Table Of ContentCavitation in Non-Newtonian Fluids
Emil-Alexandru Brujan
Cavitation in Non-Newtonian
Fluids
With Biomedical and Bioengineering
Applications
123
Emil-AlexandruBrujan
UniversityPolitechnicaofBucharest
DepartmentofHydraulics
Spl.Independentei313,sector6
060042Bucharest
Romania
[email protected]
ISBN978-3-642-15342-6 e-ISBN978-3-642-15343-3
DOI10.1007/978-3-642-15343-3
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber:2010935497
©Springer-VerlagBerlinHeidelberg2011
Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis
concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,
reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication
orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,
1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations
areliabletoprosecutionundertheGermanCopyrightLaw.
Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnot
imply, even in the absence of a specific statement, that such names are exempt from the relevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Coverdesign:WMXDesignGmbH,Heidelberg
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(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
thevapourpressurecorrespondingtotheambienttemperature.Theregionsoflow
pressuremaybeassociatedwitheitherahighfluidvelocityorvibrations.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
importantfactorinthelifeofplantsandanimals,includinghumans.
Several books and review articles have addressed general aspects of bubble
dynamicsandcavitationinNewtonianfluidsbutthereis,atpresent,nobookdevoted
totheelucidationofthesephenomenainnon-Newtonianfluids.Theproposedbook
is intended to provide such a resource, its significance being that non-Newtonian
fluidsarefarmoreprevalentintherapidlyemergingfieldsofbiomedicineandbio-
engineering,inadditiontobeingwidelyencounteredintheprocessindustries.The
objective of this book is to present a comprehensive perspective of cavitation and
bubbledynamicsfromthestandpointofnon-Newtonianfluidmechanics,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-Newtonianfluidsaredescribedinthisbook.
Itisessentialtounderstandthattheeffectsofnon-Newtonianpropertiesonbub-
ble dynamics and cavitation are fundamentally different from those of Newtonian
fluids.Arguablythemostsignificanteffectarisesfromthedramaticincreaseinvis-
cosity of polymer solutions in an extensional flow, such as that generated about a
sphericalbubbleduringitsgrowthorcollapsephase.Specifically,polymers,which
arerandomly-orientedcoilsintheabsenceofanimposedflow-field,arepulledapart
andmayincreasetheirlengthbythreeordersofmagnitudeinthedirectionofexten-
sion. As a result, the solution can sustain much greater stresses, and pinching is
stoppedinregionswherepolymersarestretched.Furthermore,manybiologicalflu-
ids, such as blood, synovial fluid, and saliva, have non-Newtonian properties and
v
vi Preface
candisplaysignificantviscoelasticbehaviour.Therefore,thisisanimportanttopic
because cavitationisplayinganincreasingly importantroleinthedevelopment of
modernultrasoundandlaser-assistedsurgicalprocedures.
Despitetheirincreasingbioengineeringapplications,acomprehensivepresenta-
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,astheelementsrequiredforanunderstandingoftherelevantprocessesare
wide-ranging.Consequently,researcherswhoinvestigatecavitationphenomenonin
non-Newtonianfluidsoriginatefromseveraldisciplines.Moreover,theresultingsci-
entificreportsareoftennarrowinscopeandscatteredinjournalswhosefocirange
fromthephysicalsciencesandengineeringtomedicalsciences.Thepurposeofthis
book is to provide, for the first time, an improved mechanistic understanding of
bubbledynamicsandcavitationinnon-Newtonianfluids.
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
cavitationinception.Thedynamicsofsphericalandnon-sphericalbubblesoscillat-
inginnon-Newtonianfluidsareexaminedusingvariousmathematicalmodels.One
mainmessagehereisthattheintroductionofideasfromtheoreticalstudiesofnon-
linear acoustics and modern optical techniques has led to some major revisions in
ourunderstandingofthistopic.Twochaptersaredevotedtohydrodynamiccavita-
tionandcavitationerosion,withspecialemphasisonthemechanismsofcavitation
erosioninnon-Newtonianfluids.
The second part of the book describes the role of cavitation and bubbles in the
therapeuticapplicationsofultrasoundandlasersurgery.Wheneverlaserpulsesare
usedtoablateordisrupttissueinaliquidenvironment,cavitationbubblesarepro-
ducedwhichinteractwiththetissue.Theinteractionbetweencavitationbubblesand
tissuemaycausecollateraldamagetosensitivetissuestructuresinthevicinityofthe
laserfocus,anditmayalsocontributeinseveralwaystoablationandcutting.These
situations are encountered in laser angioplasty and transmyocardial laser revascu-
larization.Cavitationisalsooneofthemostexploitedbioeffectsofultrasoundfor
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
frameworkwhereinnovelandimprovedsurgicaltechniquescanbedeveloped.
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
micrometerandmicrosecondscales.Thisbookisofferedtomechanicalengineers,
chemicalengineersandbiomedicalengineers;itcanbeusedforselfstudy,aswell
asinconjunctionwithalecturecourse.
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
ProfessorYoichiroMatsumoto(UniversityofTokyo),ProfessorGaryA.Williams
(University California Los Angeles), and Professor J.R. Blake (University of
Birmingham).IalsoappreciatefruitfulconversationswithandkindhelpIreceived
from Professor Werner Lauterborn (Göttingen University), Dr. Teiichiro Ikeda
(Hitachi Ltd), Dr. Kester Nahen (Heidelberg Engineering GmbH), and Peter
Schmidt.
Bucharest,Romania Emil-AlexandruBrujan
June2010
Contents
1 Non-NewtonianFluids . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 NewtonianFluids . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Non-NewtonianFluids . . . . . . . . . . . . . . . . . . . 4
1.2 Non-NewtonianFluidBehaviour . . . . . . . . . . . . . . . . . . 7
1.2.1 SimpleFlows . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.2 IntrinsicViscosityandSolutionClassification . . . . . . . 12
1.2.3 DimensionlessNumbers . . . . . . . . . . . . . . . . . . 13
1.2.4 ConstitutiveEquations . . . . . . . . . . . . . . . . . . . 15
1.3 Rheometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.3.1 ShearRheometry . . . . . . . . . . . . . . . . . . . . . . 25
1.3.2 ExtensionalRheometry . . . . . . . . . . . . . . . . . . . 29
1.3.3 MicrorheologyMeasurementTechniques. . . . . . . . . . 32
1.4 ParticularNon-NewtonianFluids . . . . . . . . . . . . . . . . . . 34
1.4.1 Blood . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.4.2 SynovialFluid . . . . . . . . . . . . . . . . . . . . . . . . 37
1.4.3 Saliva . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1.4.4 CellConstituents . . . . . . . . . . . . . . . . . . . . . . 41
1.4.5 OtherViscoelasticBiologicalFluids . . . . . . . . . . . . 43
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2 Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.1 NucleationModels . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2 NucleiDistribution . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.2.1 DistributionofCavitationNucleiinWater . . . . . . . . . 53
2.2.2 DistributionofCavitationNucleiinPolymerSolutions . . 54
2.2.3 CavitationNucleiinBlood . . . . . . . . . . . . . . . . . 55
2.3 TensileStrength . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3 BubbleDynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1 SphericalBubbleDynamics. . . . . . . . . . . . . . . . . . . . . 63
3.1.1 GeneralEquationsofBubbleDynamics . . . . . . . . . . 63
ix
x Contents
3.1.2 TheEquationsofMotionfortheBubbleRadius . . . . . . 65
3.1.3 HeatandMassTransferThroughtheBubbleWall . . . . . 81
3.1.4 ExperimentalResults . . . . . . . . . . . . . . . . . . . . 82
3.1.5 BubblesinaSound-IrradiatedLiquid . . . . . . . . . . . . 86
3.2 AsphericalBubbleDynamics . . . . . . . . . . . . . . . . . . . . 91
3.2.1 BubblesNearaRigidWall . . . . . . . . . . . . . . . . . 92
3.2.2 BubblesBetweenTwoRigidWalls . . . . . . . . . . . . . 98
3.2.3 BubblesinaShearFlow . . . . . . . . . . . . . . . . . . 98
3.2.4 Shock-WaveBubbleInteraction . . . . . . . . . . . . . . 99
3.3 BubblesNearanElasticBoundary . . . . . . . . . . . . . . . . . 101
3.4 BubblesinTissuePhantoms . . . . . . . . . . . . . . . . . . . . 107
3.5 EstimationofExtensionalViscosity . . . . . . . . . . . . . . . . 110
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4 HydrodynamicCavitation . . . . . . . . . . . . . . . . . . . . . . . . 117
4.1 Non-cavitatingFlows . . . . . . . . . . . . . . . . . . . . . . . . 118
4.1.1 DragReduction . . . . . . . . . . . . . . . . . . . . . . . 118
4.1.2 ReductionofPressureDropinFlowsThroughOrifices . . 121
4.1.3 VortexInhibition . . . . . . . . . . . . . . . . . . . . . . 123
4.2 CavitatingFlows . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.2.1 CavitationNumber . . . . . . . . . . . . . . . . . . . . . 124
4.2.2 JetCavitation . . . . . . . . . . . . . . . . . . . . . . . . 126
4.2.3 CavitationAroundBluntBodies . . . . . . . . . . . . . . 129
4.2.4 VortexCavitation . . . . . . . . . . . . . . . . . . . . . . 134
4.2.5 CavitationinConfinedSpaces . . . . . . . . . . . . . . . 143
4.2.6 MechanismsofCavitationSuppression
byPolymerAdditives . . . . . . . . . . . . . . . . . . . . 148
4.3 EstimationofExtensionalViscosity . . . . . . . . . . . . . . . . 149
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5 CavitationErosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.1 CavitationErosioninNon-NewtonianFluids. . . . . . . . . . . . 156
5.2 MechanismsofCavitationDamageinNewtonianFluids . . . . . 163
5.3 ReductionofCavitationErosioninPolymerSolutions . . . . . . . 171
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6 CardiovascularCavitation . . . . . . . . . . . . . . . . . . . . . . . 175
6.1 CavitationforUltrasonicSurgery . . . . . . . . . . . . . . . . . . 175
6.1.1 Sonothrombolysis . . . . . . . . . . . . . . . . . . . . . . 175
6.1.2 UltrasoundContrastAgents . . . . . . . . . . . . . . . . . 177
6.2 CavitationinLaserSurgery . . . . . . . . . . . . . . . . . . . . . 199
6.2.1 TransmyocardialLaserRevascularization . . . . . . . . . 199
6.2.2 LaserAngioplasty . . . . . . . . . . . . . . . . . . . . . . 202
6.3 CavitationinMechanicalHeartValves . . . . . . . . . . . . . . . 206
6.3.1 DetectionofCavitationinMechanicalHeartValves . . . . 206
