In fl uences of Polymer − Surfactant Interaction on the Drop Formation Process An Experimental Study - Dastyar et al. - 2021 - Unknown

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pubs.acs.org/LangmuirArticleInfluencesofPolymer−SurfactantInteractionontheDropFormationProcess:AnExperimentalStudyPeymanDastyar,MoloudSadatSalehi,BaharFiroozabadi,*andHosseinAfshinCiteThis:Langmuir2021,37,1025−1036ReadOnlineACCESSMetrics&MoreArticleRecommendationsABSTRACT:Theinteractionbetweenpolymerandsurfactantmoleculesaffectsthephysicalpropertiesofliquids,whichcouldbeofgreatimportanceinanabundanceofprocessesrelatedtodropformation.Polymerandsurfactantconcentrationisafactorthatdramaticallyimpactstheshapeofmolecularnetworksformedinthefluidbulkandthecharacteristicsofaformingdrop.Inthisstudy,thedeformationanddetachmentofaqueouscarboxymethylcellulose(CMC)solutions’dropscontainingdifferentconcentrationsofsodiumdodecylsulfate(SDS)arestudiedexperimentally.OurpurposeistodeterminetheeffectsofCMCandSDSconcentrationsontheparametersrelatedtotheformationprocess,includingdroplength,minimumneckthickness,andformationtime.OurresultsclearlyshowthattheincrementoftheSDSamountataconstantlowCMCconcentrationincreasesthedropdetachmentlengthandresultsinaslowerthinningprocess.However,athigherCMCconcentrations,thedroplimitinglengthreachesamaximum,indicatingtheeffectsofdisintegrationofmolecularstructuresastheSDSamountexceedsthecriticalconcentration.Moreover,thedropformationtimeisfoundtodecreasewiththeincrementoftheSDSconcentration,whichcouldbeattributedtothereductionofdynamicinterfacialtension.■INTRODUCTIONisusedwhosemoleculesarenegativelychargedand9amphiphilic.TheresultsofpreviousstudiesindicatethatThegrowthandbreakupofaliquiddropfromanozzleorDownloadedviaUNIVOFPRINCEEDWARDISLANDonMay16,2021at07:28:03(UTC).needlehavebeeninvestigatedbymanyresearchers1−4duetotheviscosityofaqueoussolutionsofthispolymerincreasesSeehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.withtheincrementofCMCconcentration.10Moreover,theitswiderangeofapplicationsencompassingcosmetics,inkjetprinting,emulsionmanufacturing,andcoating.5−7InmanyofpresenceofCMCmoleculesinwatercontributestothenon-11theseapplications,polymersandsurfactantsareusedtocontrolNewtonianpropertyofthesolution.Basedontheresearchdrops’characteristicsduetotheirsignificantimpactonthe12conductedbyGhannamandEsmail,CMC−watersolutionsliquids’physicalproperties.Therefore,understandingtheshowshear-thinningbehavior,whichincreaseswithariseininfluencesofpolymer−surfactantinteractiononfluidbehaviorCMCconcentrationbelow4%byweight.couldprovideadeepinsightintothephysicsunderlyingtheNumerousobservationsdemonstratethesignificantinflu-dropformationprocessinthepresenceofthesetwomaterials.enceofsurfactantsonthephysicalpropertiesofaqueousAddingapolymerisacommonwayofalteringthepolymersolutions.Byaddingasurfactanttoasolutionatlowrheologicalbehaviorofsolutions.Inthecaseswhereamphiphilicpolymermoleculesaredissolvedinaqueoussolutions,theyholdapositionsothattheirhydrophobicReceived:August24,2020portionshaveminimumcontactwithwatermolecules.AsaRevised:December26,2020result,polymermoleculesinteractwitheachotherandformPublished:January12,2021molecularstructures,whichleadstotheincrementofliquidviscosity.Inthepresentwork,carboxymethylcellulose8(CMC),whichisoneoftheforemostderivativesofcellulose,©2021AmericanChemicalSocietyhttps://dx.doi.org/10.1021/acs.langmuir.0c024871025Langmuir2021,37,1025−1036

1Langmuirpubs.acs.org/LangmuirArticleconcentrations,surfactantmoleculesadsorbatthefluidinlowerinterfacialtension,whosevaluecouldbeinconstantinterfaceandcausetheinterfacialtensiontodecrease.Bydependingonthesurfactanttype,propertiesoftheliquid,flow35furtherincrementofthesurfactantamountandatarate,locationontheinterface,andtime.Kovalchuketal.concentrationcalledthecriticalassociationconcentrationmeasuredthedynamicinterfacialtensionofaformingdrop(CAC),itsmoleculesbegintointeractwiththepolymerusingthedynamicsofneck-thinningandshowedthatatthemoleculesandchangetheconformationofmolecularnet-momentsclosetopinch-off,theinterfacialtensionishigher13,14works.Thepolymer−surfactantinteractionleadstoathantheequilibriumvalue.Theyalsostatedthatasthelowerslopeofthereductionofinterfacialtensionintermsofsurfactantconcentrationincreases,thedynamicinterfacialsurfactantconcentration,comparedtothatbeforetheonsetoftensiondecreasesintheneckregion.Furthermore,insome15cases,surfactantdepletionfromtheinterfaceresultsinainteraction.Athighersurfactantconcentrations,itsmicellesforminthevicinityofthepolymermolecule’shydrophobicconcentrationgradientandMarangonistresses,whichcould16increasethedurationofrupture.36,37Thedropformationportion.Theslopeofthevariationofinterfacialtensionincreasesasthesurfactantconcentrationexceedsthepolymerprocesscontainingboththepolymerandsurfactanthasbeen38saturationpoint(PSP),atwhichpolymermoleculesbecomeconsideredbyRochéandKellay,whostudiedtheformation15,17ofaliquidcrystal(5CB)dropinanambientliquid,whichsaturatedwithsurfactantparticles.Withfurtherincrementofthenumberofsurfactantmolecules,theyadsorbatthecontainedasurfactant(sodiumdodecylsulfate,SDS)andaliquidinterfaceuptothepointwherethesurfactantpolymer(poly(vinylalcohol),PVA).Theynotedthatconcentrationreachesacertainvalue,calledthecriticalmicellesurfactantpresence,alongwithapolymer,changestheneck’s39concentration(cmc).Atconcentrationsabovethecmc,freeconformationandthinningdynamics.Also,Decheletteetal.micellesforminthefluidbulkandthesolution’sinterfacialexaminedthebreakupofaliquidjetcontainingapolymer18(XanthangumandCarbopol)andasurfactant(SDS).Theytensionnolongervaries.Inaddition,polymer−surfactant19concludedthataddingasurfactanttoapolymersolutiondelaysinteractionimpactstheviscosityofthesolutions,whichdependsondifferentfactorssuchastheconcentrationofthetheruptureandincreasesthebreakuplength.Recently,Tang40polymerandsurfactant,electrostaticchargeoftheirmolecules,etal.usedpolyethyleneglycol(PEG)andSurfynol465andtemperature.20Basedonpreviousinvestigations,the(S465)asadditivestodyeinksolutionstoobservetheimpactsviscosityofaqueoussolutionsofamphiphilicpolymersrisesofviscosityandinterfacialtensionondropletformation.withtheincrementofsurfactantconcentrationuptoacertainAsexplainedintheaboveparagraphs,deformationand21breakupofdropsinthepresenceofasurfactant35−37andapoint,andathighervalues,surfactanteffectsarelost.31Theformationofliquiddropsfromanozzlehasbeenatopicpolymerhavebeenconsideredbynumerousresearchers.ofinterestoverthelastfewdecades.TheprincipalpurposeofHowever,tothebestofourknowledge,afewworkshavebeennumerousresearcherswastounderstandthevariationsofdevotedtounderstandingtheeffectsofpolymer−surfactant38−40parametersrelatedtoaformingdrop,suchasdroplength,neckinteractionondropformation.Itiswell-knownthatthickness,formationtime,andsatellitedropsize,indifferentamphiphilicpolymerchainsandsurfactantaggregateschangecircumstances.22−26Shietal.27studiedtheeffectsofviscositytheiraqueoussolutions’properties,whichsignificantlydiffersonthedeformationofdrops.Theystatedthatincrementoffromthoseofsurfactantandnon-amphiphilicpolymerviscosityresultsinalongerdropelongation,whichstemsfromsolutions.Therefore,wecouldexpectdistinctivecharacteristicstheroleofviscousforcesindampeningthecapillarypressure.ofdropformationinthepresenceofsurfactantsandpolymersHendersonetal.28carriedoutanexperimentalstudytowithhydrophobicportions,whichhasbeenrarelypaid41observethedeformationofNewtoniandropsduringtheattentionto.Inourpreviousstudy,theformationofaqueousformationstage.Basedontheirresults,theincrementofglycerolsolutions’dropcontainingasurfactantwasexplored.interfacialtensiondecreasesthelimitingdroplength.ZhangWefoundthattheadditionofasurfactanttothedropphaseandBasaran29experimentallyinvestigatedtheinfluencesofhasconsiderableeffectsondropshapeandrupture.Inthisvariousfactors,includingtheflowrate,needlediameter,andpaper,weexperimentallyinvestigatetheimpactofsurfactantphysicalpropertiesofadropphasefluid.Theirresultsrevealed(SDS)additionontheformationprocessofaqueousthatthedropdetachmentlengthdecreasesandthenriseswithamphiphilicpolymer(CMC)solutions’dropinambientair.thecapillarynumber.TheyalsoconsideredthevariationsofOurmainobjectiveistorevealtheroleofpolymer−surfactantsatellitedrops’sizeandshowedthatwiththeincrementofflowinteractioninthevariationsofimportantgeometricalandrate,thesatellitedropsbecomelarger.DavidsonandWhite30physicalparametersofdropformation,includingdroplength,numericallystudiedtheinfluenceoftheshear-thinningminimumneckthickness,andformationtimeaswellaspropertyonthedropformationprocess.Theobtainedresultssatellitedrops’size.illustratedthatshear-thinningdecreasesthedropdetachmentlengthandincreasestheneck-thinningrate;however,itseffects■EXPERIMENTALSECTIONarelesssignificantatlowReynoldsnumbers.Morerecently,Carboxymethylcellulose(CMC),usedasananionicpolymer,was31Salehietal.conductedanexperimentalstudytouncoverthepurchasedfromCDH,India.Thedegreeofsubstitution(α)andtheeffectsoftheshear-thinningpropertyofaqueouspolymermolarmassofCMCperunitareintheranges0.4−3and184.95−solutionsonaformingdrop.Accordingtotheirfindings,the437.23g/mol,respectively.Also,weobtainedsodiumdodecylsulfateincrementofshear-thinningleadstoadecreaseinthe(SDS),whichisananionicsurfactant,fromEMDMillipore,Germanyformationtime.(purity≥99%,molarmass:288.37g/mol).ThechemicalstructuresofSDSandCMCarepresentedinFigure1.ThepresenceofsurfactantsintheprocessespertinenttoDropphasefluidsinourexperimentsweresolutionsof0.5,0.75,dropformationand,ingeneral,free-surfaceflowshaveand1%carboxymethylcellulose(CMC)byweightindistilledwater.attractedmuchattentionduetotheirsignificantinfluenceonWeaimtoobservethedropbehavioraroundthecriticalmicelletheevolutionoftheliquidinterface.Accordingtopreviousconcentration(cmc)ofthesurfactantandcompareittothatofthe32−34works,adsorptionofthesurfactantattheinterfaceresultssurfactant-freecondition.Therefore,theformationprocessofpolymer1026https://dx.doi.org/10.1021/acs.langmuir.0c02487Langmuir2021,37,1025−1036

2Langmuirpubs.acs.org/LangmuirArticleliquidwassuppliedattheflowrateof150mL/husingasyringepump(SP102HSM,FanavaranNano-MeghyasCo.)toa14Gneedle,whoseinnerandouterdiameterswere1.8and2mm,respectively.Tominimizetheeffectsofambientairflowsontheprocess,theneedlewassetupinsideandontopofacubicPlexiglasshieldperpendiculartotheground.Theimagesofdropevolutionwerecapturedbyahigh-speeddigitalcamera(X-PRI,AOSTechnologiesAGCo.),andthegeometricalparametersofdropsweremeasuredbyanalyzingtheobtainedimagesinMATLAB.Inaddition,alltestswererepeatedatleastsixtimestoestablishreproducibility,andtheaverageofmeasuredvaluesisreportedinthefollowingsection.Inaddition,weconsideredtherepeatabilityofourfindingsbyobservingtheformationprocessof1%CMCsolution’sdropcontainingSDSattheconcentrationof1cmc,performed12times.Thedurationoftheprocessineachtestwasmeasured,andtheresultsareshowninFigure2.ThevariabilityofdatapointsinrelationtotheFigure1.Chemicalstructureof(a)carboxymethylcellulose([CHO(OH)(OCHCOO−Na+)])and(b)sodiumdodecyl673‑α2αNsulfate(CH3(CH2)11SO4Na).RinCMCmoleculescouldbeCH2COONaorH.Degreeofsubstitution(α)isdefinedastheaveragenumberofCH2COONagroupsperCMCmonomer,andNis9,42,43thedegreeofpolymerization.solutions’dropsintheabsenceofthesurfactantanditspresenceatconcentrationsof0.25,0.5,0.75,1,2,and3cmcisinvestigated.TodeterminethecriticalmicelleconcentrationsofSDSindistilledwateroftheCMC−watersolutions,theirinterfacialtensionatvariousSDSconcentrationsismeasuredbyFirstTenAngstrom200.Accordingtoourresults,thecriticalmicelleconcentration(cmc)ofSDSinwaterisequalto5.4mM.Also,thephysicalpropertiesofaqueousCMCsolutionsaregiveninTable1.TheseresultsshowthatthecmcvalueFigure2.Formationtimeofthe1%CMCsolution’sdropcontainingTable1.PhysicalPropertiesofCMC−WaterSolutionsthesurfactantatthecriticalconcentrationforrepeatedtests.interfacialtensionininterfacialmeanformationtimewasmeasuredusingthecoefficientofvariationthetensionatcriticalmicellesurfactant-criticalmicellegivenineq1,whereN,Ti,andT̅arethenumberoftests,formationdensityconcentrationfreestateconcentrationoftimeobtainedforeachtest,andtheaverageformationtime,fluid(kg/m3)(cmc)(mM)(mN/m)SDS(mN/m)respectively.Thevalueofthisstatisticaltoolisfoundtobe2.63%,CMC0.5%997.9664.328.1whichshowsthatwecouldbeassuredoftherepeatabilityoftheexperiments.CMC0.75%998.67.562.127.7CMC1%999.8106027.61N2∑()TTi−̅N−1i=1Cv=T̅(1)increasesasthecarboxymethylcelluloseconcentrationrises,which44accordswellwiththeliterature.Inamixtureofsurfactantandpolymerinwater,surfactantmoleculesinteractwithhydrophobic■RESULTSANDDISCUSSIONpartsofthepolymermoleculesandadsorbonthem.AftersaturationEffectofSDSontheRheologyofCMCSolutions.Theofpolymermolecules,theindependentmicellesinthesolutionbulkviscosityofthedropphaseaffectsthedropdeformationinthe20form.Therefore,asthenumberofpolymermoleculesinthevicinityofpinch-off.Ithasbeenstatedthatthesolutionsofsolutionrises,moresurfactantparticlesarerequiredtoadsorbonCMCandwaterhaveashear-thinning(pseudoplastic)them,leadingtoenhancementofthecriticalmicelleconcentration.property,whichincreasesonraisingtheCMCconcentra-Furthermore,thedensityofthesolutionsismeasuredwitha10,11tion.Tojustifythebehaviorofpolymersolutions’dropsinhydrometer.Accordingtotheobtainedresults,surfactantconcen-trationhasanegligibleeffectonthisparameter.Besides,asshowninthepresenceofasurfactant,theviscosityofCMCsolutionsTable1,thedifferencebetweenthedensitiesofCMCsolutionsiscontainingdifferentsurfactantconcentrationsinawiderangeinsignificant,whichsuggeststhattheinfluenceofdensityintheofshearrates(0.1≤γ̇≤10001/s)ismeasuredusingtheformationprocesscouldbeignoredwithagoodapproximation.rheometerPhysicaMCR301.Figure3illustratestheresultsSurfactant-freeaqueousCMCsolutionswereprepared48hbeforeregardingtheSDSconcentrationsof0,0.5,1,and3cmcforthetestsandwerehomogenizedonarollermixerfor12h.Afterward,aqueousCMCsolutions,accordingtowhichtheviscosityofSDSwasadded(ifneeded),andthesolutionswerehomogenizedsolutionsdecreasesastheappliedshearraterises.Also,itcansimilartowhatmentioned.Also,tominimizetheprobabilityofthebeseenthatatlowshearrates,theviscositydifferencebetweenbubbleexistenceinthesolutions,theywereputinthemotionlessstateforatleast24h.thesolutionswithdifferentamountsofsurfactantisgreaterTheexperimentalapparatusandprocedurearesimilartothosethanthatathighershearrates.ForallCMCsolutions,thedescribedindetailinourpreviouspaper.41Alldropformationtestssurfactantadditiontoasolutioncausedtheviscositytowereperformedinambientairatthetemperatureof25±0.5°C.Theincreaseconsiderably.However,astheshearraterises,the1027https://dx.doi.org/10.1021/acs.langmuir.0c02487Langmuir2021,37,1025−1036

3Langmuirpubs.acs.org/LangmuirArticleFigure3.Variationwithshearrateoftheviscosityof(a)0.5%,(b)0.75%,and(c)1%aqueousCMCsolutionsatSDSconcentrationsof0,0.5,1,and3cmc.Figure4.(a)Zero-shearviscosity(μ0)ofthesolutionsof0.5,0.75,and1%CMCandwateratSDSconcentrationsbetween0and3cmc.(b)Variationoftheflowbehaviorindex(n)asafunctionofSDSconcentrationforCMCandwatersolutions(black,blue,andredsymbolsarerelatedtothesolutionsof0.5,0.75,and1%CMCandwater,respectively).(c)Schematicrepresentationoftheinteractionofsurfactantandpolymermolecules,astheSDSconcentrationincreases.SDSparticlesinteractwithhydrophobicportionsofpolymermoleculesandcausetheexpansionofmolecularstructuresandincreasetheliquidviscosity.AthigherSDSconcentrations,polymermoleculesseparatefromeachotherduetotheexistenceofonemicelleforeachhydrophobe,andtheviscositydecreases.viscosityvalueofsurfactant-ladensolutionsbecomesquiteμ0μ()γ̇=21/2−nclosetothatofsurfactant-freesolutions.(1+())kγ̇(2)ThedataobtainedforviscosityintermsoftheshearrateisThevariationsofμ0andnwithsurfactantconcentrationfor45fittedtothethree-parametermodelofCarreau,asgivenineqCMCsolutionsareshowninFigure4a,b,respectively.Ascan2,whereμistheviscosity,μ0isthezero-shearviscosity,kisthebeseen,onincreasingtheSDSconcentration,thezero-shearviscosityofsolutionsincreasesbelow1cmcandshowsaconsistencyindex,γ̇istheshearrate,andnistheflowbehaviordecreaseatconcentrationsbeyond1cmc.Also,theflowindex.behaviorindexforCMCandwatersolutionsdecreaseswith1028https://dx.doi.org/10.1021/acs.langmuir.0c02487Langmuir2021,37,1025−1036

4Langmuirpubs.acs.org/LangmuirArticleFigure5.Nondimensionalized(a)droplengthand(b)minimumneckthicknessofthe0.75%CMCsolution’sdropatsurfactant(SDS)concentrationsof0,0.5,1,2,and3cmcasafunctionofthetimeremainingtobreakup.Theimagesaboveandbelowthedatapointsinfigure(a)refertosurfactantconcentrationsof0and2cmc,respectively.Onthecontrary,infigure(b),theimagesbelowthepointsarerelatedtothesurfactantconcentrationof2cmc,andtheimagesabovethepointsrefertothesurfactant-freestate.theriseofsurfactantconcentrationupto1cmc(exceptforthesurfactantaggregatesonsolutions’viscosity.Theseionssolutionof0.5CMC,inwhichcaseitssurfactantconcentrationcouldscreentheelectrostaticforcesbetweenSDSandCMCrisesfrom0.5to0.75cmc)andreachesaminimumatthismolecules,whichcausetheexpansionofmolecularstructuresconcentration.Theobservedtrendforμandncanbeand,consequently,reducetheviscosity.53,54Besides,Na+ions0explainedbyelectrostaticandhydrophobicinteractioncouldalsoadsorbontothemixedsurfactantmicelles’interfacebetweensurfactantandpolymermolecules,asshowninFigureandreducetherepulsiveforcesbetweensurfactants’negatively4c,whichschematicallyillustratesthepolymer−surfactantchargedheadgroups.Thisphenomenonstabilizessurfactantinteractioncausedbymolecules’hydrophobicbehavior.Asmicellesandmolecularstructuresandraisestheliquid44,55mentionedpreviously,CMCmoleculeshavehydrophobicviscosity.AccordingtoFigure4a,thementionedfactorispartsthatinteractwiththoseofnearbymoleculesandformdeterminativeatconcentrationslowerthan1cmcandclosetomolecularstructures.Also,asthesemoleculesaredissolvedinthisvalue.Asthesurfactantamountexceeds1cmc,freewater,Na+ionsseparatefromCMCmoleculesanddisperseinsurfactantmicellesareformedinthesolutionbulk.Sincethesefluidbulk.Consequently,therewillberepulsiveforcesbetweenmicelles’electrostaticchargeisnegative,repulsiveforcesnegativelychargedpolymermoleculesthatopposetheirbetweenthemcontributetothecontractionofthemolecularinteraction.Nonetheless,hydrophobiceffectsareabletostructureandcoulddecreasetheviscosityatconcentrations56−58overcometheelectrostaticrepulsionandcontributetotheabove1cmc.creationofmolecularnetworks.SDSparticles,similartoCMC,Inaddition,itcanbeseenfromFigure4bthat,withthearenegativelychargedandreleaseNa+ionsupongettingincrementofthesurfactantconcentration,theshear-thinningdissolvedinwater.Ontheotherhand,surfactantstendtobehaviorofaparticularCMCsolutionincreasesandshowsaminimizetheircontactwithwatermoleculesduetotheeffectsdecreaseastheconcentrationexceeds1cmc.Theshear-oftheirhydrophobicheadgroups.Therefore,itcouldbestatedthinningbehaviorofthesolutionscouldbeascribedtothe21thatbyaddingsurfactantstothesolution,theyareattractedbydisintegrationofmolecularnetworksundershearstress.Itishydrophobicpartsofpolymerchains,whereaselectrostaticconspicuousthattheseparationofmoleculesofthemoreforcesresistpolymer−surfactantinteraction.Asthesurfactantcomplexnetworksresultsinagreaterreductionoftheviscosityconcentrationexceedsthecriticalassociationconcentrationandalowerflowbehaviorindex,whichisevidentinFigure4b.(CAC),hydrophobiceffectsarestrongenoughtooverweighAlso,accordingtoFigure4a,thevariationofμ0for0.5%CMC46repulsiveforces,andSDSparticlesinteractwiththesolutionislessthanthatfor0.75and1%CMCsolutions,hydrophobicpartsofCMCmoleculesandadsorbonthem,indicatingthatthesizeandcomplexityofmixedaggregates47whichresultsintheexpansionofmolecularnetworks.Sincereducesignificantlyasthepolymerconcentrationdecreases.thesenetworksarerodlikestructures,theyinterconnectwithAlso,electrostaticeffectsandthenumberofNa+ionscouldbe48−50nearbymolecularaggregates,whichresultsintheotherreasonsfortheobservedtrend.50−52enhancementofsolutionviscosity.WithafurtherincreaseInfluencesofPolymer−SurfactantInteractionontheinthesurfactantconcentrationbelowcmc,micellestructuresDropFormationProcess.OurobservationsshowtheformontheCMCmolecules’backbone.Accordingly,theconsiderableeffectofsurfactantadditiononthedropsolution’sviscosityrisesandatacertainsurfactantconcen-elongationandthinningprocess.Figure5a,bdemonstrates53tration,whichislowerthancmc,reachesitsmaximumvalue.theevolutionofthenondimensionalizeddroplength(L/d)Athigherconcentrations,thereisonemicelleforeachandtheminimumneckthickness(hmin/d)intimeforthe21hydrophobicgroupofpolymermolecules.Asaresult,thesolutionof0.75%CMCattheSDSconcentrationsof0,0.5,1,polymerintermolecularbondsarelost(Figure4c)andthe2,and3cmc.tandt0denotethetimeelapsedfromtheliquidviscosityreduces.WeshouldalsoconsidertheinfluencesmomentatwhichthedropbeginstoformandthedetachmentofelectrostaticforcesbetweenNa+ionsandpolymer−time,respectively.AscanbeseenfromFigure5a,thedrop1029https://dx.doi.org/10.1021/acs.langmuir.0c02487Langmuir2021,37,1025−1036

5Langmuirpubs.acs.org/LangmuirArticlelengthincreasedslightlyfromthebeginningoftheprocess,andtheshearrateappliedtothefluidpassingalongtheneckatacertainpoint,whichisafewmomentsaftertheappearanceincreasesduetotheriseintheflowrate,whichleadstoaoftheneck,itrosesharply.Betweenthementionedmomentreductionintheliquidviscosity.Basedonthedataillustratedandtheseparationinstant,thedroplengthincreasesoninFigure4b,withanincreaseinthesurfactantconcentrationincreasingthesurfactantconcentrationupto2cmcandshowsbelow1cmc,theshear-thinningpropertyrises,which30,31adecreasewiththeincrementoftheconcentrationfrom2to3expeditestheneckruptureandreducesthedroplength.cmc.Theoppositeofthistrendisobservedfortheneck-Byfurtherincrementofthesurfactantamount,thethinningrate.Figure5bshowsthatataspecificmomentpseudoplasticityofthesolutionsdecreasesandcausestheremainingtobreakup,theneckthicknessdecreaseswiththedroptohavemoretimetoelongate.AccordingtotheenhancementoftheSDSconcentrationto2cmcandthenaforementionedexplanationsandFigure5a,b,thezero-shearincreases.Thisphenomenoncanbejustifiedbyconsideringviscosityandthereductionofinterfacialtensionplayakeyroletheinfluencesofdifferentforcesondropdeformation.Duringindeterminingthethinningkineticsanddroplengthwhenthetheneckingprocess,acurvatureisdevelopedattheneck’ssurfactantconcentrationisbetween0and1cmc.Byincreasinginterfaceprofile,whichcausesthecapillarypressuretobetheconcentrationfrom1to2cmc,despitethereductionofcreated,whichhasadirectrelationshipwiththeinterfacialzero-shearviscosity,otherfactorssuchasthedecreaseintension,accordingtothefollowingequationpseudoplasticityandinterfacialtensionhavedominanteffectsσondropdeformation.However,theincrementofthesurfactantp=amountfrom2to3cmccausestheinfluenceofzero-shearcrc(3)viscositytoovercomeotherfactors.Inaddition,Marangoniwherepcisthecapillarypressure,σistheinterfacialtension,stressescouldalsobeconsideredasaneffectivefactorindropandrcisthecurvatureradius.Thecapillarypressuremakesthedeformationnearthepinch-off,asmentionedabove.liquidtobeevacuatedfromtheneckregion,thereforereducingVariationwithSDSconcentrationofthedetachmentlengththecurvatureradius.ItisevidentthatthepresenceofSDSofCMCsolutions’drop(Ld)isshowninFigure6.Ldismoleculesreducestheinterfacialtension,whichcausesthe29capillarypressuretodecrease.Moreover,becauseofthesuddenincrementoftheneck’sinterfaceareaandconvectiveflowsinthedropbulk,thesurfactantdensityattheinterfaceis59lowercomparedtotheequilibriumstate.Therefore,providedthattheadsorptionofSDSparticlesontotheinterfaceisslowcomparedtothedropformationprocess,theinterfacialtension36,60ishigherthantheequilibriumvalueandincreasesasthe32,34pinch-offapproaches.Hence,theinterfacialtensionalongtheneckmightdecreasebyincreasingtheSDSconcentration,evenabovethecmcvalue,whichresultsintheslowerneckingprocessandenhancementofthedroplength.Basedonpreviousinvestigations,insomecases,thesurfactantandpolymermolecule’sdepletionfromtheneck/37threadinterfacegeneratesaforceimbalance,whichcouldslowdowntheneckingprocess.Asmentionedintheaboveparagraph,theincrementoftheinterfaceareaandfluidflowFigure6.Nondimensionalizeddropdetachmentlengthoftheneartheinterfacecausethedepletionofsurfactantandaqueoussolutionsof0.5,0.75,and1%CMCatsurfactant(SDS)polymermolecules.Duetothefactthatthevariationsintimeconcentrationsbetween0and3cmc.oftheinterfaceareaalongtheneckarenotuniform,andthevelocityoffluidflowindifferentlocationsisnotconstant,adensitygradientofsurfactantandpolymermoleculesiscreatedmeasuredwithinamaximumof1msremainingtopinch-off.attheinterface,whichresultsintheinterfacialtensiongradientAsstatedforFigure5a,b,inaslowerthinningprocess,thedropandMarangoniflows.Thisphenomenoncouldalsocausetheismorelikelytoelongate,andtherefore,itsdetachmentlengthdroplengthandpinch-offtimetoincrease.However,itshouldincreases.AccordingtoFigure6,thesametrendisobservedforbementionedthattheeffectsofsurfactantandpolymerthevariationofLdintermsofSDSconcentrationfortheconcentrationonthestrengthofMarangonistressesarenotsolutionsof0.75and1%.Giventhatthezero-shearviscositypreciselyknownhere,andmorestudiesarerequiredtoreachaandshear-thinningbehaviorofthesolutionsof0.75and1%conclusiveresult.CMCvarywithSDSadditioninthesameway(Figure4a,b),Ontheotherhand,theliquidviscosityopposestheneckthedescriptionsprovidedforFigure5a,barealsoapplicableto22,25,27rupturebydampeningthecapillarypressure.Accordingthe1%CMCsolution’sdrop.However,forthesolutionoftoFigure4a,theincrementofthesurfactantconcentrationup0.5%CMC,raisingtheSDSamountintherangebetween0toacriticalvalueresultsinahigherzero-shearviscosityandand3cmcresultsintheincrementofdroplimitinglength.Thereducesthethinningrate.However,atconcentrationsabove1datashowninFigure4aindicatesthatthevariationofzero-cmc,theadditionofasurfactantcausesthezero-shearviscosityshearviscosityofthe0.5%CMCismuchlessthanthatofthetodecrease,whichleadstoareductioninthethinningrateand0.75and1%CMCsolutions.Hence,itcouldbestatedthatdropelongation.Theotherfactorthataffectsdropdeformationreducingthezero-shearviscosityduetotheincrementofistheshear-thinningbehaviorofthepolymer−surfactantsurfactantconcentrationfrom2to3cmcdoesnotovercomesolutions.Inthethinningstage,thecross-sectionalareaofthetheimpactofothereffectivefactorsincludingtheinterfacialneckdecreasesasthedetachmentmomentnears.Asaresult,tensionandpseudoplasticity,andconsequently,thedetach-1030https://dx.doi.org/10.1021/acs.langmuir.0c02487Langmuir2021,37,1025−1036

6Langmuirpubs.acs.org/LangmuirArticlementlengthshowsanincreasingtrendintheconcentrationrangebetween0and3cmc.Inaddition,itisevidentfromFigure6thatthedetachmentlengthofthe0.5%CMCsolution’sdropincreasesslightlywithSDSconcentration.Incontrast,variationsinthelengthof0.75and1%CMCsolutions’dropareconsiderable,whichcouldalsobeascribedtothechangeinzero-shearviscosityofthesolutionsonaddingthesurfactant,asexplainedbefore.Apartfromtheinfluencesofsurfactants,CMCconcentrationisafactorthataffectsthedropshapeafterthegenerationoftheneck.Figure6exhibitsthatataconstantsurfactantconcentration,limitingdroplengthshowsanincreasewithCMCconcentration.ThisaccordswellwithintuitionbecausethenumberofCMCmoleculesinthesolutionnotonlyleadstolargermolecularnetworksbutalsoincreasestheirnumber,whichincreasestheviscosityandalsotheshear-thinningproperty(Figure4a,b).Astheviscousforcesareenlarged,Figure8.Dropformationtimeasafunctionofsurfactant(SDS)capillarypressureisdampedoutfurther,whichalsoleadstoconcentration.slowerneck-thinning.InFigure7,theevolutionintimeoftheDuringthedropevolution,severalexternalforcesareappliedtothedropconnectedtotheneedle,andtheybalanceuntilthe61endofthefirststage.Asthesecondstagebegins,theforcebalanceislost,andthedropneckforms.Ingeneral,themainexternalforcesappliedtoaformingdropareinterfacialtensionanddrag,whichopposethedropbreakup,andthegravityaswellaskineticforcesthattendtoseparatethedropfromtheneedle.Tobettercomprehendandcomparethemagnitudeofthementionedforces,theirvalues(intermsofN)arecalculatedapproximatelyasasampleforthedropof0.75%CMCwithoutasurfactantat400msremainingtobreakup61(Figure9)usingeqs4−7,whereρdisthedensityofthedropFigure7.VariationsintimeofthedimensionlessminimumneckthicknessofaqueousCMCsolutions’dropatthesurfactant(SDS)concentrationof1cmc.dimensionlessminimumneckthicknessofCMCsolutions’dropisshownforjusttheSDSconcentrationof1cmc.Apparently,itcouldbeobservedthatatacertainmomentremainingtobreakup,theminimumneckthicknessdecreasesastheCMCconcentrationrises.Therefore,withintheconstanttimeduration,thedropneckthicknessnarrowslesser,indicatingthattheprobabilityofdropelongationincreaseswiththeincrementoftheCMCconcentration.Moreover,itcouldbededucedfromFigures5−7thatastheneck-thinningprocessbecomesslower,thedropdetachmentlengthincreases.TheformationtimeoftheaqueousCMCsolutions’dropasFigure9.Shapeof0.75%CMCsolution’sdropintheabsenceofaafunctionofSDSconcentrationispresentedinFigure8.Thesurfactantat400msremainingtobreakup.Thedirectionoftheforcesincrementofthesurfactantamountresultsinadecreaseintheispresentedinthepicture.formationtimeoftheCMCsolutions’drop.Moreover,theobtainedresultsshowthatthedurationoftheprocesshasnodependenceontheCMCconcentration.Forexplainingthisphase,gisgravitationalacceleration,Visthedropvolume,62behavior,wecanconsidertheformationprocessintwowhichiscalculatedbytheimageprocessingmethod,uisthe41stages,whichleadstoabetterunderstandingoftheeffectsofvelocityoffluidexitingtheneedle,Qistheflowrateofthedifferentforcesondropevolution.Thefirststageisfromthedropphase,σistheinterfacialtension,θistheanglebetweenbeginningoftheprocesstotheneckformationinstant,andthethedropsurfaceandtheneedle,ristheradiusoftheformingsecondstagebeginsfromtheendofthefirststageandlastsdrop,udropisthegrowingvelocityofthedrop,whichisuntilthepinch-offmoment.measuredusingthedatapresentedinFigure5a,μcisthe1031https://dx.doi.org/10.1021/acs.langmuir.0c02487Langmuir2021,37,1025−1036

7Langmuirpubs.acs.org/LangmuirArticleFigure10.Instantaneousshapeoftheformingdropsof(a)0.5%CMCsolutionwithoutsurfactant,(b)0.5%CMCsolutioncontainingasurfactantattheconcentrationof1cmc,(c)0.75%CMCsolutionwithoutsurfactant,(d)0.75%CMCsolutioncontainingasurfactantattheconcentrationof1cmc,(e)1%CMCsolutionwithoutsurfactant,and(f)1%CMCsolutioncontainingasurfactantattheconcentrationof1cmc.Theremainingtimetodetachmentmomentispresentedatthebottomofeachimage.viscosityofair,andμdisthezero-shearviscosityofthedropForabetterdemonstrationofthisconcept,theevolutionofphase.CMCsolutions’drop,inconditionsinwhichtheyarefreeofsurfactantandsurfactant-ladenatthecriticalconcentration,is−4gravitationalforceFgg=∼ρdV10(4)depictedinFigure10.Basedonourcalculations,thefirststage’sdurationdecreasedbyapproximately40%forthreekineticforceFu=∼ρdQ10−7CMCsolutionswhenthesurfactantisadded.However,theK(5)surfactantincreasedthedurationofthesecondstagebynearly−425%.Basedontheseobservations,itcouldbeclaimedthatinterfacialtensionforceFσ=·∼πσdsin()θ10(6)addingthesurfactanthasoppositeeffectsintwostages.Nonetheless,thetotalformationtimeshowsadecreaseversusijjμμcd+yzz−8thesurfactantconcentration,whichsuggeststhatthedragforceFuD=4rπμcdropjjjzzz∼10surfactant’sinfluencesinthefirststagedeterminethevariationsk0.66μμcd+{(7)ofthedropformationtime.TheresultsshowthatthemagnitudeofinterfacialtensionMoreover,Figure10showsthatatequalsurfactantandgravitationalforcesisabout3or4ordershigherthanconcentration,theincrementoftheCMCconcentrationraisedothers,indicatingthattheeffectsofdragandkineticforcesonthesecondstage’sduration,whilethevariationsofthefirstdropdeformationcanbeneglected.Therefore,withagoodstage’stimeareinsignificant(comparedtothedurationofthatapproximation,thefirststage’sdurationcanbeconsideredtostage).Althoughinthesurfactant-freestate(Figure10a,c,e),beaffectedjustbyinterfacialtensionandgravitationalforces.thetotalformationtimeincreaseswiththeincrementoftheConsequently,itcanbestatedthattheincrementoftheSDSCMCconcentration,whichisinaccordancewiththe31concentrationleadstoalowerinterfacialtension,whichcausesliterature,itdoesnotshowanyparticulartrendinthethetimerequiredtostrikeabalancebetweengravityandthesurfactant-ladenstate(Figures8and10).Thiscouldbemaximuminterfacialtensionforcestodecrease.Inthesecondexplainedbyconsideringthattheinterfacialtensionofthestage,asdiscussedpreviously,internalforcesaredecisivesolutionsisalmostconstantatthesamesurfactantconcen-factorsindropdeformation.ThecapillarypressurereducesthetrationastheCMCpercentageischanged(Table1).Hence,neckthicknessandcausesthedroptodetach,whereasthethedurationofthefirststagevariesslightlywithCMCviscousforcesresistthecapillarypressureandtendtoincreaseconcentration,whichcouldbeattributedtothesmalltheseparationtime.Also,thereductionoftheinterfacialdifferencebetweenthephysicalpropertiesofsolutionsortensionforce,whichdecreasesthecapillarypressure(eq2),experimentaluncertainties.Furthermore,enhancementoftheandthecreationofMarangonistressesattheneckinterfacedurationofthesecondstagewithanincrementoftheCMCleadtoanincreaseinthesecondstageduration.amountisaresultofviscosityincrementduetothelarger1032https://dx.doi.org/10.1021/acs.langmuir.0c02487Langmuir2021,37,1025−1036

8Langmuirpubs.acs.org/LangmuirArticlemolecularnetworksandweakereffectsofcapillarypressure.Inmosttestscarriedoutinthiswork,satellitedropsareBecausethefirststageismuchlongerthanthesecondstage,itsformedaftertheformationoftheprimarydrop.Accordingtoroleindeterminingthetotalformationtimehasbeenourobservations,thesatellitedropsizeissignificantlyaffecteddominant.bySDSconcentration.InFigure12,theimagesofsatelliteAccordingtoFigure10b,d,f,thethreadshapeattheinstancessoclosetotherupturechangesconsiderablybyaddingthesurfactanttothedropphasefluid.Itcouldbeseenthatinthesurfactant-freestate(Figure10a,c,e),thethreadconformationatthemomentofpinch-off(t0−t=0)isroughlycylindrical.Ontheotherhand,inthepresenceofasurfactant(Figure10b,d,f),thethreadinterfaceisunevensothatanamountoffluidisshowntobetrappedinaparticularsectionalongthethread.ThiscouldbejustifiedbyconsideringtheinfluencesofMarangonistressesonthedeformationofthedropinterface.AsshowninFigure11,thedropneckstretchesFigure12.Imagesofsatellitedropsintheformationprocessof0.5CMCsolutions’drop(a)withoutSDSandinitspresenceatconcentrationsof(b)0.5,(c)1,and(d)3cmc.dropsrelatedto0.5%CMCsolutioninthesurfactant-freestateandinthepresenceofasurfactantatconcentrationsof0.5,1,and3cmcarepresentedasthesamples.Itcouldbeseenthatintheprocesswithoutasurfactant(Figure12a),asmallsatellitedropisformed.However,thepresenceofasurfactantFigure11.Sketchofthedistributionofsurfactantmoleculesatthe(Figure12b−d)causeditssizetoincreasenoticeably.Figureinterfaceofthedropneckandconsequentchangeinitsshape.The12indicatesthatwiththeincrementofSDSconcentrationupsurfactantdensitygradientresultsinthegenerationofMarangonito1cmc,thesatellitedropsizeincreased.Nonetheless,astheflowstowardtheregionswithhighinterfacialtensionandconcentrationrisesto3cmc(Figure12d),thesatellitedropisaccumulationoffluidinaparticularsectionoftheneck.Polymermoleculesarenotdepicted.smallerthanthatoftheconcentrationsof0.5and1cmc.Astheliquidthreadstretchesovertime,twocurvaturesdeveloponitsinterfaceneartheprimarydropandliquidconependantfromtheneedle.Asaresult,capillarypressureiscreatedintheseneartherupturemoment,whichcausesthesurfactantregions,whichcausesthethreadtorupture.Duetothefactmolecules’concentrationtodecreaseinthemiddleportionthattheradiusofcurvatureatthebottomzoneissmalleroftheneck(thesurfactantdistributionalongtheneckinterfacecomparedtothatneartheneedle,thethreadfirstbreaksupcouldalsobedifferentdependingonvariousexperimentalfromthelowerpart.Afterward,threadpinch-offoccursintheconditions).Therefore,Marangoniflowsaregeneratedfromupperpart,whichresultsinthecreationofsatellitedrop.regionswithlowinterfacialtensiontothosewhereinterfacialTherefore,thelengthoftheliquidthreadatthepinch-offtensionishigh.Thisphenomenoncausesthefluidtobemomentisafactorthataffectsthesizeofthesatellitedrop.Onaccumulatedinasectionoftheneck,asillustratedinFigure11.theotherhand,MarangoniflowscouldalsoenlargethesatelliteAccordingtoFigure10,atCMCconcentrationsof0.5anddrops,dependingontheirdirectionandstrength.Asillustrated0.75%,aconcentratedvolumeoffluidisseenatthemiddleinFigure11,anamountoffluidcollectedinthemiddlepartofpartofthethreadofthesurfactant-ladendrop,whichobviouslytheliquidthreadcouldformasatellitedropafterthepinch-off.showsthatsurfactantdepletionfromthisregionwasmoreHence,itcouldbeclaimedthatMarangoniflowsenhancethesignificantcomparedtotheupperandlowerpartsoftheprobabilityofsatellitedropformationandtheirsize.Basedonthread.However,attheCMCconcentrationof1%,theFigure12,theincrementinsatellitedropsizeduetothethicknessofthethreadfromtheregionneartheneedletoitspresenceofasurfactantcouldbeascribedtothecreationofmiddlepartisnoticeablygreaterthanotherregionsoftheMarangoniflowsonthethreadsurfaceandincrementofthethread,indicatingthatCMCconcentrationhasinfluencedthelimitingthreadlength(Figure10a,b).Inaddition,itseemsthatSDSdensitydistributionalongtheinterfaceand,therefore,thewhentheSDSconcentrationis3cmc,theMarangonistressesdirectionofMarangoniflows.Inaddition,giventhatCMCattheinterfaceofthethreadareweakercomparedtothatmoleculesalsohaveahydrophobicproperty,itcouldbewhentheSDSconcentrationis0.5or1cmc,whichcausestheexpectedthattheyadsorbatthedropinterfacesimilartoSDSsatellitedropvolumetodecrease.molecules,andthedropdeformationcouldcausethegenerationofMarangonistresses.Nonetheless,Figure10■CONCLUSIONSillustratesthatintheabsenceofSDS,thethreadthicknessTherheologyoftheaqueousamphiphilicpolymersolutionsisdiffersslightlyalongit.Consequently,itcouldbededucedthatdramaticallyaffectedbytheformationofmolecularnetworkstheMarangonistressescausedbythedensitygradientofandtheelectrostaticforcesbetweenmoleculesandfreeNa+polymermoleculesarenotstrongenoughtoaffecttheionsinthesolutionbulk,whichcouldchangethebehaviorofa31conformationofthethread.formingdrop.Theadditionofasurfactanttoanaqueous1033https://dx.doi.org/10.1021/acs.langmuir.0c02487Langmuir2021,37,1025−1036

9Langmuirpubs.acs.org/LangmuirArticlepolymersolutioncausesthesurfactantmoleculestoadsorbon■AUTHORINFORMATIONthepolymermoleculesduetointeractingwiththeirhydro-CorrespondingAuthorphobicparts,whichexpandsthemolecularstructuresandBaharFiroozabadi−DepartmentofMechanicalEngineering,influencestheinterfacialtension,viscosity,andnon-NewtonianSharifUniversityofTechnology,Tehran009821,Iran;behaviorofthesolution.Inpreviouslyreportedstudies,ithasorcid.org/0000-0002-4774-0896;Phone:+9821beenshownthatthesementionedpropertiesdependon66165521;Email:firoozabadi@sharif.edu;Fax:021-variousfactors,includingthepolymerandsurfactant6600002121,53concentrations.Herein,weexperimentallystudiedtheinfluencesofpolymer−surfactantinteractiononthedropAuthorsformationprocess.ThevariationofdifferentparametersPeymanDastyar−DepartmentofMechanicalEngineering,pertinenttodropformation,suchasdroplength,minimumSharifUniversityofTechnology,Tehran009821,Iran;neckthickness,andtheformationtime,wasinvestigatedinorcid.org/0000-0002-1922-8545termsofthesurfactantandpolymerconcentration.MoloudSadatSalehi−DepartmentofMechanicalWedemonstratedthatthezero-shearviscosityandshear-Engineering,SharifUniversityofTechnology,Tehranthinningpropertyofthepolymersolutionsrisewithan009821,Iranincrementofthesodiumdodecylsulfate(SDS)concentrationHosseinAfshin−DepartmentofMechanicalEngineering,toacriticalvalue(cmc)anddecreaseathigherconcentrations.SharifUniversityofTechnology,Tehran009821,IranAsaresult,surfactantadditioninfluencesthedropCompletecontactinformationisavailableat:deformation,which,basedonourobservations,couldbehttps://pubs.acs.org/10.1021/acs.langmuir.0c02487differentdependingonthepolymerconcentration.TheforgoingresultsclearlyshowedthatatthecarboxymethylNotescellulose(CMC)concentrationof0.5%,theincrementoftheTheauthorsdeclarenocompetingfinancialinterest.SDSconcentrationgaverisetothedropdetachmentlength.However,athigherconcentrationsofCMC,thedetachment■ABBREVIATIONSlengthreachesamaximumattheconcentrationof2cmc,CMC,carboxymethylcellulose;cmc,criticalmicelleconcen-whichisduetothecompetitionbetweentheeffectivefactorsintration;SDS,sodiumdodecylsulfatetheneckingprocess,includingtheinterfacialtension,viscosity,andMarangonistresses.Also,atallSDSconcentrations■consideredinthispaper,thedropdetachmentlengthwasREFERENCES(1)Zhang,X.DynamicsofgrowthandbreakupofviscouspendantfoundtorisewiththeincrementofCMCconcentration,dropsintoair.J.ColloidInterfaceSci.1999,212,107−122.which,inthesituationwithoutasurfactant,accordswellwith(2)Lee,B.S.;Cho,H.J.;Lee,J.G.;Huh,N.;Choi,J.W.;Kang,I.S.31themeasurementsofSalehietal.Inaddition,ourresultsDropformationviabreakupofaliquidbridgeinanACelectricfield.suggestedthatthereisaninverserelationshipbetweentheJ.ColloidInterfaceSci.2006,302,294−307.droplengthandthethinningrateoftheneckbecauseasthe(3)Dinic,J.;Sharma,V.Computationalanalysisofself-similarminimumneckthicknessdecreases,thedrophasmoretimetocapillary-driventhinningandpinch-offdynamicsduringdrippingelongate.usingthevolume-of-fluidmethod.Phys.Fluids2019,31,No.021211.Besides,dropformationwasconsideredasatwo-stage(4)Kovalchuk,N.M.;Nowak,E.;Simmons,M.J.Kineticsofliquidprocess,anditwasshownthattheenhancementofthebridgesandformationofsatellitedroplets:Differencebetweenmicellarandbi-layerformingsolutions.ColloidsSurf.,A2017,521,surfactantconcentrationsignificantlyreducesthefirststage’s193−203.timeandincreasesthedurationofthesecondstage.(5)Liu,H.;Altan,M.C.Scienceandengineeringofdroplets:Nonetheless,forallaqueousCMCsolutions,theincrementfundamentalsandapplications.Appl.Mech.Rev.2002,55,B16−B17.oftheSDSamountreducedthetotalformationtime.Onthe(6)Hoath,S.D.FundamentalsofInkjetPrinting:TheScienceofInkjetotherhand,noparticulartrendwasobservedforformationandDroplets;JohnWiley&Sons,2016.timeonincreasingtheCMCconcentration,whereasit(7)Roche,M.;Aytouna,M.;Bonn,D.;Kellay,H.Effectofsurfacéincreasedthesecondstage’sduration.Theimagesofdroptensionvariationsonthepinch-offbehaviorofsmallfluiddropsintheshapenearthepinch-offmomentalsoshowedthatthethreadpresenceofsurfactants.Phys.Rev.Lett.2009,103,No.264501.thicknessbecomesnonuniformalongitduetothepresenceof(8)Toğrul,H.;Arslan,N.ProductionofcarboxymethylcellulosefromsugarbeetpulpcelluloseandrheologicalbehaviourofSDS.Thisphenomenonwasexplainedbyconsideringthecarboxymethylcellulose.Carbohydr.Polym.2003,54,73−82.effectsofMarangonistressesondropdeformation,whichalso(9)Lopez,C.G.;Colby,R.H.;Cabral,J.T.Electrostaticandsignificantlyincreasesthesizeofthesatellitedrops.TheimageshydrophobicinteractionsinNaCMCaqueoussolutions:Effectofofsatellitedropsassociatedwiththesolutionof0.5%CMCdegreeofsubstitution.Macromolecules2018,51,3165−3175.werepresented,anditwasrevealedthatthesizeofsatellite(10)Yang,X.H.;Zhu,W.L.ViscositypropertiesofsodiumdropincreaseswhentheSDSconcentrationrisesto1cmc.carboxymethylcellulosesolutions.Cellulose2007,14,409−417.However,withthefurtherincrementoftheSDSconcentration(11)Cancela,M.A.;Alvarez,E.;Maceiras,R.Effectsoftemperatureto3cmc,thesatellitedropsizedecreases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