yang 2010 advances in heat transfer

8/12/2019 Yang 2010 Advances in Heat Transfer

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ADVANCESINHEATTRANSFERVOL.42

PlasmaDischargeinWaterYONGYANG,ALEXANDERFRIDMAN,andYOUNGI.CHO*

DepartmentofMechanicalEngineeringandMechanics,DrexelUniversity,Philadelphia,PA19104,USA

I.IntroductionA.NEEDS FOR PLASM A WATER TREATM ENT1. CoolingWaterManagement

Water is used as a cooling medium in large centralized airconditioningsystemsaswellasinthermoelectricpowerplants.Inbothcases,thecoolingwater plays an essential role in removing heat from condensers. Since theevaporation of pure water is the basic means to remove heat from thecondensers, the concentration of mineral ions in circulating cooling waterincreaseswithtime,resultinginhardwaterwithinaweekevenifsoftwaterisusedasmakeupwater.Hence,apartofthecirculatingwaterisperiodicallyorcontinuouslydischargedinordertomaintaintheproperconcentrationofthemineralionsincirculatingcoolingwaterintheformofblowdown.

Thermoelectricpowerplantsproduceabouthalfofthenationselectricity.AccordingtotheUSGeologicalSurveys(USGS)waterusesurveydata[1],thermoelectric generation accounted for 39% (136 billion gallons per day[BGD]) of all freshwater withdrawals in the nation in 2000, second only toirrigation(seeFig.1) [ 1].Furthermore,theaveragedailynationalfreshwaterconsumption for thermoelectric power generation is predicted to increasefromthecurrent4BGDfortheproductionofapproximately720GWelec-tricityto8BGDfor840GWin2030(seeFig.2 ) [2].

In the cooling water management, it is important to distinguish betweenwater withdrawal and water consumption. Water withdrawal representsthetotalwatertakenfromasource,whilewaterconsumptionrepresentstheamount of water withdrawal that is not returned to the source. Freshwaterconsumptionfortheyear1995(themostrecentyearforwhichthesedataareavailable) is presented in Fig. 3. Freshwater consumption for thermoelectric*Currentaddress:DepartmentofMechanicalEngineeringandMechanics,DrexelUniversity,Philadelphia,PA19104,USA

AdvancesinHeatTransfer 179 Copyright2010ElsevierInc.Volume42ISSN00652717 AllrightsreservedDOI:10.1016/S00652717(10)420031


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180 Y.YANGETAL.

Domestic,1%Publicsupply,13%

Mining,1%

Irrigation,40%

Livestock,1%

Aquaculture,1%

Industrial,5%

Thermoelectric,39%

FIG. 1. U.S. freshwater withdrawal (2000). Source: USGS, Estimated use of water in theUnitedStatesin2000,USGSCircular1268,March2004.Addupmaynotbeequalto100%duetorounding.

10 900

Case1

Case2

Case3

Case4

Case5

Generation

2005 2010 2015 2020 2025 2030

Year

Waterconsu

mption(BGD)

8508

8006

Therm

oelectric

generatingcapacity(GW)

750

700

650

4

2

0 600

FIG. 2. Average daily national freshwater consumption for thermoelectric powergeneration 20052030 (predicted). Source: DOE/Office of Fossil Energys Energy & WaterR&DProgram,2008.usesappearslow(only3%)whencomparedwithotherusecategories(irriga-tion was responsible for 81% of water consumed). However, even at 3%consumption,thermoelectricpowerplantsconsumedmorethan4BGD[1].

A modern 1000MW thermoelectric power plant with 40% efficiency wouldreject1500MWofheatatfullload.Thisisroughlyequivalentto512106Btu/handusesabout760,000gal/minofcirculatingwaterbasedon18Ftemperaturedifferenceincondenser[3].Asheatisremovedviatheevaporationofpurewateratacoolingtower,theneedforthemakeupwaterisabout7500gal/minforthetypical fossil plant, which resultsin10milliongallonsaday[3].


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181PLASMADISCHARGEINWATER

Commercial,1%

Thermoelectric,3%

Mining,1%

Industrial,3%

Livestock,3%

Domestic,6%

Irrigation,81%

FIG.3. U.S.freshwaterconsumption(1995).Source:USGS,EstimateduseofwaterintheUnited

States

in

1995,

USGS

Circular

1220,

1998.

Addup

may

not

be

equal

to

100%

due

to

rounding.

Oneofthecriticalissuesinthecoolingwatermanagementisthecondensertubefoulingbymineralionssuchascalciumandmagnesium.Sincecalciumcarbonate(CaCO3)problemismostcommonincoolingwater,onecanusethetermcalciumscaletoreferallscalescausedbymineralions.Inordertoprevent or minimize the condenser tube fouling, the cycle of concentration(COC) in wet recirculation cooling systems is often kept at 3.5. Sinceincreasing

the

COC

can

reduce

the

amount

of

makeup

water,

the

water

consumption can be reduced with the increased COC. For example, if onecan increase the COC to 8, the freshwater consumption can be reduced byapproximately25%,meaningthatthemakeupwatercanbereducedby2.5milliongallonsadayina1000MWthermoelectricpowerplant.

Since the amounts of mineral ions in circulating cooling water primarilydependontheCOC,thecondenser tube fouling alsodependsontheCOC.Hence, the issue in the cooling water management is to increase the COCwithout the condenser fouling problem. The present review deals with aninnovative

water

treatment

technology

utilizing

plasma

discharges

in

water,

with which one can increase the COC without the fouling problem incondenser tubes. The key issue is how to precipitate and remove mineralionssuchascalciumandmagnesiumfromcirculatingcoolingwatersothatthe CaCO3 scales can be prevented at the condenser tubes and at the sametimetheCOCcanbeincreased.

2. WaterSterilizationTheavailabilityofcleanwaterisanissuethathasparalleledthecontinual

increaseinwaterconsumptionduetobothglobalpopulationgrowthandtheeconomicdevelopmentinanumberofdevelopingcountries.Fromaglobal


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182 Y.YANGETAL.

perspective,anestimated1.1billionpeopleareunabletoacquirecleansafewater [4]. As estimated by the Environmental Protection Agency (EPA),nearly 35% of all deaths in developing countries are directly related tocontaminated water [5]. The need for improved water treatment exists onboth political and humanitarian dimensions. Contaminated water can beattributed to a number of factors, including chemical fouling, inadequatetreatment,deficientorfailingwatertreatment,andpoordistributionsystem.An additional cause of contamination is the presence of untreated bacteriaand viruses within the water. Even in the United States, the increasedpresence ofEscherichiacoli (E.coli),alongwith variousotherbacteria,hasbeenacauseforconcern.

Inanefforttoinactivatebacteria,thereareseveralcommerciallyavailablemethodssuchaschemicaltreatments,ultraviolet(UV)radiation,andozoneinjection technologies. The experimental success and commercialization ofthesewatertreatmentmethodsarenot,however,withoutdeficiencies.Withregard to human consumption, chemical treatments such as chlorinationcould render potable water toxic. Although both UV radiation and ozoneinjectionhavebeenproventobepracticalmethodsforthedecontaminationofwater,theeffectivenessofsuchmethodslargelydependsuponadherencetoregimentedmaintenanceschedules.Itisbecauseofthesedeficienciesthatthe importance of research and development of new and improved watertreatmentmethodscontinuestogrow.B.PREVIOUS STUDIES ON THE PLASM A WATER TREATM ENT

Inrecentyears,thereisanincreasinginterestinthestudyofpulsedelectricbreakdown in water andother liquidsas it finds more applications in bothindustryandacademicresearches.Alargenumberofpapersandconferencecontributions were published during the last few years. Highvoltage (HV)electricaldischargesinwaterhavebeen showntobeabletoinducevariousreactions including the degradation of organic compounds [ 613 ], thedestruction of bacteria and viruses [ 1419 ], the oxidation of inorganic ions[2025 ],andthesynthesisofnanomaterialsandpolymers[ 2629 ].Thereac-tions are usually thought to be initiated by various reactive species, UVradiation,shockwaves,highelectricfield,orintenseheatproducedbypulsedelectricdischarge.Theconcentrationofthereactivespeciesandtheintensityof the physical effects largely depend on the discharge type and solutionproperties.

Locke[27 ]publishedacomprehensivereviewontheapplicationofstrongelectricfieldsinwaterandorganicliquidswith410referencesin2006.Theyexplainedindetailthetypesofdischargesusedforwatertreatment,physicsofthedischarge,andchemicalreactionsinvolvedinthedischargeinwater.


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Morerecently,BruggemanandLeys[ 29]publishedanotherreviewpaperonnonthermal plasma in contact with water. They discussed three differenttypes of plasmas: direct liquid discharges, discharges in gas phase with aliquidelectrode, anddischargesinbubblesinliquids.Adifferent excitationmethod for each type was discussed individually. In addition, plasmacharacteristics of the different types of plasma in liquids were discussed.Currently several research groups around the world actively study plasmadischargesforwatertreatment,whichwillbebrieflydiscussednext.

SchoenbachandhiscolleaguesatOldDominionUniversityhavestudiedthe electrical breakdown in water with submillimeter gaps between pinand plane electrodes by using optical and electrical diagnostics with atemporalresolutionontheorderof1ns[ 3034 ].ByusingaMachZehnderinterferometer,theelectricfielddistributionintheprebreakdownphasewasdetermined by means of the Kerr effect, which indicates a change in therefractiveindexofamaterial.Valuesofelectricfieldsinexcessofcomputedelectric fields, which reached over 4MV/cm for applied electrical pulsesof 20ns duration, were recorded at the tip of the pin electrode. The resultsof this research have found bioelectric applications in the constructionofcompactpulsepowergenerators.

Locke and his colleagues at Florida State University have qualitativelystudied the production of reductive species by pulsed plasma discharge inwaterusingdifferentchemicalprobes[ 3537 ].Theyshowedthattheforma-tionofprimaryradicalsfromwaterdecompositionoccurredinthedischargezone.Theimmediateregionsurroundingthedischargezonewasresponsiblefor radical recombination to form products that diffused into bulk waterwhere the radicals participated in bulk phase reactions. The rate of theformation of reductive species in the pulsed streamer discharge increasedas the input power to the system increased, offering a possibility that in amixtureofaqueouscontaminantssomepollutantsoracomponentofcertainpollutants could degrade by reductive mechanisms, thereby increasing thedegradationefficiencyoftheprocess.

Graves and his colleagues at the University of California, Berkeley, pre-sentedauniquemethodtoinactivatemicroorganismsin0.9%NaClsolution(i.e.,normalsalinesolution)bymeansofmicroplasmas[ 17].TheyemployedE. coli bacteria to investigate the disinfection efficiency of the device. Thedeviceconsistedofathintitaniumwirecoveredbyaglasstubeforinsulationexcept forthetipof thewire and ground electrode.Microbubblescould beformed at both electrodes from the application of an asymmetric highfrequency,highvoltage.Repetitivelightemissionwasobservedinthevicinityofthepoweredelectrode.Morethan99.5%ofE.coliwasdeactivatedin180s.

SatoandhiscolleaguesatGunmaUniversity,Japan, studiedthe environ-mental and biotechnological applications of HV pulsed discharges in water.


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ApulseddischargewasformedinwaterbyapplyingaHVpulseinpointto-planeelectrodesystems[3842].They foundthat bubbling through a hollowneedleelectrodemadeitpossibletoraisetheenergyefficiencyinthedecom-positionoforganicmaterialsbyreducingtheinitialvoltageofthedischarge.Oxygengasbubblingwasfoundtobeeffectiveforthedecompositionbecauseoftheformingofactivespeciesoriginatingfromoxygengas.

Sunka and other researchers from the Institute of Plasma Physics,Academy of Sciences of the Czech Republic, developed a pulsed coronadischarge generator in water using porous ceramiccoated rod electrodes(shown in Fig. 9) [ 4345 ]. They studied the properties of the ceramic layeranditsinteractionwiththeelectrolyteandreportedthatsurfacechemistryattheelectrolyte/ceramicsurfaceinterfacewasanimportantfactoringenerat-ing electrical discharges in water using porous ceramiccoated electrodes.Initiationofthedischargeinwaterusingthesetypesofelectrodesdependedonthesurfacechargeoftheceramiclayerinadditiontothepermittivityandporosityoftheceramiclayer.Thesurfacechargecouldbedeterminedbythepolarity of applied voltage, and pH and the chemical composition of aqu-eoussolution.ByapplyingbipolarHVpulsestoeliminatepossiblebuildupofanelectricalchargeontheceramicsurface,largevolumeplasmacouldbeproducedinwaterintherangeofkilowatts.

Recently, Yang and his colleagues from Drexel Plasma Institute, DrexelUniversity, reported the formation of liquidphase nonequilibrium plasmainwater.Sinceplasmaswereonlyconsideredtoexistthroughtheionizationofgases,peoplehadbelievedthatplasmasinliquidsmusthavebeengener-atedinsidegasphasebubblesproducedthroughintenselocalheatingorviacavitation andcould be sustained within those bubbles. For the generationofnonequilibriumplasmainliquids,apulsedpowersystemwasoftenusedwith 32112kV pulse amplitude, 0.512ns pulse duration, and 150ps risetime.Themeasurementswereperformedwitha4PicosICCDcamerawithaminimum gate time of 200ps. It was found that discharge in liquid waterformed in a picosecond time scale, and the propagation velocity of thestreamers wasabout5000km/s.ThereducedelectricfieldE/n0 atthe tipofthe streamer was about 200 Td. Both the propagation velocity and thereducedelectricfieldinthetestweresimilartothestreamerpropagationingas phase, indicating that the plasma could be formed in liquid phasewithoutphasechange.Thedetailsoftheexperimentwillbediscussedlater.C.PROCESS OF CONVENTIONAL ELECTRICAL BREAKDOW N IN WATER

Althoughalargenumberofstudieswereconductedonelectricdischargesingases,studiesontheelectricbreakdowninliquidshavebeenlimitedbythehigh density of liquids and a short mean free path of electrons, therefore


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requiringaveryhighelectricfieldE/n0.ThecriticalbreakdownconditionforgascanbedescribedbythePaschencurve,fromwhichonecancalculatethebreakdown voltage. A value of 30kV/cm is a wellaccepted breakdownvoltageofairat1atm.Whenoneattemptstoproducedirectplasmadischargein water, a much higher breakdown voltage on the order of 30MV/cm isneededbasedonthePaschencurveduetothedensitydifferencebetweenairandwater.Alargenumberofexperimentaldataonthebreakdownvoltageinwatershowed,however,thatthebreakdownvoltageinwaterwasofthesamemagnitude as for gases. In other words, the breakdown of liquids can beperformed not at the extremely high electric fields required by the Paschencurve but at thosethatonlyslightly exceed the breakdown electric fieldsinatmosphericpressuremoleculargases.Thisinterestingandpracticallyimpor-tanteffectcanbeexplainedbytakingintoaccountthefastformationofgaschannelsinthebodyofwaterundertheinfluenceofanappliedhighvoltage.When formed, the gas channels give the space necessary for the gas break-downinsidewater,explainingwhythevoltagerequiredforthebreakdowninwaterisofthesamemagnitudeasthatingases.

To generate electrical discharges in water, usually one needs to have apulsedHVpowersupply.Waterisapolarliquidwitharelativepermittivityof"r=80. The electrical conductivity of water ranges from about 1mS/cmfor distilled water to several thousandmS/cm for cooling water, dependingon the amount of dissolved ions in water. Given that a specific water isexposedtoanelectricpulsewithadurationofDt,whenDt>>"r"0/,where"0 is vacuum permittivity and is the conductivity of water, the aqueoussolutioncanbeconsideredasaresistivemedium[28 ].Forsuchalongelectricpulse,theelectrolysisofwatertakesplacewiththeproductionofhydrogenand oxygen. For the case of a much shorter pulse duration, i.e., whenDt


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(a) (b)

Y.YANGETAL.

FIG. 4. Images of plasma discharge in water: (a) pulsed corona; (b) pulsed arc, producedatDrexelPlasmaInstitute.

TABLEISUMMARY OF THE CHARACTERISTICS OF PULSED CORONA, PULSED ARC,AND PULSED SPARK

DISCHARGE IN WATER [26,27,4655]Pulsedcorona Pulsedarc PulsedsparkNonthermaldischarge.

Highoperatingfrequency(1001000Hz).

Currenttransferredbyslowions.

Streamerfilamentsdonotpropagateacrosselectrodegap.

Afewjoulesorlessperpulse.

WeaktomoderateUVgeneration.Weaktomoderate

shockwave.Relativelylowcurrent,i.e.,

peakcurrentlessthan100A.

Thermaldischarge.

Lowoperatingfrequency(


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shorteningofthestreamerlengthduetothefastercompensationofthespacechargeelectricfieldsontheheadofstreamers.Subsequently,ahigherpowerdensity,i.e.,ahigherplasmadensity,inthechannelcanbeobtained,result-inginahigherplasmatemperature,ahigherUVradiation,andthegenera-tionofacousticwaves.

Inthearcorsparkdischarges,thecurrentistransferredbyelectrons.Thehighcurrentheatsasmallvolumeofplasmainthegapbetweentwoelectro-des, generating quasithermal plasma, where the temperatures of electronsand heavy particles are almost equal. When a HV, highcurrent dischargetakesplacebetweentwosubmergedelectrodes, alarge partoftheenergyisconsumedintheformationofathermalplasmachannel.ThischannelemitsUV radiation, and its expansion against the surrounding water generatesintense shockwaves. The shockwave can directly interact with the microor-ganismsinwater.Ofnoteisthatthepressurewavescanscattermicroorgan-ismcolonieswithintheliquid,thusincreasingtheirexposuretoinactivationfactors. For the corona discharge in water, the shockwaves are weak ormoderate,whereasforthepulsedarcorsparktheshockwavesaregenerallyverystrong.

When the plasma discharge is initiated between two electrodes, the med-ium between the two electrodes is ionized creating a plasma channel. Theplasma discharge generates UV radiation and converts surrounding watermolecules into active radical species due to the high energy level producedbythedischarge.Themicroorganismscouldbeeffectivelyinactivated,whilethe organic contaminants could be oxidized through contact with activeradicals.Thechemicalkineticsofthesereactionsremainsanareaofsignifi-cantresearch[ 27,29 ].Variousactivespeciescanbeconsideredasthebypro-ducts of plasma discharge in water. The production of these species byplasma discharge is affected by a number of parameters such as appliedvoltage,risetime,pulseduration,totalenergy,polarity,theelectricconduc-tivity of water, etc. Among the active species, hydroxyl radical, atomicoxygen, ozone and hydrogen peroxide are the most important ones for thesterilizationandremovalofunwantedorganiccompoundsinwater.TableIIsummarizes the oxidation potentials of various active species produced byplasma in water, which ranges from 1.78V (hydrogen peroxide) to 2.8V

TABLEIIOXIDATION POTENTIAL OF ACTIVE SPECIES PRODUCED BY PLASMA IN WATER [56]

Activespecies Hydroxyl Atomicoxygen(O) Ozone(O3) Hydrogenperoxideradical(OH) (H2O2)

Oxidationpotential 2.8V 2.42V 2.07V 1.78V


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(hydroxylradical).Notethatfluorinehasthehighestoxidationpotentialof3.03V,whereaschlorine,whichisoneofthemostcommonlyusedchemicalsforwaterdecontamination,hasanoxidationpotentialofonly1.36V.

Inadditiontotheaforementionedactivespecies,theelectricalbreakdownin water produces UV radiation (both VUV and UV). VUV (i.e., vacuumUV), as the name indicates, can only propagate in vacuum because it isstrongly absorbed by air or water. For pulsed arc discharge, the hightemperature plasma channel can function as a blackbody radiation source.The maximum emittance is in the UVa to UVc range of the spectrum(200400nm) [28,55 ],asdetermined bythe StephenBoltzmannlaw.Wateris relatively transparent to UV radiation in this wavelength range. Theenergy per photon ranges from 3.1eV to 6.2eV. UV radiation has proventobeeffectivefordecontaminationprocessesandisgainingpopularityasameansforsterilizationbecausechlorinationleavesundesirablebyproductsinwater. The radiation in the wavelength range of 240280nm may cause anirreparabledamagetothenucleicacidofmicroorganisms,preventingpropercellularreproduction,andthuseffectivelyinactivatingthemicroorganisms.

Alternatively, the photons can provide the necessary energy to ionize ordissociatewatermolecules,generatingactivechemicalspecies.Recently,itissuggestedthatthe UVsystemmay produce chargedparticles inwatersuchthat charge accumulation occurs on the outer surface of the membraneof bacterial cell. Subsequently, the electrostatic force on the membraneovercomes the tensile strength of the cell membrane, causing its rupture atapointofsmalllocalcurvatureastheelectrostaticforceisinverselypropor-tionaltothelocalradiussquared[5759 ].

Sinceoneofthemajorapplicationsoftheplasmadischargeinwaterisinthe development of a selfcleaning filter to be discussed later in this reviewarticle, the ability for the discharge to generate shockwaves will be brieflysummarized next. When a HV, highcurrent discharge takes place betweentwoelectrodessubmergedinwater,alargepartoftheenergyisconsumedonthe formation of a thermal plasma channel. The expansion of the channelagainst the surrounding water generates a shockwave. For the corona dis-chargeinwatertheshockwavesareoftenweakormoderate,whereasforthepulsedarctheshockwavesarestrong.Thedifferencearisesfromthefactthattheenergyinputinthearcorsparkdischargeismuchhigherthanthatinthecorona.

Similarly, between the arc and spark, the arc produces much greatershockwaves due to its higher energy input. The water surrounding theelectrodes becomes rapidly heated, producing bubbles, which help the for-mationofaplasmachannelbetweenthetwoelectrodes.Theplasmachannelmay reach a very high temperature of 14,00050,000K, consisting of ahighlyionized,highpressure,andhightemperaturegas.Thus,onceformed,


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the plasma channel tends to expand. The energy stored in the plasmachannelisdissipatedviaboth radiationandconduction tothesurroundingcool liquid water and mechanical work. At the liquidgas phaseboundary,thehighpressurebuildupintheplasmaistransmittedintothewaterinter-faceandanintensecompressionwave(i.e.,shockwave)isformed,travelingatamuchgreaterspeedthanthespeedofsound.Notethattheshockwaveshave another benefit in the sterilization process through a good mixing ofwater tobetreated,significantly enhancingthe plasmatreatmentefficiencyasintheaforementionedselfcleaningfilterperformance.

However, the plasma discharge for water treatment is not without defi-ciencies.OneoftheconcernsintheuseofasharpneedleasaHVelectrodeistheadverseeffectassociatedwiththeneedletiperosion.Inapointtoplanegeometry, a large electric field can be achieved due to the sharp tip of theneedle with a minimum applied voltage V. For a sharp parabolic tip ofthe needle electrode, the theoretical electric field at the needle tip becomesE/V/r,whereristheradiusofcurvatureoftheneedletip.Asindicatedbythe above equation, the electric field at the tip of the electrode is inverselyproportional to the radius of curvature of the needle tip. Hence, themaximum electric field could be obtained by simply reducing the radiusof curvature r, which is much easier than increasing the voltage as themaximum value of the voltage is usually restricted by the electric circuit aswellasinsulationmaterialsusedaroundelectrodes.

Sunka [60] pointed out that the very sharp tip anode would be quicklyerodedbythedischarge,andonehadtofindsomecompromisebetweentheoptimum sharp anode construction and its lifetime for extended operation.Also it was demonstrated recently that the erosion of electrodes at pulseelectricdischargeinwaterwouldresultintheproductionofmetalandoxidenanoparticlesinwater.Theseparticlesareverydifficulttoremoveoncetheyenterthedrinkingwater systemduetotheirnanometersizes,andpotentialdangertohumanbodyisnotclearlyknown.

Anotherconcernintheapplicationofpulsedelectricdischargesinwateristhelimitationposedbytheelectricalconductivityofwaterontheproductionof such discharges [60]. In the case of a low electric conductivity below10mS/cm, the range of the applied voltage that can produce a coronadischarge without sparking is very narrow. On the other hand, in the caseof a high electric conductivity above 400mS/cm, which is the typical con-ductivityoftap water,streamers becomeshortandtheefficiencyofradicalproduction decreases. In general, the production of hydroxyl radicals andatomic oxygen is more efficient at water conductivity below 100mS/cm.Thus, this is one of the major challenges in the application of plasmadischarges for cooling water management as the electric conductivity ofmostcoolingwaterisattherangeof20002500mS/cm.


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II.UnderwaterPlasmaSourcesA.DIRECT DISCHARGES IN LIQUID

Various electrode geometries have been studied for the generation ofplasma discharges in liquid. Figure 5 shows some of the typical electrodeconfigurations. Note that only the cases where both the HV electrode andground electrode are placed in liquid are shown here. Among them, thepointtoplane geometry has been the most commonly used configuration(shown in Fig. 5 (a)). Also a pointtoplane geometry with multiple pointswasused togeneratealargevolumecoronadischargeinwater(Fig.5(b)).For pulsed arc discharges, a pointtopoint electrode geometry was oftenused(Fig.5(c)).

(a) (b) (c)

(f)(e)(d)

(g)

FIG. 5. Schematics of electrodegeometries usedforplasmadischargesinliquid:(a)singlepointtoplane;(b)multiplepointstoplane;(c)pointtopoint;(d)pinhole;(e)wiretocylinder;(f)diskelectrode;(g)compositeelectrodewithporousceramiclayer.


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191

(a) (b)

PLASMADISCHARGEINWATER

Asmentionedintheprevioussection,oneoftheconcernsintheuseofasharp needle as the HV electrode is the tip erosion due to the intense localheatingatthetip.Toovercomethelimitationoftheneedleplateconfigura-tion, pinhole electrodes (also called a diaphragm discharge, as shown inFig. 5 (d)) with large surface areas were developed, where the HVand ground electrodes are separated by a dielectric sheet with a small hole[ 6164 ]. When high voltage is applied on the electrodes, an intense electricfield could be formed around the pinhole. Subsequently, a predischargecurrent could be concentrated in the small hole, leading to strong thermaleffects,resultingintheformationofbubbles.Pulsedcoronadischargeoccursinsidethebubblesatthepinholebecauseofthehighelectricfield.Thelengthof the streamers generated is decided by the parameters such as waterconductivity,thesizeofthepinhole,flowvelocitythroughthepinhole,andvoltage polarity. Similar to the corona discharge in the pointtoplane geo-metry,apulsedarcdischargecouldbeformedoncethestreamerbridgesthetwo electrodes. Figure 6 shows (a) pulsed corona and (b) arc dischargesthroughapinholeproducedatDrexelPlasmaInstitute.

Anothercriticalissuethatresearchersarefacingistoincreasethevolumeof an active plasma discharge region, for industrial applications with alarge water flow rate. Clearly the pointtoplane electrode geometry wouldbedifficulttoscale upforsuchanindustrialapplication. Alsoitisdifficultto discharge uniformly at multiple pinholes. In order to effectively treat alarge volume of water with plasma discharges, different approaches couldbe used including a wirecylinder geometry (Figs. 5 (e) and 7), a diskgeometry (Fig. 5 (f)), and a concentric cylinder geometry with a HV centercomposite electrode coated with a thin layer of porous ceramic (Figs. 5 (g)and 9 ).

FIG. 6. Imagesof plasma dischargesthroughapinhole:(a)pulsedcorona;(b)pulsedarc,producedatDrexelPlasmaInstitute.


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FIG. 7. Timeintegrated image of discharges generated using a wirecylinder geometryin water, where tungsten wire and stainless steel mesh cylinder were used. Chamberdimensions:44mmID,100mmlength[65].

Theg e o m e t r yu s i n gm u l t i p l ed i s k ss h o w ninF i g .5(f)u t i l i z e dan u m b e roft h i nc i r c u l a rs t a i n l e s ss t e e ld i s ke l e c t r o d e ss e p a r a t e dbyd i e l e c t r i cl a y e r sto p r o d u c ep u l s e d m u l t i c h a n n e l d i s c h a r g e s in w a t e r [ 66 ].The t h i c k n e s s ofthe d i s k e l e c t r o d e s was a b o u t 80mm. The d i a m e t e r of the a c r y l d i s k wass l i g h t l yg r e a t e rt h a nt h a tof thes t a i n l e s ss t e e ld i s ksot h a t p r e b r e a k d o w nc u r r e n t was l i m i t e d to a s m a l l a r e a e n c l o s e d by a p a i r of the a c r y l i c d i s k sand the c i r c u m f e r e n t i a l e d g e of the s t a i n l e s s s t e e l d i s k . S u c h a c o n f i n e -m e n t of the c u r r e n t a l l o w e d w a t e r to be h e a t e d and e v a p o r a t e d in t h i ss m a l la r e a ,p r o m o t i n gthei n i t i a t i o nofp l a s m ad i s c h a r g e s .Thee d g eofthes t a i n l e s s s t e e l d i s k was r o u n d e d s u c h t h a t the r a d i u s of c u r v a t u r e of thee d g e was a b o u t h a l f of the d i s k t h i c k n e s sd.H e n c e , the m a x i m u m e l e c t r i cf i e l d at the e d g e was e s t i m a t e dto beE2U/d, s t a y i n g r e l a t i v e l y c o n s t a n tw i t hah i g h l e v e lv a l u ec o m p a r a b l etoap o i n t t o p l a n eg e o m e t r yt h r o u g h -out the d i s c h a r g e p r o c e s s . F u r t h e r m o r e , a l a r g e v o l u m e p l a s m a c o u l dbe p r o d u c e d by s t a c k i n g m u l t i p l e d i s k s t o g e t h e r . F i g u r e 8 s h o w sp h o t o g r a p h s of p u l s e d m u l t i c h a n n e l d i s c h a r g e a r r a y s g e n e r a t e d w i t htwo s t a i n l e s s s t e e l d i s k s .

As mentioned previously, Sunka and his coworkers developed a HVcomposite electrode coated with a thin layer of porous ceramic [28,43 ].Suchanelectrodecanbeusedinawidevarietyofgeometricalconfigurations,includingwirecylinderandplanargeometry.Theroleoftheceramiclayeristoenhancetheelectricfieldontheanodesurfacebytheconcentrationofthe


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FIG. 8. Pulsedmultichanneldischargearrayinwatergeneratedby twostainlesssteel diskelectrodesseparatedbyadielectriclayer[66].

predischargecurrentinsmallopenporessothatalargenumberofdischargechannelscouldbedistributeduniformlyandhomogeneouslyontheelectrodesurface. The composite electrodes can be made in various dimensions,enabling the construction of reactors that can operate at average powerintherangeofkW.Figure9showsimagesofmultichannelpulsedelectricaldischarges in water generated using porousceramiccoated metallicelectrodes.

FIG.9. Multichannelpulsedelectricaldischargeinwatergeneratedusingporousceramic-coatedmetallicelectrodes[43].


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194 Y.YANGETAL.

B.BUBBLE DISCHARGES IN LIQUIDIn e n g i n e e r i n g a p p l i c a t i o n s of p l a s m a d i s c h a r g e s in l i q u i d s , h i g h

v o l t a g e , h i g h p o w e r d i s c h a r g e s are o f t e n n e e d e d for the g e n e r a t i o n ofb r e a k d o w n in l i q u i d s as w e l l as for d e s i r e d p r o c e s s i n g . For e x a m p l e,h i g h e l e c t r i c a l c u r r e n t a n d / o r h i g h l i q u i d t e m p e r a t u r e can s t e r i l i z e w a t e r .In t h i s c a s e , the h i g h e n e r g y s u p p l i e d by a p o w e r s o u r c e is f i r s t u s e d toe v a p o r a t ethel i q u i da d j a c e n ttotheHVe l e c t r o d e ,g e n e r a t i n ggasb u b b l e st h a t are s u b s e q u e n t l y i o n i z e d by l a r g e e l e c t r i c f i e l d s c a u s e d by the h i g hv o l t a g e .L i q u i dt e m p e r a t u r e sins u c ha p p l i c a t i o n sareu s u a l l yh i g h ,atl e a s tl o c a l l y n e a r the b r e a k d o w n l o c a t i o n s , due to the e x c e s s p o w e r d i s s i p a t e din the l i q u i d . H o w e v e r , in s o m e c i r c u m s t a n c e s h i g h t e m p e r a t u r e is notd e s i r e d . For s u c h a p p l i c a t i o n s , a n o n t h e r m a l p l a s m a s y s t e m t h a t cang e n e r a t e g a s p h a s e p l a s m a s in c o n t a c t w i t h l i q u i d s is o f t e n u s e d . S i n c ethe g a s p h a s e p l a s m a can o n l y i n t e r a c t w i t h the l i q u i d t h r o u g h the g a s l i q u i d i n t e r f a c e , a m a x i m i z a t i o n of the i n t e r f a c e a r e a is u s u a l l y d e s i r e d ,w h i c hcanbea c h i e v e dbyu s i n gb u b b l ep l a s m a s ,i . e . ,p l a s m a sg e n e r a t e dins m a l l b u b b l e s s u s p e n d e d in l i q u i d . N o t e t h a t the r a t i o of the a r e a ofg a s l i q u i d i n t e r f a c e to the t o t a l gas v o l u m e is i n v e r s e l y p r o p o r t i o n a l tothe r a d i u s of the gas b u b b l e s . Ma n y d i f f e r e n t c o n f i g u r a t i o n s h a v e b e e nu s e d as s h o w n in F i g . 10 ( a ) ( e ) .

Similartodirectdischargesinwater,themostcommonlyusedconfigura-tionisthepointtoplaneconfiguration,wherethepointelectrodewasmadeof a smalldiameter hollow tube to inject gas into water [6770 ]. Differenttypesofgaswereuseddependingonapplications.Forexample,oxygengaswasoftenusedtopromotetheformationofoxygenradicals.

Alternatively,gaswasbubbledbetweentwometalelectrodes(Fig.10(b)).The dischargeoccurredbetween theelectrodes byapplying theHV,produ-cingOHradicalthatwasdetectedbyaspectroscopictechnique[71,72 ].

Another interesting discharge in liquid was to use a gas channel, insidewhich two metal electrodes were placed to generate plasma discharge(Fig. 10 (c)) [ 73,74 ]. The gas is continuously supplied through the hollowtube, flowing around the electrodes from both sides and exiting from theopen ends at the middle of the reactor (see Fig. 10 (c)). The gases comingfrom the top and bottom merge into one where two point electrodes wereclosely positioned, forming a stable gas channel between the two metalelectrodes. Subsequently, the generated discharge was an arc dischargewhichwascooledandstabilizedbythesurroundingwater.

Aoki and his coworkers [75] studied radio frequency (RF)excited dis-charges inargonbubbles inadielectric covered metalrodand wirereactor(Fig. 10 (d)). First, bubbles were formed in front of the slot antenna (seeblack area in the figure) by microwave heating of water where water in an


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HVHV Gasflow

HVGasflow

(a) (b) (c)

SolutionOutletfor PumpQuartzrodwaterandbubbles Slot

Quartztubeantenna

Quartz230 Innerelectrode

Outerelectrode80mm25mm Microwave

WaveguideBubblecontrolplate

13.56MHz

Thermocouple

Argaswater

(d) (e)


FIG. 10. Schematics of electrode geometries for bubble discharge: (a) pointtoplane;(b)parallelplate;(c)gaschannelwithliquidwall;(d)RFbubbledischarge[75];(e)microwavebubbledischarge[77].

evacuated vessel at a vapor pressure of 5kPa was evaporated by a slightincrease in the temperature above the boiling point (room temperature).In the second step, microwave breakdown took place inside bubbles filledwithwatervapor.Inthethirdstep,thebubblescontainingtheplasmamovedup due to the upward force by buoyancy. After that, new water filled thevacant space in front of the slot antenna. These steps were successivelyrepeated forming a large number of bubble plasmas. Microwaveexcitedplasmain water with or withoutexternally introduced bubbles was studiedbyIshijama(Fig.10(e))[76,77 ]andNomura[7880 ].


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196 Y.YANGETAL.

III.DynamicsofNon-EquilibriumPlasmainLiquidWaterA.EXPERIM ENT SETUP

Typically,theelectricbreakdownofliquidsisinitiatedbytheapplicationof high electric field on the electrode, followed by rapid propagation andbranchingofplasmachannels.Usuallyplasmasareonlyconsideredtoexistthrough the ionization of gases, and for all cases described above, theproduction of plasmas in liquids was believed to first generate bubblesthrough heating or via cavitation and sustain the plasmas within thosebubbles.Thequestionis,isitpossible toionizetheliquidwithoutcrackingandvoidformation?

Toanswerthisquestion, Yangandhiscoworkers [81]used twodifferentpulsed power systems. The first pulsed power system generated pulses with27kV pulse amplitude, 12ns pulse duration, and 300ps rise time. Thevoltage waveform is shown in Fig. 11. The second system generated max-imum 112kV pulses with 150ps rise time and duration on the halfheightabout500ps.ThevoltagewaveformisshowninFig.12 .Dischargecellhadapointtoplate geometry with the point electrode diameter of 100mm. Thedistance between the point and plate electrodes was 3mm. The measure-ments were performed with the help of 4 Picos ICCD camera with a mini-mum gate time of 200ps and spectral response of 220750nm. Figure 13showstheschematicdiagramoftheexperimentsetup.

0

5

10

15

Voltage(kV) 20

25

30

2 0 2 4 6 8 10 12 14 16

Time(ns)

FIG. 11. Voltage waveform produced from the nanosecondduration power supply usedbyYangetal. [81].


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0

25

Voltage(kV)

50

75

100

125

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Time(ns)

FIG.12. VoltagewaveformproducedfromthesubnanoseconddurationpowersupplyusedbyYangetal. [81].

Signal

generator

HV

ICCD

FIG.13. SchematicdiagramoftheexperimentsetupusedbyYangetal. [81].

B.RESULTS AND D ISCUSSIONSItwasfoundthatdischargeinliquidwaterdevelopedinnanosecondtime

scale. The diameter of the excited region near the tip of the HV electrodewas about 1mm. The discharge demonstrated a typical streamertypestructure,asshowninFig.14 .Nobubblingorvoidformationwasobserved.Thus, the discharge observed had a nature completely different from thatof the discharges initiated by electrical pulses with a longer rise time [82 ].Ishijima [77 ] reported that the pulses with 40ns rise time and 18kV ampli-tude producedthe velocityof dischargepropagation about2.5km/s during


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198 Y.YANGETAL.

FIG. 14. Image of a nanosecondduration discharge in water taken at a camera gateof100msbyYangetal. [81].

the initial phase of the discharge. Both the shadowgraph and Schlierenimagessuggestedthatthebrancheswereofgaseousnature.

Inthecaseofashortrisetime,dischargepropagationwithavelocityofupto200km/swasobservedduringtheveryinitialstageofthedischarge,whichcorresponded to the moment of voltage increase (Fig. 15 ) [81 ]. Typical

30Initiation Darkphasesecondstroke

25

20

15

10

Cameragate:1nsTimeshift:1ns

0

Voltage(kV)

2 0 2 4 6 8 10 12 14 16

Time(ns)

FIG.15. ImagesshowingthedynamicsofnanoseconddurationdischargeemissionandHVpotentialonelectrodetakenatacameragateof1ns[81].


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emitting channel diameter was about 50mm, and propagation length was0.50.6mm for 27kV. When voltage reached the maximum, the dischargestopped and the dark phase appeared (t=6 9 ns in Fig. 15 ). Duringthis phase, discharge could not propagate probably because of both spacecharge formation and electric field decrease. Voltage decrease on the HVelectrode led to the reverse stroke formation and second emission region(t=1014nsinFig.15 ).Thismeansthatthechannelslosttheconductivity,while the trailing edge of the nanosecond pulse generated a significantelectric field and the excitation of the media. This effect can be consideredas a proof that there was no void formation or phase transition during thefirststageofthedischarge.

Dischargedevelopmentinthecaseof110kVisshowninFig.16 .Itisclearthattheplasmachannelwasgeneratedduringvoltageincreasetime,i.e.,lessthan 150ps. Observed propagation velocity reached 5000km/s (5mm/ns)andwas almost the same asthe typicalvelocity of streamer propagation inair. Typical channel diameter was estimated as d=50100mm, with theradius of curvature at the tip of streamer of about 20mm. Thus, one couldestimatethereducedelectricfieldatthetipofthestreamerstobeabout200Td, if equipotential was assumed between the plasma channel and theelectrode.Again,thiselectric field strength wasalmostthesame as theoneat the tip of streamer propagating in air. Figure 17 shows the dischargegeometry dependence on the pulsed voltage applied. The length of thechannels decreased gradually with increasing voltage, a phenomenon

250

225

200

175

150

125

100

75

50

25

0

Voltageonelectrode(kV)

Cameragate:500psTimeshift:50ps

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Time(ns)

FIG.16. ImagesshowingthedynamicsofnanoseconddurationdischargeemissionandHVpotentialonelectrodetakenatacameragateof0.5ns[81].


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200

Upeak:46kV Upeak:53.5kV Upeak:80.5kVdU/dt:0.31MV/ns dU/dt:0.36MV/ns dU/dt:0.54MV/ns

Upeak::92kV Upeak:103.5kV Upeak:110kVdU/dt:0.61MV/ns dU/dt:0.69MV/ns dU/dt:0.73MV/ns

Y.YANGETAL.

FIG.17. Subnanoseconddurationdischargedevelopmentfordifferentvoltages[81].

which, for fixed pulsed duration, indicated that the streamer velocitydecreased. For voltage below 50kV, discharges could not start during500ps,andsubsequentlyemissionwasnotobserved.

In summary, the dynamics of excitation and quenching of nonequilibrium plasma in liquid water were investigated, and the possibility offormation of nonequilibrium plasma in liquid phase was demonstrated.Based on these findings, it was concluded that the mechanism of thestreamer development in liquid phase in the picosecond time scale wassimilartotheionizationwavepropagationingases[81 ].

IV.AnalysisofMicrosecondStreamerPropagationThe study of liquidphase nonequilibrium plasma in liquid water

described above opens doors to new potential applications in the areassuch as bacterial sterilization, organic compound destruction, and materialsynthesis. However, for most underwater plasma related applications, themore conventional microsecondduration pulses could be used. Hence, it isimportant to get a better understanding of the key physical mechanisms ofthe breakdown process. In most cases, the electric breakdown of liquids isinitiatedbytheapplicationofahighelectricfieldontheelectrode,followedbyrapidpropagationandbranchingofstreamers.Theoverallmechanismiscomplex as it involves different physical processes including field emission,


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bubbleformation,ionization,heating,vaporization,etc.Thus,itisdifficulttoincludealltheeffectsinasingleanalyticalmodel.Anumberofproposedtheoriesfortheinitiationofthebreakdownofdielectricliquidsareavailableintheliterature[ 8388 ].Theinitialbubbleformationcouldbeattributedtopreexisting cavities in water, direct ionization, field assisted emission, or

jouleheatinginducedbylocalfieldemission.However,theexactmechanismisstillunclear.

Despite different mechanisms proposed, most initiation theories lead tothe formation of a lowdensity region where selfsustained electron ava-lanches take place. Thus, the next question is what the driving force is tosustain and expand the cavity to form complex geometrical structures.Similar to the initiation process, the propagation is complicated because itinvolves interactions between plasma, gas, and liquid phases of the media.Recent experiments demonstrated the existence of different modes of pro-pagation, where both a primary streamer mode with a slow velocity and asecondary streamer mode with a high velocity were observed [82 ]. Severalmodels were proposed to correlate electric field with streamer velocity[8991 ]. Different effects, including liquid viscosity, trapping of positiveandnegativecarriersintheconductingchannel,andlocalelectricchargeatstreamer head, were taken into account. But again, there is not yet acommonlyacceptedmodel.

Theobjectiveofthepresentsectionistodevelopatheoreticalframeworkinordertobetterunderstandthepropagationofstreamersofelectricdischargein water subjected to high voltage. The breakdown process is usually char-acterized by two typical features of breakdown: rapid propagation of dis-chargestreamersandhightendencyofbranchingandformationofrandomdendriticstructures.Therefore,thepresentstudyconsistsoftwocomponents:quantitative model for possible mechanisms to produce the driving forceneeded to sustain and promote the propagation, and stability analysis of asinglecylindricalfilamentwithsurfacechargesinanexternalelectricfield.

Despitethefactthatthemechanismisnotfullyunderstood,thepropaga-tion of streamers during electric breakdown of water clearly involves thedisplacement of adjacent liquid along their paths. The process requires adriving force, which is to be discussed in this section. Two quantitativemodels have been developed: one is based on the electrostatic effect on thestreamerwater interface, and the other a more traditional local heatingeffect.Comparisonismadetoexaminethevaliditiesofthetwomodels.A.ELECTROSTATIC MODEL

AschematicdiagramofthepresentelectrostaticmodelisshowninFig.18(a).A thin needle electrode with a rounded tip is aligned perpendicular to a


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202 Y.YANGETAL.

Ground Ground(a) (b)

electrode electrode

Liquid LiquidErr

Electricfield2r0

z

Ez

Electrode Initialbubble Electrode Filament Surfacecharge

FIG.18. Initiationsof(a)bubbleformationand(b)cylindricalfilamentformationinwater[92].

ground plate electrode. High voltage 0 is applied on the needle electrode.AccordingtoKupershtokh,liquidscouldbecomephaseunstableunderahighelectricfieldstrengthsothatgaschannelscouldformalongelectricfieldlines[93]. The time required for breakdown ignition in the channels can be esti-matedasb=(kIn0)1, w h e r e kI isthedirectionizationratecoefficientandn0isthemoleculedensity[18].Underatmosphericpressure,n0 isintheorderof1019cm3, w h i l e kI isintheorderof1010 to109cm3/sinthereducedelectricfieldE/n0 of103V cm2 [94].Hence,b isintheorderof0.11ns.Fornegativedischarges,duetothehighermomentumtransfercollisionfrequencyandthusalowmobilityintheliquidphase,electronstendtodepositonthegasliquidinterfaceandchargeitnegatively.Forpositivedischarges,thehighmobilityofelectrons would leave the interface charged positively. Under both circum-stances,itis possiblethatthecharged interfacewouldbepushedtodisplacetheliquidunderexternalelectricfieldbyelectrostaticforce.

A simplified calculation can be made to examine whether or not theelectrostaticforcewouldbesufficienttoovercometheresistanceofwaterattheinterface.Thepressureduetothesurfacetension,,onawaterinterfaceofasphericalbubblewitharadiusofcurvaturer,canbeapproximatedbytheYoungLaplace equationp=2/r. With r1mm and =72.8104N/m,the surface tension pressure is 15kPa. The ultimate strength of water ofapproximately 30MPa must be exceeded for rupturing the liquid [95].Considering forces due to charged particles only and ignoring those due tofieldgradientsandmaterialpropertygradients,theelectricforceattheinter-facebecomessimplytheelectrostaticforce,L,whichistheproductofchargedensity per unit area and the electric field E, i.e., L=eE, where e isthe charge per electron. For E=108V/cm, should have a value of1012 charges/cm2.Forelectronswithanaverageenergyof1eV,theelectronthermalvelocitycanbeestimatedas6107cm/s.Soamodestelectrondensityof 1013cm3 will provide the flux necessary to charge the surface to thebreaking point within 1ns. Although these estimations for water rupturing


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alsoneglectbothlossmechanismsandtheenergyrequirementstoovercomethehydrodynamicresistance,theelectrostaticmechanismstillseemsalikelycandidate for streamer propagation, and such forces may dominate atnanosecondtimescale.

The growth of a plasma filament is determined by the conservationequations of mass, momentum, and energy. To quantify the breakdownprocess described above, the equations for the formation and propagationoftheplasmafilledfilamentsaredefinedas[96 ]

@ 2lTT H u 1

@t DvHr20@u u Hu1HP 0 2@t

@ P u2Z u2 H u Z TE2 3

@t 2wheretistime;andParetheradialdensityandpressureinsidestreamer,respectively; u is the velocity of streamer; T is the temperature; l is thethermalconductivity;DvH is theevaporation heat of water;r0 is the radiusof streamer; Z is the internal energy of ionized gas; E is the electric fieldstrength; and is the electric conductivity. It is usually difficult to directlysolveEqs.(1)(3)becauseofthehighnonlinearityoftheequations.

For simplification, thestreameris assumedtobeacylinder with ahemi-sphericaltipasshowninFig.18(b).Thereferenceframeisfixedonthetip.The radius of the filament is r0. Although it appears from photographicevidences that the filament is usually of a conical shape, the cylindricalapproach is still a good approximation when the length of the filament ismuchgreaterthantheradius.Theelectricconductivityinsidethefilamentcouldbedescribedas

2nee 4

mvenwheremisthemassof electronandven isthe frequency of electronneutralcollisions. Note that ven is proportional to the gas number density andthevalueofven/pisusuallyintheorderof109s1Torr1[94].SunkameasuredthebroadeningoftheHlineprofile,whichiscommonlyusedtocharacterizethedensityofplasma,reportingtheelectrondensityinsidestreamersduringthe initial phase of water breakdown, to be in the order of 1018cm3 [60 ].


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204 Y.YANGETAL.

Withwatervaporpressureof20Torrsaturatedattheroomtemperature,theelectricconductivityinsidethefilamentcanbeestimatedtobeintheorderof107S/m, a value which is comparable to those for metals. So the filamentcould be regarded as equipotential with the electrode, and thus couldbe treated as an extension of the electrode throughout the expansion.The external fluid provides drag force and constant external pressure forthedevelopmentofthefilament.Gravityisneglectedherebecausethebodyforceinducedbygravityismuchsmallerthanelectricforces.

Theelectricfieldoutsideaslenderjetcanbedescribedasifitwereduetoan effective linear charge density (incorporating effects of both free chargeandpolarizationcharge)ofchargedensityonthesurface.Sincethechargedensityinliquidcanbeignoredcomparingwiththatonthefilamentsurface,one can have the following equation for the space outside the filament byapplyingLaplaceequationintheradialdirection:

1 @ @Fr 0 5

r@r @rwithboundaryconditionr=r0=0andr=R=0.Risthedistancebetweenanode and cathode. Since the filament could be regarded as an extensionoftheelectrode,Rdecreasesasthestreamerpropagatesthroughthegap.

Solvingtheaboveequationwithanassumptionofnegativedischarge,theradialelectricfieldEr andlocalsurfacechargedensityr canbewrittenas@F F0

Er 6@r r0 lnR=r0

F0r "Er0 "r"0 7r0 lnR=r0

Thereisnoanalyticalsolutionfortheelectricfieldatthehemisphericaltipof the filament. A frequently used approximation is Ez 0/r0. Here theequation for the electric field at the tip of a needle in a needletoplanegeometrydevelopedbyLamaandGallowasused[97 ]:

2F0Ez 8

r0ln4R=r0Similarly,thelocalchargedensityatthetipis

2F0z "Ez "r"0 9r0ln4R=r0


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FromEqs.(6)(9),onecanconcludethattheradialdirectionelectrostaticpressureEexertedonthesidewallofthestreamerisweakerthantheaxialdirection electrostatic pressure on the tip. Note that both electrostaticpressures are roughly inversely proportional to r02, meaning that at theinitial stageof thefilament growthwhenr0 issmall, theelectrostaticforceson both directions are strong and the filament will grow both axially andradially.Adirectconsequenceofboththeaxialandradialexpansionsofthestreamerchannelisthelaunchingofcompressionwavesintoadjacentliquids[ 82]. At some critical point, the electrostatic force reaches a balance withhydrodynamic resistance acting on the surface in the radial direction first,whilethefilamentcontinuestogrowintheaxialdirection.

Experimentally recorded propagation speeds of the filaments varieddepending on the measurement techniques, ranging from a few km/s to100km/s[82,98,99 ].Inspiteofthediscrepancyobservedbydifferentgroups,thepropagationwasclearlyinthesupersonicregime.Thus,theformationofshockwavesshouldbetakenintoconsideration(seeFig.19 ).Thedragforceon the tip of the streamer, which is a stagnation point, equals the forceproducedbythetotalhydrodynamicpressure:

2 1 1M2Phd P1 1 CM22 101 1 2

whereP1 is ambient pressure;P1((2/1)M12 ( 1 / 1)) is the pres-surebehindshockfront;isthespecificheatratioofwater;M1 istheMachnumberofstreamer;M2 istheMachnumberaftertheshockfront;andCis

Shockwave

2r0

Err

EZZ

P Y/r

2Y/r

M2M1

P1Phd

FIG.19. ForcebalancefortheelectrostaticmodelproposedbyYangetal. [92].


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206 Y.YANGETAL.

the speed of sound in liquid. The relationship between M1 and M2 can bewrittenas[ 100 ]

1M122M22 112M12 1Equatingthehydrodynamicpressuretothesumoftheelectrostaticpres-

sure and the pressure produced by surface tension at the tip can give thefollowingequationforstreamerpropagation:

F02 2 1 1 2 2

4"r"0 2 P1 M12 CM2 12r0 ln24R=r0 1 1 2 r0Thebalancebetweentheelectrostaticforceandtheforceproducedbythe

totalhydrodynamicpressureintheradialdirectioncanbegivenasF20 1 2 "r"0 P1 CM2 132r0 ln2R=r0 2 r0

Note that there are three unknowns,M1,M2, a n d r0, in the above equa-tions. So it is possible to solve Eqs. (11)(13) simultaneously, when theappliedvoltage0 andtheinterelectrodedistanceRarespecified.

To demonstrate the validity of the present model, the filament radiuspredicted by the model is shown in Fig. 20 . For a typical interelectrode

0

20

40

60

80

100

Filamentradiu

s(m)

R=0.1cm

R=1cm

R=10cm

5 10 15 20 25 30

Appliedvoltage

FIG.20. Variationsoffilamentradiusasafunctionofappliedvoltageandinterelectrodedistance[92].


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Machnumber

12.5

12.0

11.5

11.0

10.5

10.0

9.5

9.0

5 10 15 20 25 30

R=0.1cm

R=1cm

R=10cm

Appliedvoltage(kV)


FIG.21. VariationsofMachnumberofstreamerasafunctionofappliedvoltageandinterelectrodedistance[92].

distance of 1cm, the filament radius increases from 3mm t o 5 0 mm as theappliedvoltagerisesfrom5kVto30kV.Thevalueiscomparabletotypicalexperimentalvalues.Forexample,Anreportedthatthelightemissionfromthedischargewasrestrictedtoachannelof100mmdiameter,indicatingtheinteractionofchargedparticlesintheregion[82 ].

Figure 21 shows the filament propagation speed as a function of0 andR. The calculated propagation speed from the present model is around15km/s, which is higher than the primary streamer speed but lower thanthe secondary streamer speed reported by An and his coworkers [82 ]. TheMach number increases moderately with the applied voltage, a phenom-enon which is understandable from the point of view of energy conserva-tion. The streamer propagation velocity is relatively independent of theinterelectrode distance. For an applied voltage of 30kV, the Mach num-ber increases from 11.2 to 12.3 when interelectrode distance decreasedfrom 10cm to 0.1cm. This is consistent with the known property ofnegative streamers as the previous experiment showed that for a givenvoltage the propagation velocity was relatively constant as the streamercrossed the gap, and while it increased as the streamer approached theplane electrode [91]. This phenomenon can be understood by Eq. (6): theinterelectrode distance R is decreased with the propagation of the strea-mers; as a result the electric field at the tip of the streamer was increased,leading to a higher propagation speed. However, the amount of theincrease in the electric field will not be significant because of the naturallogarithm in the equation.


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208 Y.YANGETAL.

B.THERM AL MECHANISMIntheelectrostaticmodeldescribedabove,itisassumedthatthetransla-

tionaltemperatureinsidethestreamerwaslow,andtheelectrostaticforceistheonlydrivingforceforthegrowthofthefilament.Theassumptionisvalidonlyattheinitialstageofthefilamentdevelopment,asthetemperaturewillkeeprisingasthemoleculesgainmoreenergythroughelectronneutralcolli-sions.Theheatingtime,,isapproximately=envt,whereenisthetimeforelectronneutralexcitationandvtisthetimeforvibrationaltranslational(vt) relaxation. For electronneutral excitation, en=1/en=1/(neken),where en is the electronneutral nonelastic collision frequency, ne is theelectron density,andken is the rate constant for electronneutral collisions.ken canbeexpressedasken=envte,whereen isthecrosssectionforvibra-tionalexcitationofH2Omoleculesbyelectronimpactandvte istheelectronthermalvelocity.

Forelectronswith anaverageenergyof1eV,thecrosssectionforvibra-1017 2 3tionalexcitationisabout= cm [101 ].ken isthusabout108cm /sas

istypical(vte=6107cm/s).Spectroscopicmeasurementsindicatedthatthestark broadening of H line corresponded to an electron density of about1018 3cm ataquasiequilibriumstate[60 ].Thus,thetypicalelectronneutralexcitationtimecanbeestimatedtobeintheorderofafewnanoseconds.Forthe vt relaxation, vt=1/(nvkvt), where nv is the density of vibrationalexcited molecules and kvt is the vt relaxation rate coefficient. For watermoleculesattheroomtemperature,kvt isabout31012cm3/s[94 ].Assum-ingthatnv isinthesameorderwithelectrondensity,vt couldbeestimatedto be in the order of several hundred nanoseconds, suggesting that heatingcantakeplaceinsidethefilamentsundersubmicrosecondtimescaleduetotheenergytransferfromtheelectronstothetranslationalenergyofthewatermolecules,andfurthermorethepropagationofthestreamerscanbecausedbythecontinuousevaporationofwatermoleculesatthetip.Heretheenergydissipation is not considered, and the actual heating time might be longer,butstillthelocalheatingmechanismunderthesubmicrosecondtimeregimeseemspossible.

To quantify the process described above, it is assumed that a smallcylindrical portion of water (i.e., see shaded portion in Fig. 22 ) evaporatesat the tip of the streamer during timeDt so that the length of the streamergrowsfromLtoLL,asshowninFig.22.Thediameteroftheevaporatedwatercylinderisassumedtobe2re.ThereisnodefinitivevalueforpressurePe insidethesmallvaporizedportiongiventheextremelyhightemperature.However,Pe canbeestimatedtobeintheorderof1000atmbecauseofthedensity difference between liquid water and vapor. Such a high pressurecould provide the driving force needed for the growth of the filament.


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Shockwave

2r0 2re

P Y/r

2Y/r

M2

L M1

P1

Pe

Po

Phd

FIG.22. ForcebalanceforthethermalmodelproposedbyYangetal. [92].

As in the previous section, one can get the force balance along the a x i a ldirectionatthetipofthefilamentassumingasteadystateconditionas

2k k1 1 2P1 M12 CM22 Pe 14

k1 k1 2 reTheenergyrequiredfortheevaporationofwatercanbecalculatedas

Ee VecpDTDvH 15whereandcp arethedensityandspecificheatofwater,respectively,andVeisthevolumeofevaporatedwater.Ve canbewrittenas

Ve r2 L 16eAfter evaporation, the overheated and overpressured water vapor will

expandradially,whilesatisfyingtheforcebalancealongtheaxialdirection,untilitreachesanequilibriumwiththeoutsidehydrodynamicpressure.Theprocess can be regarded as adiabatic under a submicrosecond time scale,andthusonecanhavethefollowingequations:

PeVs P0Vs 17e 0 s

P0 "r"0F20 18Pe r0cpDTDHlglnR=r0


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210 Y.YANGETAL.

where P0 and V0 are the pressure and volume, respectively, of the watervapor after the expansion; r0 is the radius of the filament after expansion;ands isthespecificheatratioofthewatervapor.TheforceproducedbyP0shouldbeinbalancewiththeforcescreatedbybothsurfacetensionandtotalenvironmentalhydrodynamicpressureasgivenbelow:

1 2 lP0 P1 CM2 19

2 r0Another set of equations can be obtained through the consideration of

energy conservation. The energy required to vaporize water is the electricenergy provided by the power supply. If the entire filament is viewed as acapacitorwithcapacitanceC,therequiredenergycanbecalculatedas

CF20E 202

Thecapacitanceofthecylindricalfilamentis2""0L

C 21lnR=r0

SotheenergychangerequiredtoextendthelengthbyLbecomes""0LF20E 22lnR=r0

ByequatingEtoEs,onehassffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi""0F2

re 0 23cpDTDHlglnR=r0

Assuming1duetothelowcompressibilityofwater,andrearrangingEqs.(11),(14),(18) ,(19) , a n d (23)toeliminateM2,re,andPg,onecangetasetofequationsaboutM1 andr0 asfollows:sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

C2 cpDTDHlglnR=r0P1M1

2 Pe 2 0 242M1

2 "r"0r0F02

ks"r"0F2

Per0cpDTDHl0glnR=r0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

C2 cpDTDHlglnR=r0P1 0 25

2M12 "r"0r0F02


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2.2 R=0.1cm

R=1cm2.0

R=10cm1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

Appliedvoltage(kV)

Filamentradius(m

)

0 10 20 30 40

FIG.23. Variationsoffilamentradiusasafunctionofappliedvoltageandinterelectrodedistance[92].

Forwatervapor,s canbeassumedtobe1.3[102].Forhightemperatureunderwaterdischarges,thetranslationalplasmatemperaturewasmeasuredtobebetween4000and6500K[103].Anaveragevalueof5000KisusedforDTinthepresentstudy.Figure23showstheMachnumberoffilamentpropagation,M1, as a function of 0 and R. The propagation velocity is about 50km/s,whichishigherthanthesecondarystreamervelocityof25km/sreportedbyAn[82], but lower than the value of 200km/s reported by Woodworth and hiscoworkers [99]. The discrepancy in the two measurements probably comesfrom the different techniques used for the velocitymeasurements. The valueof M1 remains constant for various values of 0 and R, i n di c at i n g that the propagation velocity of the streamers is independent of either the appliedvoltage or interelectrode distance. Similar phenomenon was observed pre-viously [82,99], where the propagation velocity of secondary streamers wasconstantoverawidevoltagerange.Figure24showsthefilamentradiusasafunctionof0 andR.Theradiusincreasesslightlyasthestreamersapproachthe other electrode, while it decreases almost linearly as the applied voltagedrops.Theabsolutevalueofr0 isaboutoneordersmallerthanthatobtainedfromtheelectrostaticmodel.Thiscanbeunderstoodifoneconsiderstheenergyrequirementsforthetwomechanisms.Fortheevaporationofwater,theenergyneededtobreakthehydrogenbondsbetweenwatermoleculesshouldbemuchgreaterthanthatrequiredtodisplacethesamevolumeofwater.

The different models based on the electrostatic force and evaporation ofwater give different results of the streamer propagation speed and filamentradius. The electrostatic model shows streamers with a larger radius and a


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Machnumber

31.64

31.62

31.60

31.58

31.56

31.54

31.52

31.50

0 5 10 15 20 25 30 35 40 45

R=0.1cm

R=1cm

R=10cm

Appliedvoltage(kV)

212 Y.YANGETAL.

FIG.24. VariationsoftheMachnumberofstreamerasafunctionofappliedvoltageandinterelectrodedistance[92].

lower Mach number, while the thermal model demonstrates that the strea-merscanmovemuchfasterbutarethinnerthanthosedeterminedfromtheelectrostaticmodel.Thedifferentfindingsfromthetwomodelssuggestthatdifferent mechanisms might be associated with the different modes of thestreamer propagation. At the initial primary streamer mode before anysignificant heat is generated, the electrostatic force might have played amajor role. The appearance of the secondary streamer requires more time,during which the electron energy can be transferred to translational energyof water molecules and subsequently evaporation becomes the dominantforce to drive the filament to move forward. The transition time betweenthe primary and secondary streamers is in the order of 100ns [ 82], a valuewhichisinaccordancewiththeheatingtimeasestimatedabove.C.STABILITY ANALYSIS

Thebreakdownprocessisusuallycharacterizedbytwofeatures:aninitialdevelopmentofthindischargechannelsandasubsequentbranchingofthesechannels into complicated bushlike patterns. Apparently, the branchingprocess isassociatedwiththeinstability ofthefilament.Inthis section, thelinear stability analysis of axisymmetric perturbation of a filament surfacewithacertainelectricchargedensityispresented.Aslongasthewavelengthof the perturbation is much smaller than the length of the filament, thestability characteristics can be approximated by considering perturbationstoachargedcylinderofconstantradiusasshowninFig.25.Histhedepthofwaveinfluence,anduisthevelocityofliquidrelativetothedisturbance.


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Water

Hu

+u

h/2

1/2kr

u ur0

z

Filament

Water


Thepeaktopeakamplitudeandwavenumberofthedisturbancearehandk, respectively. Then the surface of the perturbation can be represented bythefollowingequation:

hrr0 expikz!t 26

2where!istheoscillationfrequencyof theinstability. Toanalyze thelinearstability,thedisturbanceofthelocalelectrostaticforce,surfacetension,andhydrodynamicpressureareconsideredfollowingageometricalperturbation.Generally, the surface tension tends to minimize the surface area and sub-sequently stabilizes the disturbance, while the local enhancement of theelectrostatic force tends to push the disturbance to grow. In the referenceframethatmovestogetherwiththetipoffilament,theeffectsofthesethreeforces are considered separately for the pressure balance between the crestandtroughalongthestreamline(seeFig.19 ).1. ElectrostaticPressure

According to Eqs. (6)(9), the electrostatic pressure which can bedescribed by the product of electric field and surface charge density isproportional to the square of the local curvature of the interface, which isdifferentatthecrestandtroughoftheperturbation.Thus,theelectrostaticpressuresatthecrestandtrough,PE,c andPE,t become

2cPE;c "r"0F2 270 4

FIG.25. Schematicdiagramofdisturbanceatthesurfaceoffilament[92].


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214 Y.YANGETAL.

2tPE;t "r"0F2 280 4where

"r is the relative permittivity of water and c and t are the meancurvaturesatthecrestandtrough,respectively.Theexpressionforthemean

curvaturecanbewrittenas[104 ]1 @z@zr 1

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi @z@zr 292 3=2 rr 1 @zr2 1 @zr

SubstitutingEq.(26)intoEq.(29) ,onecangetexpressionsforMc andMt:1 h

c k2 30r0 h=2 2t 1 h k2 31r0 h=2 2

Subsequently,PE,c andPE,t canbewrittenas

!2 1 hk2cPE;c "r"0F2 "r"0F2 320 0 2

4 2r0 h 22r0 h !2 1 hk2cPE;t "r"0F2 "r"0F2 330 04 2r0 h2 22r0 h

Thus, the electrostatic pressure difference between the crest and troughbecomes

"r"0F20h "r"0F02hk2DPE PE;cPE;t 3432r0 2r0

2. SurfaceTensionThe pressures due to the surface tension across the interface at the crest

andtroughcanbewrittenas1

h

PT;c c k2 35r0 h=2 2


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PT;t t 1 h k2 36r0 h=2 2Thusthepressuredifferenceduetosurfacetensionbetweenthecressandtroughbecomes

hDPT PT;cPT;t hk2 372r0 h2=4

Sincer0>>h,theaboveequationcanbesimplifiedash

DPT hk2 382r0

3. HydrodynamicPressureWhenthereisadisturbanceontheinterfaceofthefilament,theflowspeed

of liquid will be perturbed in the depth of wave influence, inducing ahydrodynamicpressuredifferenceDPH betweenthecrestandtrough:

2

2

1 Du 1 DuDPHD u u uDu 39

2 2 2

2

whereDu/2istheperturbationintheflowspeedcausedbytheshapeofthewave.ThedynamicpressureisrelatedtotheflowspeedthroughBernoullisequation. The pressure difference from the electrostatic force and dynamiceffectoftheflowhasthesignoppositetothatofthepressuredifferencedueto the surface tension. For a balance between two kinds of oppositelydirectedpressuredifferences,onehas

h "r"

0F

0

2h "r"

0F

0

2hk2uDu 2 hk2 3 2r0 0 40r 2r0 0

InordertosolveEq.(40),theperturbedflowspeedDumustbeexpressedintermsofexperimentallymeasurablequantities.ThefollowingderivationisinspiredbyKenyon[105].

Assumingthattheperturbedflowspeedisconstantoverthedepthofwaveinfluence, the mass conservation equation through vertical cross sectionsbetweenthecrestandtroughbecomes

Du h Du hu H u H 412 2 2 2


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2 4 6 8 100

10

20

30

Rayleighmode

100V

200V

Re()

400V

k

216 Y.YANGETAL.

where H is the depth of wave influence. The above equation can bereducedto

u h DuH 42ThetheoreticalexpressionforHwasgivenbyKenyon[106 ] as

1H 43

2kUsingEqs.(42)and(43)toeliminateHandDu,Eq.(40)becomes

"r"0F2 "r"0F02k20!2 k k2 443 22r r0 0 2r0

Sincethisisaquadraticequation,therewillbetwodifferent branchesofthedispersionrelation,andaninstabilityoccursifRe(!)>0.ThefirstthingtonoteinEq.(44)isthatwhentheappliedvoltage0isequaltozeroandthesurface is flat, in other words, when the radius of the filament r0 goes toinfinity,theaboveequationreducestou2=k,whichistheequationfortheclassictwodimensionalRayleighinstability.

Figure 26 shows the instability growth rate ! at a low applied voltage,where

the

process

is

in

Rayleigh

mode.

The

dashed

line

represents

the

classic

Rayleigh instability for 0=0 an d r0! 1. For 06 r0 is finite, 0 andinstability only happensathigh wavenumbers. Whenthe voltageincreasesunder this mode, the growth rate is decreased until fully suppressed at a

FIG.26. Instabilitygrowthrate!atlowappliedvoltages.kand!arenondimensionalizedusingstreamerradiusr 3/g)1/20 andtimescalet=(r0 [92].


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2.0

30kV

1.5

1.0

20kV

0.5 10kV

0.0

k

Re()

105 104 103 102 101


FIG.27. Instabilitygrowthrate!athighappliedvoltages.kand!arenondimensionalizedasinFig.26[92].

certaincriticalvalue.Thephysicalexplanationtothiscanbeasfollows:theRayleigh instability occurs due to surface tension, a phenomenon whichalways acts to break a cylindrical jet into a stream of droplets; on theother hand, the electrostatic force, which is proportional to the square ofthe applied voltage, always acts on the opposite direction of the surfacetension.Whentheappliedvoltageincreases,theRayleighinstabilitywillbesuppressedwhenthetwoforcesarebalanced.

Asthevoltagecontinuestoincrease,theinstabilityisdictatedbytheelectro-static mode, where the electrostatic force exceeds the force created by thesurfacetensionandbecomesthedominantforce.Figure27showstheinstabil-itygrowthrate!atahighvoltage.Boththegrowthrateandtherangeofwavenumberincreaseasthevoltagerises.Thephysicsofthismodeisaconsequenceoftheinteractionoftheelectricfieldwiththesurfacechargeontheinterface;surfacetensionisaparameteroflessimportanceforthismode.Themechanismfortheinstabilityisthataperturbationintheradiusofthefilamentinducesa perturbation in the surface charge density and therefore a perturbation intheelectrostaticpressure.Atahighvoltage,theperturbationisamplifiedbythe

2fact that the electrostatic pressure PE is proportional to , causing

theinstability.IncontrasttotheRayleighmode,theinstabilityintheelectro-staticmodeisunavoidableatlowwavenumbers(longwavelength).Thismayexplainwhythefilamentalwaystendstobranchintobushlikestructures.In conclusion, the electric breakdown of water involves both the genera-tion and propagation of lowdensity channels through liquid. Different


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218 Y.YANGETAL.

physical processes and interactions between different phases of the mediashould contribute to the complexity of the problem. In the current section,different modes of the streamer propagation have been considered intosimplified steps, with each step characterized by a driving force and thecorresponding hydrodynamic drag. The effects of the electrostatic forceand local heating on the streamer propagation have been analyzed usingsimplifiedassumptions.Itisshownthatbothofthemaredominant forthestreamer propagation, but at different time scales. Furthermore, a linearinstabilityanalysishasbeenperformedonachargedcylindricalstreamerinan external electric field to understand the bushlike growth pattern ofbreakdown in liquid. It is shown that the stability may be caused by thecompetition between perturbations in the electrostatic pressure and surfacetensioncausedbythedisturbanceofthestreamergeometry.Withincreasingapplied voltage, the electrostatic instability is found to grow whereas theclassicRayleighinstabilityisfoundtobesuppressed.

V.ApplicationofSparkDischargeforScaleRemovalonFilterMembranesIn the next few sections, new developments of underwater plasma treat-

ment at Drexel Plasma Institute for various applications will be reported.First, the application of spark discharge for scale removal on filter mem-branesisstudied.Inmodernwastewatertreatment,filtersareroutinelyusedfor removing unwanted particles from water. Conventionally, microfiltra-tionmethodsareusedtoremovesuspendedparticlesfromwater.Wheneverafilterisusedinawatersystem,thepressuredropacrossthefiltergraduallyincreaseswithtimeand/ortheflowrategraduallydecreaseswithtime.Thisreducedperformanceofafilterisduetotheaccumulationofimpurities onthefiltersurface,andthecloggedareabecomessitesforbacterialgrowthforfurther reducing the opening in the filter surface, increasing the pumpingcost. Therefore, in order to continuously remove suspended particles fromwater,thefiltermustbereplacedfrequently,aprocesswhichisprohibitivelyexpensiveinmostindustrialwaterapplications.Toovercomethedrawbacksof frequent filter replacement, selfcleaning filters are commonly used inindustry. Although there are a number of selfcleaning filter technologiesavailable on the market, most selfcleaning filters use a complicatedbackwash method, which reverses the direction of flow during the cleaningphase. Furthermore, the water used in the backwash must be clean filteredwater, which reduces the filter capacity. Aforementioned drawbacks ofthe conventional filter technologies motivated the authors to develop anewselfcleaningfilterusingsparkgeneratedshockwaves.


41/114


As illustrated in previous sections, strong shockwaves can be formedduringtheprocessofpulsedarcorsparkdischarge.Theenergytransferredtotheacousticenergycanbecalculatedas[107 ]

Z24rEacoustic Pr;t P0dt 45

0C0whereristhedistancefromthesparksourcetothepressuretransducer;0 isthedensityofwater;C0 isthespeedofsoundinwater;andP0 istheambientpressure.Onecanconcludethatthepressurecreatedbythesparkdischargeis much higher than ambient pressure at positions close to the source.Traditionally, the highpressure shockwave is studied for HV insulationand

rock

fragmentation,

while

recently

it

has

found

more

applications

in

other areas including extracorporeal lithotripsy and metal recovery fromslagwaste[ 108110 ].

Inordertovalidatetheconcepttousesparkdischargeforfiltercleaning,an experimental setup was built where discharges could be produced inwater, and pressure drop across a filter surface was measured over time atvarioussparkfrequenciesandflowconditions.Itwashypothesizedthattheenergy deposited by the spark shockwave onto waterfilter interface wasenoughtoremovethecontaminantshavingVanderWaalsbondswithfiltersurface.

The

objective

of

the

study

was

to

examine

the

feasibility

of

a

selfcleaningwaterfiltrationconceptusingsparkdischargesinwater.

A.EXPERIM ENT SETUPAnexperimentalsystemwasdesignedtotest theeffectivenessoftheself

cleaning filter concept using spark discharges in water under various flowconditions. The system consisted of two parts: a flow loop with a filter tosimulateacoolingtowerwatersystemandapulsedpowersystemtoproducesparkdischargesinwater.AschematicdiagramofthetestloopisshowninFig. 28 . To simulate deposits on filter surfaces, artificially hardened waterwithhardnessof1000mg/LofCaCO3 wasmadebyaddingcalciumchloride(CaCl2)andsodiumcarbonate(Na2CO3)inproperproportionstotapwater.To minimize the abrasion of mechanical parts by CaCO3 particles, a peri-stalticpump(FPU259,OmegaInc.,Stamford,CT)wasusedtocirculatethehardwaterinthetestloop.Theflowrateinthetestsystemwasvariedfrom50mL/minto400mL/minusinga valveinaflow meter.Inallexperiments5% of the untreatedwaterwasbypassed for the purpose of the creation ofthetangentialflowalongthefiltersurface.Itisofnotethatsometangentialflowwasbelievedtobenecessaryforthesuccessfulremovaloftheunwanteddepositsfromthefiltersurfaceusingthesparkgeneratedshockwaves.


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220

Premixedwaterandparticles Flowmeter Peristalticpump

Pressuretransducer

Computer

Tangentialflow Clean

waterflowMagneticstirrer Filtercase

Y.YANGETAL.

FIG.28. SchematicdiagramofthetestingloopusedbyYangetal. [111].

Usually filters have to be cleaned or replaced when excessive amounts offoreignmaterialsareaccumulatedonthefiltersurface.Thedecisiontocleanorreplace a filter is often based on the changes in flow rate or pressure dropacrossthefilter.Whenthepressuredropincreasestoapredeterminedvalueortheflowratereducestoapredeterminedvalue,thefilteriscleanedorreplaced.In the present experiment, the pressure drop across the filter with a filtersurface area of 25cm2 was measured using a differential pressure transducer(PX137015AV, Omega Inc., Stamford, CT). The analog signal from thepressure transducer was collected and digitized by a data acquisition system(DI148U,DataqInstruments,Akron,OH)andprocessedbyacomputer.

Apulsedpowersysteminthepresentstudyconsistedofthreecomponents:a highvoltage power supply with a capacitive energy storage, a sparkgapbasedswitch,andadischargesourceimmersedinwater.AschematicdiagramofthepulsedpowersystemisshowninFig.29.TheHVpulseswereprovidedbyapulsedpowersupply.Thepowersupplychargedan8.5nFcapacitorbankandthepulsewastriggeredbyanairfilledsparkgapswitch.Arcdischargewasinitiatedintheswitchfromtheovervoltageproducedbythepowersupplyandcapacitor, and the spark gap made use of a very low impedance of arc totransfer highpower energy within nanoseconds. Power deposited into waterwasanalyzedbymeasuringthecurrentpassingthroughthedischargegapandthevoltagedropinthegap.Formeasurementsofthecurrent,amagneticcorePearsoncurrentprobewasutilized(1V/Amp1/0%sensitivity,10nsusablerisetime,and35MHzbandwidth).Voltagewasmeasuredusingawideband-width1:1000voltageprobe(PVM4,NorthStarResearchCorp.,Albuquerque,NM).Signalsfromthecurrentandvoltageprobeswereacquiredandrecordedbya digital phosphor oscilloscope (DPS) (500MHz bandwidth, 5109 samples/s,TDS5052B, Tektronix, Beaverton, OR). Acquired data were then integratedusingacustomizedMATLABcode.


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Sparkgap

Electrode

Water

Filter

Membrane

AC

Control

board

FIG.29. SchematicdiagramofapulsedpowersystemusedinthestudybyYangetal. [111].

30 100

Appliedvoltage(kV) 20

Current

Voltage

80

10 60

0 40

10 20

020

2030

0 10 20 30 40 50 60 70 80 90

Time(s)

Current(A)

FIG.30. Typicalvoltageandcurrentwaveformsofapulseddischargeinwater[111].

Typical voltage and current waveforms are shown in Fig. 30 . A fast risetime(8ns)wasobtainedwiththeclosureofasparkgapswitch.Thepeak-topeak voltage was 29.6kV. The initial steep rise in the voltage profileindicated the time moment of breakdown in the spark gap, after which thevoltageslightlydecreasedwith timeover the next12ms dueto along delaytimewhilethecoronawasformedandtransferredtoaspark.Therateofthevoltage drop over time depends on the capacitance used in the test. Thecurrentprofileshowsthecorrespondinghistorieswhichshowinitiallysharppeaksandthenverygradualchangesoverthenext12ms.Att12ms,therewas a sudden drop in the voltage indicating the onset of a spark or themoment of channel appearance, which was accompanied by sharp changesin both the current and voltage profiles. The duration of the spark wasapproximately 3ms, which was much shorter than the duration of the cor-ona.Itisworthto mentionthat the energy dissipated inelectrolysis canbe


44/114

222 Y.YANGETAL.

comparable with, or even higher than, the energy deposited in spark, espe-cially at highconductivity water conditions, because of the conductioncurrent. The pulsed energy stored in the capacitor Eb was about 2.0J,whichwascalculatedas

Eb 0:5CV2 46bwhereCwas8.5nFandVb thecapacitorvoltagewas21.5kV.Thevaluewasmuch lower than the peaktopeak electrode voltage because of the oscilla-tion in electric circuit upon the closing of spark gap. By integratingthe voltage and current, the energy deposited into spark discharge wascalculatedas

Z t2Ep VtItdt 47

t1whereV(t)andI(t)arethevoltageandcurrentmeasuredbytheoscilloscope,respectively, and t1 and t2 are the starting and ending times of the spark,respectively. The result was approximately 1.9J/pulse, showingmost oftheenergystoredinthecapacitorfinallywentintothesparkdischarge.

Thesparkdischargesourceinwaterconsistedofastainlesssteel316wireelectrode(anode)witharadiusof2mmandanexposedlengthof5mm,anda stainless steel mesh which acted as both a filter surface and groundedcathode.Thetipoftheanodeelectrodewassharpenedto0.2mmdiametertoprovideafieldenhancement.Thedistancebetweentheanodeelectrodeandstainlesssteelmeshwas10mm.Theopeninginthestainlesssteelmeshwas10mm. The electric conductivity of the tap water (provided by the City ofPhiladelphia) used in the experiment was approximately 400mS/cm. Thevalue was maintained at 1000mS/cm after the introduction of CaCl2 andNa2CO3. No significant change was observed in the conductivity after theapplicationofthesparkdischarge.

B.RESULTS AND D ISCUSSIONFigure31showsthechangesinthepressuredropundervariousflowrates

ranging from 200mL/min to 400mL/min without spark discharge. Thepressure drop for a flow rate of 400mL/min was approximately 50 Torr atthebeginningofthetest,whichapproachedtoanasymptoticvalueofabout400 Torr at t=3.5min, indicating that the filter was fully covered by theparticles. In all three cases of different flow rates, the pressure drop slowlyincreased during the first 30s. In the following 23min the pressure dropincreasedratherrapidly,arrivingatrespectiveasymptoticvalues.


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0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

50

100

150

200

250

300

350

400

450

Pressuredrop(Torr)

400mL/min

300mL/min

200mL/min

Time(min)

0

50

100

150

200

250

300

350

400

450

Pressuredrop(Torr)

400mL/min300mL/min

200mL/min

0 2 4 6 8 10

Time(min)


FIG.31. Changesinpressuredropatthreedifferentflowrateswithanartificiallyhardenedwater[111].

FIG.32. Variationsofpressuredropafteronesinglesparkdischargeatthreedifferentflowrateswithanartificiallyhardenedwater[111].

Figure 32 shows the longtime response of the pressure drop across thefiltersurfaceafteronesinglesparkdischargeatthreedifferentflowratesof200, 300, and 400mL/min. One could visually observe that some particles


46/114

_ _

224 Y.YANGETAL.

weredislodgedfromthefiltersurfaceandwerepushedawayfromthefiltersurfacebytangentialflow,andasuddenchangeinthepressuredropimme-diately following the single spark discharge confirmed the removal of thedepositsfromthefiltersurface.

The cleaning effect can be explained by the pressure pulse produced byspark discharge. A number of researchers studied the bubble growth byspark discharge in water [112115 ]. One of the most effective models isKirkwoodBethemodelasgivenbelow[107 ]:

R_ :: 3 R_ : 2 R_ R_ R :1 R R 1 R 1 H 1 H 48

C 2 3C C C CwhereCandHarethespeedofsoundofthewaterandthespecificenthalpyat the bubble wall, respectively. R is the radius of the bubble wall.The overdots denote the derivatives with respect to time. By expressingthetimederivativeofspecificenthalpyasafunctionofderivativeofplasmapressure P inside the bubble, Lu showed that it was possible to solve Pas[107 ]

"

1=2#2n=n12 n1 n1

Pr; tr A 1 G B 49n1 n1 rC2

whereA,B, andn are constants (A=305.0MPa,B=304.9MPa,n=7.15);risthedistancefromthesourceofthesparktothepressuretransducer;and

HRR rRGR ; tr t 50

2 C0Using the above equation, Lu simulated that for a spark discharge with

energyof4.1J/pulse,themaximumpressureatadistanceof0.3mcouldbeupto 7atm [107].The cleaningeffect was dueto therapid pressurechangeproducedbyasparkdischarge.

With a single pulse, it took approximately 3min for the pressure drop toreturn to its asymptotic value after the application of the single spark dis-charge.Thissuggeststhatone needstorepeatedlyapplyspark dischargestoeffectivelyremovetheparticlesfromthefiltersurfaceoveranextendedperiod.

Figure 33 shows the changes in the pressure drop over time for threedifferent flow rates. One spark discharge was applied every minute fromthesupplywaterside(i.e.,untreatedwaterside)wheretheaccumulationofsuspended particles takes place. For the case of 300mL/min, the pressuredropdecreasedfromthemaximumasymptoticvalueof350Torrto230Torrafter the first spark discharge. Since water with particles was continuously


47/114

Pressuredrop(Torr)

450

400

350

300

250

200

150

100

50

0

400mL/min

300mL/min

200mL/min

0 2 4 6 8 10

Time(min)


FIG. 33. Changes in pressure drop under repeated pulsed spark discharges with anartificiallyhardenedwater[111].

circulated through the filter surface, the pressure drop began to increaseimmediately after the completion of the first spark discharge as shown inFig.32 .Thesecondandthirdsparkdischargesfurtherreducedthepressuredrop to 170 and 125 Torr, respectiv

yang 2010 advances in heat transfer

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