MeasurementsofthePrimaryBjerknesForceinaCavitatingUltrasonicFieldBy

MasonSmith

AthesissubmittedtothefacultyofTheUniversityofMississippiinpartialfulfillmentoftherequirementsoftheSallyMcDonnellBarksdaleHonorsCollege.

OxfordMay2019

Approvedby

________________________________Advisor:Dr.JoelMobley

________________________________Reader:Dr.CecilleLabuda

________________________________Reader:Dr.JosephGladden

ii

©2019BradleyMasonSmithALLRIGHTSRESERVED

iii

DEDICATION

Iwouldliketodedicatethisworktomyparents,BillyandRochelle.Iamforever

gratefulfortheamountofloveandcarethattheyhaveinvestedinme.

iv

ACKNOWLEGEMENTS

IwouldfirstliketothankDr.JoelMobley.Hehasbeenanexcellentmentor

andresearchadvisor.IfitwerenotforDr.Mobley,thenIwouldneverhavelearned

abouttheBasicAcousticSummerSchool(BASS)program.ItwasduringtheBASS

programthatIparticipatedinresearchattheNationalCenterforPhysicalAcoustics

(NCPA).IamverythankfulforDr.Mobleyallowingmetheopportunitytoworkwith

himandamthankfulforhispatienceincompletingthisthesis.

Iwouldnextliketothankmyreaders.Dr.LabudaandDr.Gladdenvery

kindlyagreedtobereadersforthiswork,soifitwerenotforthem,Iwouldnothave

beenabletocompletethisthesis.

MynextthankyouisforRandaBaioni.Shehasbeenmybestfriendsincewe

firstmetinHonors101.Shehashelpedmethroughtoughtimesandcontinuesto

stillsupportme.Iamverygratefulforourfriendship.

Tomyfather,mother,andbrothers,thankyouforbelievinginme.Thankyou

foryourloveandsupportofme.

Andfinally,IwouldliketothanktheSallyMcDonnellBarksdaleHonors

Collegeforencouragingmetocompletethisthesis.Iamverythankfulforthis

opportunitytosharemyresearch.

v

ABSTRACT

Cavitationistheresultwhentherearerapidchangesinpressureinaliquid.

Thesevapor-filledcavitiescanoccurwhenultrasoundpropagatesthroughwaterat

sufficientpower.Thevolumesofthesecavitiescanpulsateandcanevencouplewith

theradiationpressurefromtheultrasound.Theresultisatranslationalforceonthe

bubbles.ThistranslationalforceonthebubbleiscalledtheprimaryBjerknesforce.

ThesecondaryBjerknesforceistheresultoftwopulsatingcavities,butthisforceis

ignoredsincethebuoyantforceandtheprimaryBjerknesforcearethedominant

forces.Immediatelybeforeabubblebeginstorise,thenetforceonthebubbleis

equaltozero.Therefore,theprimaryBjerknesforceandthebuoyantforceare

equal.TheprimaryBjerknesforcecanbeindirectlymeasuredbymeasuringthe

diameter(andthusthevolume)ofabubbleimmediatelybeforeitrises.Diameters

ofbubblesweremeasuredusingavideocamcorderandanopen-sourceprogram

calledImageJ.Threesetsofdataweretaken.Eachsetofdataincludesfourcritical

bubbles.TheprimaryBjerknesforcerangesfrom0.15µNto0.41µN.Recent

researchandfutureworkarediscussed.

vi

TABLEOFCONTENTS

1INTRODUCTION......................................................................................................................................1

2THEPROPAGATIONOFULTRASOUNDTHROUGHWATER...............................................2

3THEPRIMARYBJERKNESFORCE...................................................................................................3

3.1THEORYOFTHEPRMIARYBJERKNESFORCE................................................................3

3.2EQUATIONOFTHEPRIMARYBJERKNESFORCE...........................................................5

4INITIALRESEARCHOFTHEPRIMARYBJERKNESFORCE..................................................6

4.1SETUPFORTHESCATTEREDLIGHTMETHOD...............................................................6

4.2METHODS.......................................................................................................................................12

4.3DATAANDRESULTS.................................................................................................................20

5RECENTRESEARCHOFTHEPRIMARYBJERKNESFORCE...............................................26

5.1IMPROVEMENTOFMETHODS..............................................................................................26

5.2RECENTDATAANDRESULTS...............................................................................................28

6CONCLUSIONS.......................................................................................................................................31

7FUTUREWORK.....................................................................................................................................32

vii

LISTOFFIGURESANDTABLES

Figure1:PictureofVilhelmBjerknes.............................................................................................12

Figure2:Schematicdiagramofthesetup.....................................................................................15

Figure3:Pictureofsetup.....................................................................................................................16

Figure4:Close-upoftransducerandreflector...........................................................................17

Figure5:Lineofbubbles......................................................................................................................19

Figure6:Fieldofcavitation.................................................................................................................21

Figure7:Close-upofcavitation.........................................................................................................22

Figure8:Close-uptoillustratestructure......................................................................................23

Figure9:Schematicsetupoflaserlight.........................................................................................25

Figure10:Laserwithcollimatorandaperture..........................................................................26

Figure11:Illuminatingaplaneofcavitation...............................................................................28

Figure12:Close-upofaplaneofbubbles.....................................................................................29

Figure13:CriticalDiameters..............................................................................................................30

Figure14:CriticalVolumes.................................................................................................................31

Figure15:CriticalForces.....................................................................................................................32

Table1:ClassificationofBubbles.....................................................................................................33

Table2:SomeDataforSets.................................................................................................................33

Table3:SummaryofMeasurements...............................................................................................33

Figure16:Bubblesindiffuselight...................................................................................................35

Figure17:Recentmeasurement.......................................................................................................37

Figure18:Side-by-sidecomparison................................................................................................38

Figure19:Hydrophonescanoftransducer..................................................................................41

1INTRODUCTION

Thephysicalphenomenonofsoundisonethatmostpeoplearefamiliarwith.

Thebranchofphysicsthatisconcernedwiththepropagationofmechanicalwaves

throughsolids,liquids,andgasesisknownasacoustics.Thestudyofacousticsdates

back to the 6th century BCE when Pythagoras mathematically described the

propertiesofstringedmusicalinstruments(Karamanides,2006).Astimeprogressed

andthestudyofnaturally-occurringphenomenawasunifiedinwhatwenowknow

asthescienceofphysics,mechanicalwavesbecamebetterunderstoodanddescribed

inmathematicalterms(Berg,2018).Soundcanbeclassifiedaccordingtofrequency.

Theseclassificationsare infrasound(soundwithfrequenciesbelowwhichhumans

canhear),sound(soundswithfrequencieswhichhumanscanhear),andultrasound

(sound with frequencies above which humans can hear). While the study of

infrasoundandsoundcoveravarietyofsubjects,thestudyofultrasoundrevealsa

widevarietyofapplicationsandunusualphenomena.

Ultrasound was first encountered in the 18th century by Italian scientist

Lazzaro Spallanzani during his study of echolocation in bats (Bates, 2011).

UltrasoundwasfirstproducedbyhumanswhenSirFrancisGaltoncreatedwhatis

nowknownasaGaltonwhistle(HistoryofUltrasound|Timelinesince1794,2014).

Ultrasoundhasmanyusefulapplications.Oneoftheseapplicationsisnon-destructive

testing(NDT)whichwasfirstproposedin1929byRussianscientist

1

Sergei Sokolov (A Brief History of Non-Destructive Testing, 2014). The use of

ultrasoundinmodernmedicineismadepossiblebytheuseofultrasonictransducers.

Thesetransducersmakeuseofthepiezoelectriceffect,whichwasdiscoveredin1880

byFrenchphysicistsPierreandPaul-JacquesCurie(Piezoelectricity,2018).Thestudy

of the primary Bjerknes force is one that ismotivated by innovations inmodern

medicinefordrugdelivery.Oneproposedwayofdeliveringdrugstoparticularsites

withinabodyistousepolymer-coatedmicrobubbles(Memolietal,2018).Therefore,

itisimportanttoknowhowtheprimaryBjerknesforceinteractswithmicrobubbles.

2

2THEPROPAGATIONOFULTRASOUNDTHROUGHWATER

Whenultrasoundofsufficientpowerpropagatesthroughwater,itcancreate

cavitationbubbles.Thesearegas-filledcavitiesthatareformedduringthenegative

pressure phase of the acoustic cycle. A small air pocket on a piece of particulate

matter,whichisitselftoosmalltobeseen,growsduringthenegativepressurephase.

As itgrows,gasesdissolved in thewateraredrawninto thebubble,allowing it to

grow to a size large enough to be visualized. Acoustic cavitation is a high power

phenomenon. At low powers, ultrasound will propagate through the water as a

normalwavewithoutchangingthestructure(e.g.,introductioncavitationbubbles)

ofthemedium.Oncethebubblesaregenerated,theycanbetrappedbythegradient

intheultrasonicpressurefield.

3

3THEPRIMARYBJERKNESFORCE

3.1THEORYOFTHEPRIMARYBJERKNESFORCE

It was in 1906 when Norwegian physicist Vilhelm Bjerknes (Figure 1)

publishedFieldsofForce.InFieldsofForce,Bjerknesbeginsbydescribingelectric

andmagneticfields.Hethenextendsthistreatmentofelectricandmagneticfieldsto

fields–specificallythoseinhydrodynamics–thathaveanalogousproperties.Itwas

inthiswaythatBjerkneswasabletomathematicallyderivethetranslationalforceon

bubblesinanacousticfield.

Gasesaredissolvedinliquids.Thesegasesinwatercanbeexcitedandthus

canincreaseinvolume.Whenthesegasesincreaseinvolume,gas-filledbubblesform.

Gas-filled bubbles that are subject to an acoustic pressure field undergo volume

oscillations.Thesevolumeoscillationscancouplewithanon-zeroacousticpressure

gradient.TheresultisatranslationalforceknownastheprimaryBjerknesforce.The

primaryBjerknesforceisequaltothenegativeproductofthetime-varyingvolumeof

abubbleandthepressuregradient. If thisproductvarieswithtime, thenthetime

averageistaken.

𝐹 = − 𝑉 𝑡 𝛻𝑃(𝑟, 𝑡)

ThistranslationalforcewasfirstformulatedbyBjerknes(1906)butwaslater

described by Blake (1949). As ultrasound travels through water, dissolved gases

increaseinvolumeandbecomegas-filledbubbles.Ifthesegas-filledbubbles

4

Figure1

PictureofVilhelmBjerknes.Bjerknes(1862-1951) was a Norwegian physicist whohelped establish the modern field ofmeteorology. It is after Bjerknes for whichthe primary Bjerknes force is named.https://snl.no/Vilhelm_Bjerknes

5

occur at pressure antinodes, theymigrate away. These gas-filled bubbles become

trappedbypressuregradientsandbegintocoalesce.Theforcesonthesebubblesare

thebuoyantforce,theprimaryBjerknesforce,andthesecondaryBjerknesforce.The

secondary Bjerknes force is a force between two pulsating bubbles and is not

consideredinthisworkbecauseweareassumingthatthetheprimaryBjerknesforce

hasthemostinfluenceonthetrappingofabubbleinthefield.

3.2EQUATIONOFTHEPRIMARYBJERKNESFORCE

TheprimaryBjerknesforceisgivenby

𝐹 = − 𝑉 𝑡 𝛻𝑃(𝑟, 𝑡)

The time-varyingvolume𝑉(𝑡) canbedescribed in termsof a time-varying radius

givenby

𝑅𝑅 +32𝑅i =

1𝜌 𝑃k +

2𝜎𝑅k

− 𝑃m𝑅k𝑅

no

−2𝜎𝑅−4𝜇𝑅𝑅

− 𝑃k − 𝑃 𝑡

where𝑅kistheequilibriumradiusofabubble,𝑃kisthehydrostaticpressure,𝑃misthe

vaporpressureinsidethebubble,𝜅isthepolytropicindexofthegas,𝑃(𝑡)isthetime-

varyingpressure,and𝜌, 𝜎,and𝜇aretheliquiddensity,thesurfacetension,andthe

viscosityoftheliquid,respectively(Leighton,1989).Thisequationisknownasthe

Rayleigh-PlessetequationandisderivedfromtheNavier-Stokesequationunderthe

assumption that thebubblesare spherically symmetric.When theacoustic field is

continuous,themagnitudeoftheprimaryBjerknesforcecanbewrittenas

𝐹 = 𝛼𝑃u𝜋𝑓𝑉k𝑐y

where 𝛼 is a constant, 𝑃u is the pressure amplitude, 𝑓 is the frequency, 𝑉k is the

equilibriumvolumeofabubble,and𝑐yisthespeedofsoundinwater.

6

4INITIALRESEARCHOFTHEPRIMARYBJERKNESFORCE

4.1EXPERIMENTALSETUP

ThesetupformeasuringtheprimaryBjerknesforceincludesbothopticaland

acoustic instruments. The purpose of the measurement system is to provide

estimatesoftheprimaryBjerknesforce.Theapproachisknownasthescatteredlight

methodandwas themethodused in thiswork todetermine the force.This setup

allowsforthedirectmeasurementofthevolumesofbubbles.Fromthevolumesof

bubbles, buoyant forces can be calculated. It is from the buoyant forces that the

primaryBjerknesforceonbubblescanbecalculated.Inthismethod,lightisscattered

offofthebubblesinaforwardscatteringmanner.Whenlightisforwardscattered,

thebubbles areonly visible fromaparticulardirection (i.e., from thedirection in

whichthelightistraveling).Thisisanalogoustoseeingdustinaroominasunbeam.

Thesunlightthatisincidentofthedustscattersforwardinawaythatmakesthedust

visible,whileinthebackwarddirectionthedustisnotvisible.Figure2isaschematic

diagramofthesetupforthescatteredlightmethod.Figure3isapictureofthesetup.

Anultrasonictransducerisimmersedinwaterandisconnectedtoaradiofrequency

(RF)generator.TheRFgeneratorprovidesasinusoidalvoltagetothepiezoelectric

crystal in the transducer and allows for adjustments of the frequency and power

appliedtothetransducer.Figure4isapictureofthetransducerandthemetalplate.

Theredblockisusedtoraisethereflectorsoitis

7

8

9

10

closertothetransducer.Asultrasoundpropagatesthroughthewater,itstrikesthe

reflector and travels back towards the transducer. Ultrasound in a liquid is a

longitudinalwave,andtheinterferenceofthecounter-propagatingwavescreatesa

standingwave.Thewavesgeneratecavitationbubbleswhicharetrappedinthenodes

ofthestandingwave.Conversely,theantinodesofthestandingwaveareplacesfrom

whichbubblesmove.Figure5isapicturethatdemonstratesbubblesthataretrapped

in nodes. These nodes are places where pressure is zero, and conversely, the

antinodesareplaceswhere thepressure oscillateswithmaximumamplitude.The

spacingbetweenthebubblesisequaltoone-halfofthewavelengthoftheultrasound.

The speed of sound in water 𝑐 can be calculated by using a fifth-order

polynomialthatwasfittedtoexperimentaldatapoints(Marczak,1997).Thisfifth-

orderpolynomialis

𝑐 = 𝑎`𝑇`b

`cd

where𝑎earecoefficientsandwhere𝑇istemperaturein°C.Pluggingthecoefficients

intothissum,

𝑐 = 1.402385×10j + 5.038813×10lj 𝑇 + −5.799136×10lb 𝑇o

+ 3.287156×10lp 𝑇j + −1.398845×10lq 𝑇r

+ 2.787860×10lso 𝑇b

Thetemperatureofthewaterwas21°CinFigure5.Thismeansthat𝑐 ≈ 1485m/s.

Thefrequency𝑓oftheultrasonictransducerwas1.2MHz.Therefore,thewavelength

𝜆oftheultrasoundwas

𝜆 =𝑐𝑓

11

12

𝜆 =1485m ∙ sls

1.2×10lysls

𝜆 = 1.24mm

Thewavelengthwasmeasuredtobe1.27mm,apercentdifferenceofonly2%relative

tothetheoreticalvalue.

4.2METHODS

Aswasmentionedintheprevioussection,thecavitationiscapturedonavideo

camcorder that isplaced in frontof the tankandadjustedso that thebubblesare

clearlyvisualized.Figure6isanimagetakenofthecavitation.Atfirstglanceitmay

not appear that there is much regularity in the cavitation field, but there exist

repeatingstructures.ThiscanbeseeninFigures7and8.Anexamplesofastructure

thatrepeatsmultipletimesthroughoutthecavitationfieldisthesidelobe.

Oneofthegoalsofthisresearchwastoclassifybubblesbasedontheirsizes

andhowtheybehave.Thebubblesthatareexaminedfirstarethosethatweclassify

assmall.Inthismethod,itwasnotpossibletodeterminetheforcesonthesebubbles

becausetheyremaintrappedthroughouttheexperiment,sothesebubblesarenot

mentioned in Table 1. Nevertheless, these smaller bubbles are important and

therefore are described here. They have a radius of approximately 0.05mm. The

bubbles that aremost prominent among them are the ones along strands. These

bubbles are stationary relative to the larger bubble types. Their motion consists

mostly of small displacements from what can be considered their equilibrium

positions. As a result, they remain fixed in the ultrasound field. Medium, or

transitional, bubblesoccurwhere stationarybubbles coalesce.Theybegin tohave

largedisplacementsfromwhatcanbeconsideredtheirequilibriumpositions.Large,

13

Figure6Fieldofcavitation.Thisfigureshowsthe“cloud”ofcavitation.

14

15

16

orcritical,bubblesareofprimaryinterest.Criticalbubblesmaybethesamesizeor

largerthantransitionalbubbles.Beforecriticalbubblesbegintorise,theirrangesof

motion are quite large. A critical bubblewill begin to rise once its buoyant force

exceedstheprimaryBjerknesforce.

ToestimatethemagnitudeoftheprimaryBjerknesforce,thevolumeofthe

bubbleneedstobemeasured.DevelopedbytheNationalInstitutesofHealth(NIH)

in 1997, ImageJ (https://imagej.nih.gov/ij/download.html) is an open-source

programthatwasusedtomeasurethediameterofbubbles.ImageJcanhelpfacilitate

precisemeasurements.However,theprecisionofmeasurementsisonlyasgoodas

thescalesetbyauser.

There were two main issues encountered when identifying and tracking

criticalbubbles.Thefirstissuewasthenumberofbubblesinthecloudofcavitation.

Thereexistalargenumberofbubblesinacloud.Usingwaterthathasbeendistilled

anddegassedhelpsreducetheamountofcavitationbutnotbyasignificantamount.

Thesecondissuewasidentifyingthelocationofthebubblewithinthecloud.Datais

recordedwithavideocamcorder,and it isnotpossible tomeasure thedepthofa

criticalbubblefromatwo-dimensionalimage.Asolutiontothesetwoproblemsisto

illuminate a plane of the field of cavitation. This is analogous to computed

tomography(CT),aninvaluablediagnosticimagingtoolthatallowsdoctorstoview

“slices” of patients’ bodies. The concept of illuminating a plane in the cloud of

cavitationisillustratedinFigure9.Laserlightiscollimatedandispassedthrougha

thinaperture.ThisisshowninFigure10.Theresultisaplane-likebeamofcollimated

laser light that is incident on the field of cavitation. Figure 11 shows how the

17

Figure9 Schematicsetupoflaserlight.Thisfigureillustratestheconceptforilluminatingaplaneofcavitationwithlaserlight.

18

Figure10 Laserwithcollimatorandaperture.Attachedtothislaser isabeamexpanderandanaperture.Thebeamexpanderwidensthediametersof the the laser light and forms it into a column, and the aperturerestricts the laser light to a plane thatwill illuminate a sliceof thecavitationcloud.

19

cavitation field appearswhenever a plane of interest is illuminated. Thismethod

allows one to focus on a single plane rather than the entire cavitation field. The

advantageisthatwecanfocusattentiononagroupofbubblesratherthananentire

cavitation cloud, as visualized in Figure 12. This makes it easier to identify the

positionsofcriticalbubbles.

4.3DATAANDRESULTS

Data were collected in three sets. Each set of data consists of four

measurements.Thedata includes thepowerand the frequencysettingson theRF

generatorandtheapproximatelocationofthecriticalbubbles.Table2listssomeof

thedata.Theseapproximatelocationsareidentifiedfromthefrontofthesetup(i.e.,

from where the video camcorder was placed). The reason that the power and

frequencywere variedwas so that the reflectedpower from the generator to the

transducerwasataminimum.Inotherwords,thepowerandfrequencywerevaried

sothatthemaximumamountofpowerprovidedwasusedbythetransducer.Figures

13through15listtheaveragecriticaldiameters,theaveragecriticalvolumes,andthe

averagecriticalforces,respectively,foreachdataset.Thediameterofeachbubbleis

measuredineachset.Thecriticaldiametersarethenaveraged.Inasimilarway,the

criticalvolumesandthecriticalforcesarecalculatedforeachbubbleineachset.Table

3summarizestheinformationpresentedinthesefigures.

20

Figure11 Illuminating a plane of cavitation. The top picture is a referencepicturefor thebottompicture.Thebottompictureshowsaplaneofbubblesthatisilluminatedwithlaserlight.

21

22

23

24

25

Table1:ClassificationofBubbles MotionSmall/stationary Slightlymovearoundandarearranged

instrandsMedium/transitional Movearoundmorethanstationary

bubblesbutdonotriseLarge/critical Movearoundjustasmuchas

transitionalbubblesandareabletoriseTable1Thistablesummarizestheclassificationofbubbles.

Table2:SomeDataforSets Power(W) Frequency(MHz) Approximate

Location

Set1 10 1.12

Middleoffieldbetweenthe

transducerandthereflector

Set2 15 1.10

Middleofthefieldbetweenthe

transducerandthereflector

Set3 20 1.00Middleofthefieldtotherightofthe

transducerTable2Thistablelistssomedataforthesetsofbubbles.

Table3:SummaryofMeasurements AverageCritical

Diameter(mm)AverageCriticalVolume(pmR)

AverageCriticalForces(µN)

Set1 0.30(5) 15(6) 0.15(6)Set2 0.38(3) 28(5) 0.28(5)Set3 0.43(1) 41(2) 0.41(2)

Thistableliststheaveragecriticaldiameters,averagecriticalvolumes,and average critical forces for the sets. The numbers in parenthesesindicatetheuncertaintyinthelastdigit.

Table3

26

5RECENTRESEARCHOFTHEPRIMARYBJERKNESFORCE

5.1IMPROVEMENTOFMETHODS

TheinitialmeasurementsoftheprimaryBjerknesforcerangedfrom0.15µN

to0.41µN.Asmentionedbefore,thesemeasurementsshouldreallybereferredtoas

estimates.AforcethatiscomparabletotheprimaryBjerknesforceistheweight(on

Earth)ofasinglegrainofsand.

One problem with the scattered light method was the uncertainty of the

diameterofthebubbles.Inadditiontonotknowingtheexactdiametersofbubbles,

the exact location of the bubbles remained unknown. Again, the locations of the

bubbles were approximate and were based on their positions relative to the

transducer.Fortunately,thesetwoproblemscanberesolved.

Thefirstoftheseproblemsarisesfromthescatteredlight.Whenlightscatters

fromabubble,itmayrefractseveraltimesinsideabubblebeforeitexits.Thismakes

thebubbleappearbright.Theresultisabubblethatisnotwelldefined.Insteadof

scatteringlightfromthebubbles,itwasdecidedthatitwouldbebettertohavelight

bediffusedandtobebehindthebubbles.Thisallowstheedgesofthebubblestobe

welldefined,asshowninFigure16.

Asolutiontothesecondproblemmentionedistosimplyuseasecondcamera

thatis90°fromthefirst.Thisallowsforthedeterminationofthepositionsofcritical

bubblesinthreedimensions.

27

Figure16 Bubbles in diffuse light. This figure shows how well defined thebubblesarewheneverlightisdiffusedbehindthebubbles.

28

5.2RECENTDATAANDRESULTS

Results from the improved setup agreewith results from the initial setup.

Figure17showsacriticalbubble(indicatedbythearrow)thathasadiameterof1.04

mm.Itsposition,asmeasuredfromtheorigin𝑂oftheaxis,isalsogivenandisinunits

ofmm.TheprimaryBjerknesforceonthiscriticalbubblewascalculatedtobe5.8µN.

Figure18showsaside-by-sidecomparisonofacriticalbubblethatisviewedfrom

differentangles.TheimprovementofmethodsformeasuringtheprimaryBjerknes

forceispartofanon-goingworktobereportedinthefuture.

29

𝑂

Figure17 Recentmeasurement.ThisisFigure13butincludesameasurementthat offers a more precise determination of the diameter andpositionofthebubblethanisofferedbythescatteredlightmethod.

30

Figure18 Side-by-sidecomparison.Thebubblesthatareencircledinredarethesamebubbles.Thepictureon the left is taken from the frontof thetank,andthepictureontherightistakenfromthesideoftank.

31

6CONCLUSIONS

Measuring the primary Bjerknes forces on bubbles is possible by first

measuringthediametersofbubbles.Oncethediametersofbubblesareknown,the

volumesofthebubblescanbecalculated,thusleadingtothebuoyantforces.These

buoyantforcesareequalinmagnitudetotheprimaryBjerknesforcesimmediately

beforethebubblesbegintorise.TheprimaryBjerknesforcesrangedfrom0.15µNto

0.48µN.TheinitialmeasurementsoftheprimaryBjerknesforcewerebasedonthe

scatteredlightmethod.Thismethodwillberefinedinfutureworkbyusingdiffuse

lightinsteadofscatteredlight.Inadditiontothediffuselight,asecondcamerawillbe

usedsothatthelocationofthebubblesinthreedimensionscanbemeasured.

32

7FUTUREWORK

Measurements of theprimaryBjerknes forcehavebeen establishedbut do

needtoberefined.Onegoaloffutureworkistoimprovethequalityoftheimagesso

that the diameters of the bubbles can be better determined. In addition to better

measurementsof thediametersofbubbles,more setsofdata shouldberecorded.

Eachsetofdatashouldvaryinpowerandfrequencysothattrendscanbeidentified.

Also, measurements of the primary Bjerknes force should be compared to

predictions.AhydrophonescanoftheacousticpressureisshowninFigure19.These

predictions will compare the radiation pressure measured in a location to the

radiationpressurepredictedbyamodel. Itwouldbeadvantageous tousecode to

automatethemeasuringofcriticalbubblesandtheirlocationsrelativetoanorigin

andtotrackthemotionofcriticalbubbles.

33

Figure19 Hydrophonescanoftransducer.Thesegraphsshowthemagnitudeoftheacousticpressureasafunctionofdistance.Thepictureontheleftshowstheacousticpressureasviewedlookingdirectlyupatthefaceofthetransduceratadistanceofapproximately7cm.Thepictureoftherightisaside-viewofthemagnitudeoftheacousticpressure.

34

REFERENCES

Bates,M.(2011).Discoveringsonarinbats,AmericanAssociationfortheAdvancementofScience,Available:https://www.aaas.org/discovering-sonar-bats,(datelastviewed:01-May-19).RetrievedMay1,2019,fromhttps://www.aaas.org/discovering-sonar-batsABriefHistoryofNon-DestructiveTesting,(2014).ABriefHistoryofNon-DestructiveTesting-Non-DestructiveTesting(NDT)Blog,Available:http://tspndt.com/non-destructive-testing-industrial-supplies-blog/a-brief-history-of-non-destructive-testing,(datelastviewed:01-May-19).RetrievedMay1,2019,fromhttp://tspndt.com/non-destructive-testing-industrial-supplies-blog/a-brief-history-of-non-destructive-testingBerg,R.E.(2018).Acoustics,EncyclopædiaBritannica,Available:https://www.britannica.com/science/acoustics/Modern-advances,(datelastviewed:01-May-19).RetrievedMay1,2019,fromhttps://www.britannica.com/science/acoustics/Modern-advancesBlake,F.G.,Jr.(1949).“BjerknesForcesinStationarySoundFields,”TheJournaloftheAcousticalSocietyofAmerica,21,551–551.HistoryofUltrasound|Timelinesince1794,(2014).UltrasoundTechnicianSchools,Available:http://ultrasoundschoolsguide.com/history-of-ultrasound/,(datelastviewed:01-May-19).RetrievedMay1,2019,fromhttp://ultrasoundschoolsguide.com/history-of-ultrasound/Karamanides,D.(2006).Pythagoras:pioneeringmathematicianandmusicaltheoristofAncientGreece,RosenCentral,NewYorkLeighton,T.G.,Walton,A.J.,andPickworth,M.J.W.(1990).“PrimaryBjerknesforces,”EuropeanJournalofPhysics,11,47–50.Marczak,W.(1997).“Waterasastandardinthemeasurementsofspeedofsoundinliquids,”TheJournaloftheAcousticalSocietyofAmerica,102,2776–2779.Memoli,G.;Baxter,K.O.;Jones,H.G.;Mingard,K.P.;Zeqiri,B.AcoustofluidicMeasurementsonPolymer-CoatedMicrobubbles:PrimaryandSecondaryBjerknesForces.Micromachines2018,9,404.Piezoelectricity,EncyclopædiaBritannica(2018),Available:https://www.britannica.com/science/piezoelectricity,(datelastviewed:01-May-19).RetrievedMay1,2019,fromhttps://www.britannica.com/science/piezoelectricity

35

TheHistoryofUltrasound,BMUS,Available:https://www.bmus.org/about-ultrasound/history-of-ultrasound/,(datelastviewed:01-May-19).RetrievedMay1,2019,fromhttps://www.bmus.org/about-ultrasound/history-of-ultrasound/

36