Cavitation in Non-Newtonian Fluids Emil-Alexandru Brujan Cavitation in Non-Newtonian Fluids With Biomedical and Bioengineering Applications 123 Emil-Alexandru Brujan University Politechnica of Bucharest Department of Hydraulics Spl. Independentei 313, sector 6 060042 Bucharest Romania [email protected] ISBN 978-3-642-15342-6 e-ISBN 978-3-642-15343-3 DOI 10.1007/978-3-642-15343-3 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010935497 © Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface Cavitation is the formation of voids or bubbles containing vapour and gas in an otherwise homogeneous fluid in regions where the pressure falls locally to that of the vapour pressure corresponding to the ambient temperature. The regions of low pressure may be associated with either a high fluid velocity or vibrations. Cavitation is an important factor in many areas of science and engineering, including acous- tics, biomedicine, botany, chemistry and hydraulics. It occurs in many industrial processes such as cleaning, lubrication, printing and coating. While much of the research effort into cavitation has been stimulated by its occurrence in pumps and other fluid mechanical devices involving high speed flows, cavitation is also an important factor in the life of plants and animals, including humans. Several books and review articles have addressed general aspects of bubble dynamics and cavitation in Newtonian fluids but there is, at present, no book devoted to the elucidation of these phenomena in non-Newtonian fluids. The proposed book is intended to provide such a resource, its significance being that non-Newtonian fluids are far more prevalent in the rapidly emerging fields of biomedicine and bio- engineering, in addition to being widely encountered in the process industries. The objective of this book is to present a comprehensive perspective of cavitation and bubble dynamics from the stand point of non-Newtonian fluid mechanics, physics, chemical engineering and biomedical engineering. In the last three decades this field has expanded tremendously and new advances have been made in all fronts. Those that affect the basic understanding of cavitation and bubble dynamics in non-Newtonian fluids are described in this book. It is essential to understand that the effects of non-Newtonian properties on bub- ble dynamics and cavitation are fundamentally different from those of Newtonian fluids. Arguably the most significant effect arises from the dramatic increase in vis- cosity of polymer solutions in an extensional flow, such as that generated about a spherical bubble during its growth or collapse phase. Specifically, polymers, which are randomly-oriented coils in the absence of an imposed flow-field, are pulled apart and may increase their length by three orders of magnitude in the direction of exten- sion. As a result, the solution can sustain much greater stresses, and pinching is stopped in regions where polymers are stretched. Furthermore, many biological flu- ids, such as blood, synovial fluid, and saliva, have non-Newtonian properties and v vi Preface can display significant viscoelastic behaviour. Therefore, this is an important topic because cavitation is playing an increasingly important role in the development of modern ultrasound and laser-assisted surgical procedures. Despite their increasing bioengineering applications, a comprehensive presenta- tion of the fundamental processes involved in bubble dynamics and cavitation in non-Newtonian fluids has not appeared in the scientific literature. This is not sur- prising, as the elements required for an understanding of the relevant processes are wide-ranging. Consequently, researchers who investigate cavitation phenomenon in non-Newtonian fluids originate from several disciplines. Moreover, the resulting sci- entific reports are often narrow in scope and scattered in journals whose foci range from the physical sciences and engineering to medical sciences. The purpose of this book is to provide, for the first time, an improved mechanistic understanding of bubble dynamics and cavitation in non-Newtonian fluids. The book starts with a concise but readable introduction into non-Newtonian fluids with a special emphasis on biological fluids (blood, synovial liquid, saliva, and cell constituents). A distinct chapter is devoted to nucleation and its role on cavitation inception. The dynamics of spherical and non-spherical bubbles oscillat- ing in non-Newtonian fluids are examined using various mathematical models. One main message here is that the introduction of ideas from theoretical studies of non- linear acoustics and modern optical techniques has led to some major revisions in our understanding of this topic. Two chapters are devoted to hydrodynamic cavita- tion and cavitation erosion, with special emphasis on the mechanisms of cavitation erosion in non-Newtonian fluids. The second part of the book describes the role of cavitation and bubbles in the therapeutic applications of ultrasound and laser surgery. Whenever laser pulses are used to ablate or disrupt tissue in a liquid environment, cavitation bubbles are pro- duced which interact with the tissue. The interaction between cavitation bubbles and tissue may cause collateral damage to sensitive tissue structures in the vicinity of the laser focus, and it may also contribute in several ways to ablation and cutting. These situations are encountered in laser angioplasty and transmyocardial laser revascu- larization. Cavitation is also one of the most exploited bioeffects of ultrasound for therapeutic advantage. In both cases, the violent implosion of cavitation bubbles can lead to the generation of shock waves, high-velocity liquid jets, free radical species, and strong shear forces that can damage the nearby tissue. Knowledge of these physical mechanisms is therefore of vital importance and would provide a framework wherein novel and improved surgical techniques can be developed. This field is as interdisciplinary as any, and the numerous disciplines involved will continue to overlook and reinvent each others’ work. My hope in this book is to attempt to bridge the various communities involved, and to convey the inter- est, elegance, and variety of physical phenomena that manifest themselves on the micrometer and microsecond scales. This book is offered to mechanical engineers, chemical engineers and biomedical engineers; it can be used for self study, as well as in conjunction with a lecture course. I would like to gratefully acknowledge the advice and help I received from Professor Alfred Vogel (Institute of Biomedical Optics, University of Lübeck), Preface vii Professor Yoichiro Matsumoto (University of Tokyo), Professor Gary A. Williams (University California Los Angeles), and Professor J.R. Blake (University of Birmingham). I also appreciate fruitful conversations with and kind help I received from Professor Werner Lauterborn (Göttingen University), Dr. Teiichiro Ikeda (Hitachi Ltd), Dr. Kester Nahen (Heidelberg Engineering GmbH), and Peter Schmidt. Bucharest, Romania Emil-Alexandru Brujan June 2010 Contents 1 Non-Newtonian Fluids .......................... 1 1.1Definitions.............................. 1 1.1.1NewtonianFluids...................... 1 1.1.2Non-NewtonianFluids................... 4 1.2Non-NewtonianFluidBehaviour.................. 7 1.2.1SimpleFlows........................ 7 1.2.2IntrinsicViscosityandSolutionClassification....... 12 1.2.3DimensionlessNumbers.................. 13 1.2.4 Constitutive Equations . .................. 15 1.3 Rheometry . ............................ 25 1.3.1 Shear Rheometry ...................... 25 1.3.2 Extensional Rheometry . .................. 29 1.3.3 Microrheology Measurement Techniques . ........ 32 1.4ParticularNon-NewtonianFluids.................. 34 1.4.1Blood............................ 34 1.4.2 Synovial Fluid . ....................... 37 1.4.3Saliva............................ 40 1.4.4 Cell Constituents ...................... 41 1.4.5 Other Viscoelastic Biological Fluids ............ 43 References . ............................ 43 2 Nucleation ................................ 49 2.1 Nucleation Models . ....................... 49 2.2NucleiDistribution......................... 53 2.2.1DistributionofCavitationNucleiinWater......... 53 2.2.2 Distribution of Cavitation Nuclei in Polymer Solutions . 54 2.2.3CavitationNucleiinBlood................. 55 2.3 Tensile Strength ........................... 57 References . ............................ 59 3 Bubble Dynamics ............................ 63 3.1 Spherical Bubble Dynamics