: Verlag und Druck

Stoker, J.J (1957) Water waves: the mathematical theory with applications

Interscience Publishers, New York (ISBN-10: 0471570346)