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BubbleCoalescenceandBreak-UpinAir-SpargedBubbleColumnsAphenomenologicalmodelisproposedfortheratesofbubblecoalescenceandbubblebreak-upinturbulentgas-liquiddispersions.Bubblecoalescenceismodeledbyconsideringbubblecollisionsduetoturbulence,buoyancy,andlaminarshear,andbyanalysisofthecoalescenceefficiencyofcollisions.Bubblebreak-upisanalyzedintermsofbubbleinteractionswithturbulenteddies.Amethodforthemeasurementofcoalescenceandbreak-upeventsinturbulentsystemsisdescribedandusedtotestthevalidityoftheproposedmodel.Themeasurementtechniquereliesonthemixingoftracergaseswithinbubblesuponcoalescence,inconjunctionwithMonte-Carlosimulationsofcoalescenceevents.Bothdistilledwaterandsaltsolutionsareexamined.Favorableagreementisfoundbetweenthemodelandtheindividualcoalescenceandbreakagerates,aswellaswithdataobtainedfortheaveragebubblesizeandbubblesizedistribution.MichaelJ.PrinceHarveyW.BlanchDepartmentofChemicalEngineeringUniversityofCaliforniaBerkeley,CA94720IntroductionGas-liquidcontactorsfindbroadapplicationasreactorsandseparationunitsinthechemical,mining,pharmaceuticalandbiochemicalindustries.Inthesesystemstherateoftransportofthegastotheliquidphaseoftenlimitsproductivityandisthereforeacriticaldesigncriterion.Currentdesignmethodsrelyonempiricalcorrelationswhichmaynotbeconfidentlyappliedbeyondthenarrowrangeofoperatingconditionsandgeometriesoverwhichtheyweredetermined.Theuncertaintyinbubblecolumndesignarisesfromalackoffundamentalunderstandingofthehydrodynamicsandrateprocesseswhichgovernbubblesizeandthusinterfacialarea.Bubblesizedependsonabalanceofcoalescenceandbreak-upratesinthevessel.Nobroadlyapplicablemodelfortheserateprocessesinturbulentsystemshasyetbeenpresented.Thishasbeenduetotheinabilitytomeasurebubblecoalescenceandbreak-upinsystemswherehighgasflowratespreventdirectvisualobservation.Theobjectiveofthisstudyistomeasurebubblecoalescenceandbreak-upratesinturbulentgas-liquiddispersionsandtodevelopamodelfortheserateprocessesbasedonphysicochemi-calandhydrodynamicprinciples.Theabilityofthemodeltoadequatelypredicttheindividualexperimentalrateofcoales-CurrentaddressofM.J.Prince:DepartmentofChemicalEngineering,BuckncUUniversity.Lewisburg,PA17837.cenceandbreak-upisusedtojudgeitsvalidity.Inaddition,themodelistestedagainstitsabilityto'predictbubblesizeandbubblesizedistributions.Thecoalescenceprocessisanalyzedbyexaminationofbubblecollisioneventsandthelikelihoodofcollisionsresultingincoalescence.Bubblebreak-upisexaminedintermsofbubbleinteractionswithturbulenteddies.Inadditiontothetheoreticaldevelopment,anexperimentalmethodforthemeasurementofbubblecoalescenceandbreak-upratesinturbulentsystemsisdescribed.Theeffectofinorganicelectrolytesoncoalescenceandbreak-upratesisalsoexamined.Muchofthecurrentinterestinthepredictionofbubblesizestemsfromthedesiretopredictoxygentransferratesinaerobicbiochemicalreactors.Inthesesystemstheliquidmediatypicallycontainsinorganicelectro-lyteswhichprovidemineralsformicrobialgrowth.Otherapplicationswheresaltsinfluencebubblesizearemineralflotationandtreatmentofpollutedsalinewaters.Theadditionofinorganicelectrolyteshasbeenfoundtohaveamarkedeffectonbubblesizebyanumberofinvestigators(MarrucciandNicodemo,1967;KeitelandOnken,1982;OolmanandBlanch,1986a).Changesinbubblesizemayresultfromtheinfluenceofsaltsoneitherbubblebreak-uporbubblecoalescencerates.Inthisworkthedegreetowhicheachofthesemechanismsisaffectedbysaltconcentrationisexaminedandamodelisdevelopedtopredicttheserateprocessesininorganicelectrolytesolutions.WhileinorganicsaltsareonlyoneformofAIChEJournalOctober1990Vol.36,No.101485surfacecontaminant,theanalysisforothercompoundswhichaffectthesurfacetensionwillbesimilarinmanyrespects.ModelDevelopmentBubblecoalescencePreviousexperimentalstudiesonbubblecoalescencefallintooneoftwocategories;measurementofcoalescencetimesinstagnantliquids(Marrucci,1969;KimandLee,1987),ordeterminationofcoalescenceratesfrombubblesizedataob-tainedinturbulentsystems(Calderbanketal.,1964).Neitherapproachissatisfactoryfordeterminingtherateofcoalescenceunderpracticalhydrodynamicconditions.Filmthinningtimesinstagnantliquidscannotbeusedtodeterminecoalescenceratesinmorecomplexhydrodynamicenvironments.Similarly,measurementofbubblesizesinturbulentflowsdoesnotprovideinformationontheindependentcontributionsofbreak-upandcoalescencerates,bothofwhichdeterminebubblesize.Whilevariousmodelsconsidertheserateprocessesindependentlyforthecaseofliquid-liquidsystems(CoulaloglouandTavlarides,1977;Rossetal.,1978;ValentasandAmundson,1966),thesemodelshavenotbeentestedduetoalackofexperimentaldataontheindividualrateprocesses.Therearealsodifferencesinbehaviorbetweenliquid-liquidandgas-liquidsystemswhichmustbeconsideredinmodelingbubblecoalescenceandbreak-UP.Coalescenceoftwobubblesinturbulentflowsoccursinthreesteps.First,bubblescollide,trappingasmallamountofliquidbetweenthem.Thisliquidthendrainsuntiltheliquidfilmseparatingthebubblesreachesacriticalthickness.Atthispoint,filmruptureoccursresultingincoalescence.Fromthefirststep,itisseenthatthecoalescencerateisintimatelyconnecte