NanofluidsandMass Transfer
Editedby
MohammadRezaRahimpour DepartmentofChemicalEngineering, ShirazUniversity,Shiraz,Iran
MohammadAminMakarem DepartmentofChemicalEngineering, ShirazUniversity,Shiraz,Iran
MohammadRezaKiani
FoumanFacultyofEngineering,CollegeofEngineering, UniversityofTehran,Fouman,Iran
MohammadAminSedghamiz DepartmentofChemicalEngineering, ShirazUniversity,Shiraz,Iran
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1.1 Masstransferinnanofluids........................................................................................3
1.1.1Massdiffusionofnanofluids...........................................................................6
1.1.2Convectivemasstransferofnanofluids..........................................................7
1.2
1.2.4Erosionandcorrosionoftheequipment.......................................................12
1.2.5Thermalperformanceinturbulentflowcondition........................................12
1.2.6Necessityofdefiningnewmechanisms........................................................13
1.2.7Challengesintwo-phaseheattransportapplications....................................13 1.3
1.3.2CO2
1.3.3Increasingthelifeofelectronicdevices........................................................14
1.3.4PerformanceimprovementofPV/Tsystems.................................................15
1.3.5Moreefficientcoolingofautomobileengines..............................................15
1.3.6Moreefficientheatingofbuildings...............................................................15
1.3.7Moreefficientgrinding..................................................................................15
2.1
2.2.1Single-stepmethod.........................................................................................22
2.2.2Two-stepmethod............................................................................................23
2.3
2.4
2.4.8Thermogravimetryanalysis.........................................................................33 2.4.9Inductivelycoupledplasma.........................................................................33
4.2.5Footprintofnanofluidsinthegas-liquidinteraction..................................106
4.2.6Hydrodynamicsofnanofluidsfrommass-transferviewpoint.....................107
4.3 Conclusion..............................................................................................................108
CHAPTER5Effectofnanofluidsinsolubilityenhancement 115
MaryamMeshksar,MohammadAminMakarem,Zohreh-SadatHosseini andMohammadRezaRahimpour
5.1 Introduction............................................................................................................115
5.2 Thegassolubilityenhancementmechanisms........................................................117
5.2.1Thegrazingorshuttleeffect........................................................................117
5.2.2Thehydrodynamicorboundarymixingeffect............................................118
5.2.3Theinhibitioneffectofbubblecoalescence...............................................119
5.3 Gasabsorptionenhancementbynanofluids..........................................................120
5.3.1Thenanofluidstypeeffect...........................................................................120
5.3.2Thenanoparticlesizeeffect.........................................................................122
5.3.3Thenanoparticleconcentrationeffect.........................................................123
5.3.4Thesurfactantadditioneffect......................................................................124
5.3.5ThepHeffect...............................................................................................125
5.3.6Thetemperatureeffect.................................................................................125
5.3.7Thepressureeffect.......................................................................................126
5.4 Applicationofnanofluidsforliquidsolventsolubility.........................................127
5.5 Limitationsanddrawbacksofnanofluidsusages..................................................127
5.6 Conclusionsandfuturetrends................................................................................128
CHAPTER6Heatandmasstransfercharacteristicsofmagneticnanofluids ....
GabrielaHuminic,AngelHuminicandAlinaAdrianaMinea
6.1 Introduction............................................................................................................133
6.2 Heattransfercharacteristics...................................................................................134
6.2.1Theory..........................................................................................................134
6.2.2Naturalconvectionsubjecttononuniformmagneticfield..........................134
6.2.3Naturalconvectionsubjecttouniformmagneticfield................................150
6.3 Masstransfercharacteristics..................................................................................173
6.4 Conclusionsandfutureprospectsandtrends........................................................181
CHAPTER7Conjugateheatandmasstransferinnanofluids .............................
AlinaAdrianaMinea,AngelHuminicandGabrielaHuminic
7.1 Introduction............................................................................................................189
7.2 Mechanismsofheattransferinnanofluids............................................................191
7.3 Mechanismsofmasstransferinnanofluids..........................................................191
7.4 Boilingheatandmasstransfer...............................................................................198 7.4.1Poolboiling..................................................................................................200 7.4.2Flowboiling.................................................................................................203
7.5 Techniquesforenhancementofthenanofluidscriticalheatflux.........................206
7.6 Conclusionandfutureworkandtrends.................................................................207 Nomenclature..........................................................................................................208
CHAPTER8Bionanofluidsandmasstransfercharacteristics ............................ 217 BaishaliKanjilal,NourouddinSharifi,AramehMasoumiand ImanNoshadi
8.1 Introduction............................................................................................................217
8.2 Presentstatusofresearchinnanofluids.................................................................218
8.3 Preparationandstabilizationofnanofluids...........................................................218
8.3.1Preparationofnanofluidsandbionanofluids...............................................218
8.3.2Stabilizationofnanofluids...........................................................................221
8.4 Applicationsofnanofluidsandbionanofluids.......................................................221
8.5 Typesofmasstransferprocessesinnanofluids....................................................224
8.5.1Bubbletypeabsorption................................................................................224
8.5.2Fallingfilmabsorption.................................................................................225
8.5.3Membraneabsorption..................................................................................225
8.5.4Masstransferwithphasechange.................................................................225
8.5.5Three-phaseairliftreactor............................................................................225
8.5.6Agitatedabsorptionreactor..........................................................................225
8.6 Mechanismofmasstransferenhancementinnanofluidsandbionanofluids.......225
8.6.1Shuttleorgrazingeffect..............................................................................225
8.6.2HydrodynamicsintheGLlayer..................................................................225
8.6.3ChangesinGLinterface..............................................................................226
8.7 Analogyandequivalencebetweenheatandmasstransferinnanofluids: anexperimentalandmodelingapproach...............................................................227
8.8 Bioconvection.........................................................................................................228
8.9 Ageneralmodelofbioconvection.........................................................................229
8.9.1Casestudy1—three-dimensionalstagnationpointflowof bionanofluidwithvariabletransportproperties..........................................231
8.9.2Casestudy2—bioconvectionnanofluidslipflowpastawavy surfacewithapplicationsinnanobiofuelcells............................................233
8.9.3Casestudy3—stagnationpointflowwithtime-dependent bionanofluidpastasheet:richardsonextrapolationtechnique...................234
8.9.4Casestudy4—unsteadymagnetoconvectiveflowofbionanofluid withzeromassfluxboundarycondition.....................................................237
8.9.5Casestudy5—secondgradebioconvectivenanofluidflowwith buoyancyeffectandchemicalreaction.......................................................239
8.10 Conclusionandfutureoutlook...............................................................................240
PART2:Masstransfermodellingandsimulationofnanofluids
9.10
10.2.1Finiteelementmethodapplicationonnanofluidheatandmass transfer........................................................................................................276
10.2.2Finiteelementmethodsimulation.............................................................278
10.3 Controlvolumefiniteelementmethod..................................................................282
10.3.1Fundamentalequations..............................................................................282
10.3.2Modelingofnumericalmethod.................................................................284
10.3.3Discretizationequationofgeneraltransport.............................................285
10.4 LatticeBoltzmannmethod.....................................................................................287
10.4.1ThetransportmodelofLatticeBoltzmann...............................................289
10.4.2DynamicnanoparticleaggregationbylatticeBoltzmannmethod............291
10.5 Conclusion..............................................................................................................293
CHAPTER11CFDsimulationofnanofluidsflowdynamicsincluding masstransfer .................................................................................... 297 MohammadHatami,JiandongZhouandDengweiJing
11.1 Heatandmasstransferinnanofluids.....................................................................297
11.1.1Thermalconductivity.................................................................................297
11.1.2Nanoparticlesconcentration.......................................................................297
11.1.3Nanoparticlesize........................................................................................300
11.1.4Nanoparticleshape.....................................................................................300
11.1.5Nanoparticlethermalconductivityandbasefluid....................................301
11.2 CFDmodeling........................................................................................................303
11.2.1Single-phaseapproach...............................................................................303
11.2.2Two-phaseapproach..................................................................................306
11.2.3OtherCFDapproaches...............................................................................313
11.3 Conclusion..............................................................................................................317 References...............................................................................................................317
CHAPTER12Masstransferenhancementinliquid liquidextraction processbynanofluids 327 MortezeEsfandyariandAliHafizi
12.1 Introduction............................................................................................................327
12.2 Masstransferinnanofluids....................................................................................329
12.2.1Molecularpenetrationinnanofluids..........................................................329
12.2.2Calculationofmasstransfercoefficient....................................................330
12.3 Masstransferofliquid liquidextraction.............................................................331
12.4 Nanoparticlesinliquid
12.4.1SiO2
12.4.2ZnO,ZrO2,andTiO2
12.4.3Al2O3
12.4.4MgOnanoparticles.....................................................................................338
12.4.5Fe3O4
12.5
PART3:Applicationsofnanofluidsasmasstransferenhancers
CHAPTER13Increasingmasstransferinabsorptionandregeneration processesviananofluids ..................................................................
13.1
13.2
MeisamAnsarpourandMasoudMofarahi
CHAPTER14Masstransferbasicsandmodelsofmembranes containingnanofluids
ColinA.Scholes 14.1
CHAPTER15Applicationsofmembraneswithnanofluidsandchallengeson industrialization ................................................................................ 385 ColinA.Scholes
15.1 Introductiontonanofluidsandmembranes...........................................................385
15.2 Nanofluidcharacteristics........................................................................................386
15.3 Membranecontactors.............................................................................................387
15.4 Membraneapplicationswithnanofluids................................................................389
15.4.1Liquid liquidextraction...........................................................................389
15.4.2Gas solventabsorption.............................................................................390
15.4.3Ultrafiltration/nanofiltration.......................................................................392
15.5 Membraneprocessindustrialdemonstrations........................................................393
15.6 Challengesformembranesprocesses....................................................................394
15.7 Conclusions............................................................................................................395 References...............................................................................................................395
CHAPTER16Enhancedcarbondioxidecapturebymembranecontactorsin presenceofnanofluids ..................................................................... 399 AdolfoIulianelliandKamranGhasemzadeh
16.1 Introduction............................................................................................................399
16.2 Membranecontactorstechnology..........................................................................400
16.3 Carbondioxideseparationbymembranecontactors............................................402
16.3.1Carbondioxideabsorptioninpresenceofsolidnanoparticles.................403
16.3.2Nanofluidshollowfibermembranes:modelingstudies............................403
16.3.3Modelingofcarbondioxideremovalinahollowfibermembrane contactor.....................................................................................................404
16.4 Conclusionandfutureoutlooks.............................................................................408 References...............................................................................................................409
CHAPTER17Masstransferimprovementinhydrateformationprocessesby nanofluids .......................................................................................... 413
FatemeEtebari,YasamanEnjavi,MohammadAminSedghamizand MohammadRezaRahimpour
17.1 Introduction............................................................................................................413
17.1.1Gashydratesformation..............................................................................414
17.1.2Thegashydrateformationprocess............................................................415
17.1.3Applicationofgashydrates.......................................................................416
17.2 Hydrateinhibitionversusthehydratepromotion..................................................417
17.3 Nanofluidinhydrateformation/inhibitionprocess...............................................418
17.3.1Improvementofmassexchangeduringhydrateformationby nanofluids...................................................................................................418
17.4 Conclusionsandfuturetrends................................................................................423
CHAPTER18Masstransferenhancementinsolarstillsbynanofluids
...............
18.1
AliBehradVakylabad
18.5 Onthemasstransferofsolarstills........................................................................437
18.5.1Inferredmasstransferfromheattransfermechanism...............................437
18.5.2Perspectivesofmasstransfer.....................................................................439
18.6
18.7
CHAPTER19Applicationofnanofluidsindrugdeliveryand diseasetreatment .............................................................................
YasamanEnjavi,MohammadAminSedghamizand MohammadRezaRahimpour
19.1 Introduction............................................................................................................449
19.2 Nanofluids..............................................................................................................449
19.2.1Differentvarietiesofnanofluids................................................................449
19.2.2Preparationofnanofluids...........................................................................450
19.2.3Nanofluidstabilityassessmentmethods....................................................451
19.2.4Nanofluidstabilizationprocedure..............................................................452
19.3 Nanofluid-baseddeliverysystem...........................................................................452
19.4 Targeteddrugdelivery...........................................................................................453
19.4.1Passive(physiology-based)targeting........................................................454
19.4.2Activetargeting..........................................................................................455
19.4.3Physicaltargeting.......................................................................................455
19.5 Applicationsofthenanofluid-baseddeliverysystem...........................................456
19.5.1Antibacterialactivityofnanofluids...........................................................457
19.5.2Applicationsincancertherapy..................................................................458
CHAPTER20Environmentalandindustrializationchallengesofnanofluids
20.1
NazaninAbrishamiShiraziandMohammadRezaRahimpour
20.2 Thedevastatingconsequencesofnanotechnology................................................468
20.2.1Thenanoparticleseffectonhumanhealth................................................469
20.2.2Thenanoparticleseffectontheenvironment............................................470
20.3 Nanofluidsutilizationchallenges...........................................................................470
20.3.1Long-termstabilityofnanoparticlesscattering.........................................471
20.3.2Increasedpressurelossandpumpingpower.............................................473
20.3.3Thermalperformanceofnanofluidsinturbulentflowandfully developedregion........................................................................................474
20.3.4Lessspecificheat.......................................................................................474
20.3.5Nanofluidsproductionandusageprice.....................................................474
20.4
Listofcontributors
MeisamAnsarpour
DepartmentofChemicalEngineering,FacultyofPetroleum,GasandPetrochemical Engineering,PersianGulfUniversity,Bushehr,Iran
AliBakhtyari
ChemicalEngineeringDepartment,ShirazUniversity,Shiraz,Iran
AsmaaF.Elelamy
DepartmentofMathematics,FacultyofEducation,AinShamsUniversity,Cairo,Egypt
YasamanEnjavi
DepartmentofChemicalEngineering,ShirazUniversity,Shiraz,Iran
MortezeEsfandyari
DepartmentofChemicalEngineering,UniversityofBojnord,Bojnord,Iran
FatemeEtebari
DepartmentofChemicalEngineering,ShirazUniversity,Shiraz,Iran
NayefGhasem
DepartmentofChemicalandPetroleumEngineering,UAEUniversity,Alain,UAE
KamranGhasemzadeh
UrmiaUniversityofTechnology,Urmia,Iran
AliHafizi
DepartmentofChemicalEngineering,ShirazUniversity,Shiraz,Iran
MohammadHatami
DepartmentofMechanicalEngineering,EsfarayenUniversityofTechnology,Esfarayen,Iran; InternationalResearchCenterforRenewableEnergy,Xi’anJiaotongUniversity,Xi’an,P.R.China
Zohreh-SadatHosseini
DepartmentofChemicalEngineering,ShirazUniversity,Shiraz,Iran
AngelHuminic
TransilvaniaUniversityofBrasov,Brasov,Romania
GabrielaHuminic
TransilvaniaUniversityofBrasov,Brasov,Romania
AdolfoIulianelli
InstituteonMembraneTechnologyoftheItalianNationalresearchCouncil(CNR-ITM),Rende, Italy
DengweiJing
InternationalResearchCenterforRenewableEnergy,Xi’anJiaotongUniversity,Xi’an,P.R.China
BaishaliKanjilal
DepartmentofBioengineering,UniversityofCalifornia,Riverside,Riverside,CA,UnitedStates
MohammadRezaKiani
FoumanFacultyofEngineering,CollegeofEngineering,UniversityofTehran,Fouman,Iran
MohammadAminMakarem
DepartmentofChemicalEngineering,ShirazUniversity,Shiraz,Iran
AramehMasoumi
DepartmentofChemicalEngineering,RowanUniversity,Glassboro,NJ,UnitedStates
HaticeMercan
DepartmentofMechatronicsEngineering,FacultyofMechanicalEngineering,YildizTechnical University(YTU),Yildiz,Besiktas,Istanbul,Turkey
MaryamMeshksar
DepartmentofChemicalEngineering,ShirazUniversity,Shiraz,Iran
AlinaAdrianaMinea
GheorgheAsachiTechnicalUniversityIasi,Iasi,Romania
MasoudMofarahi
DepartmentofChemicalEngineering,FacultyofPetroleum,GasandPetrochemical Engineering,PersianGulfUniversity,Bushehr,Iran;DepartmentofChemicalandBiomolecular Engineering,YonseiUniversity,Seoul,RepublicofKorea
ImanNoshadi
DepartmentofBioengineering,UniversityofCalifornia,Riverside,Riverside,CA,UnitedStates; DepartmentofChemicalEngineering,RowanUniversity,Glassboro,NJ,UnitedStates
MohammadRezaRahimpour
DepartmentofChemicalEngineering,ShirazUniversity,Shiraz,Iran
ColinA.Scholes
DepartmentofChemicalEngineering,TheUniversityofMelbourne,Melbourne,VIC,Australia
MohammadAminSedghamiz
DepartmentofChemicalEngineering,ShirazUniversity,Shiraz,Iran
NourouddinSharifi
DepartmentofEngineeringTechnology,TarletonStateUniversity,Stephenville,TX,UnitedStates
NazaninAbrishamiShirazi
SchoolofEnvironment,CollegeofEngineering,UniversityofTehran,Tehran,Iran
AliBehradVakylabad
DepartmentofMaterials,InstituteofScienceandHighTechnologyandEnvironmentalSciences, GraduateUniversityofAdvancedTechnology,Kerman,Iran
JiandongZhou
InternationalResearchCenterforRenewableEnergy,Xi’anJiaotongUniversity,Xi’an,P.R.China
1.1 Masstransferinnanofluids
Introducingnanoparticlestoworkingfluidsinenergyandchemicalsystemshasspawnedalarge numberofstudiesandhasbeeninvestigatedbymanyresearchersinthelasttwodecades.Itis observedthatthemassandthermaltransferofthebasefluidvarysignificantlywithasmallamount ofnanoparticleaddition.Physicalpropertieslikediffusivity,separation,thermalconductivity,density,viscosity,andheatcapacityoftheblendareaffectedbytheconcentration,size,andshapeof thenanoparticles.Intheirpioneeringstudy,Masudaetal. [1] reportedanimportantimprovement inthethermalconductivitywithincreasingconcentrationofultrafinenanoparticles[Al2O3/water (1.3% 4.3%vol.),TiO2/water(1.1% 2.3%vol.),andSiO2/water(1.0% 4.3%vol.)]comparedto waterasabasefluid.In Fig.1.1[2] thefundamentalmechanismsandtheirthermophysicalimpacts onthenanofluidsaresummarizedschematically.
Thereisastronganalogybetweenheatandmasstransfer.Therateofmasstransferisknownto changeasaresultofthepresenceofnanoparticlescomparedtoasingleliquidphase.Otherthan thenanoparticleaddition,thetypeofthenanoparticle,thenanoparticleconcentration,theparticle size,andtemperatureinfluencetherateofthemasstransfer,thusthesefundamentalmechanisms maychangethemasstransfercoefficient.Unlikeforthethermophysicalproperties,intheliterature theobservationsfromtheexperimentalstudiesarenotingoodagreementwitheachotherabout howthemasstransferchangeswiththesefundamentalmechanisms.Thereforethereisaneedto investigatethemasstransferinnanofluidsnotonlyforeverycolloidalblendbutalsoforeach process.
Thenanoparticlescanbecategorizedasmagneticnanoparticles,metalandmetaloxidesnanoparticles,carbon-basednanoparticlesandpolymer-basednanoparticles(see Fig.1.2) [2].Preparing nanofluidswithanimprovedstabilityisacomplicatedandexpensiveprocedure.Thenanofluids canbepreparedwithasingle-stepchemicalmethod.Alternatively,atwo-stepmethodcanbe employedwhichcanbechemicalorphysical.Mostlysurfactants,ultrasoundvibration,orultrasonicationtechniquesareusedinthetwo-stepmethodstoimprovelong-termstabilityofthedispersion. Nonhomogeneousdispersionandsedimentationaretwoimportantchallengesthatneedtobe addressedinnanofluidapplications.
NanofluidsandMassTransfer.DOI: https://doi.org/10.1016/B978-0-12-823996-4.00001-X Copyright © 2022ElsevierInc.Allrightsreserved.
FIGURE1.1
Thefundamentalmechanismsthataffectsthethermalconductivityofnanofluids
AdaptedfromQ.Lin,Z.Ning,F.Yanhui,M.E.Efstathios,Z.Gaweł,J.Dengwei,etal.,Areviewofrecentadvancesinthermophysical propertiesatthenanoscale:fromsolidstatetocolloids,Phys.Rep.843(2020)1 81
Thenanoparticlecanbeintheshapeofasphere,brick,cylinder,platelet,orblade.Theexperimentalobservationshaveshownthattheshapeofthenanoparticleaffectsthephysicalpropertyof thenanofluidconsiderably.Forinstance,inanexperimentalstudy,Timofeevaetal.andBijoyetal. [3,61] investigatedtheeffectsoftheshapeofthenanoparticlesandrevealedthatnanofluidswith platelet-shapednanoparticlesexhibithigherthermalconductivitycomparedtocylindricaland brick-shapednanoparticles.Additionally,TaslimahandDaniel [4] observedthattheblade-shaped nanoparticlesimprovedthethermalconductivitymorethanplatelet,cylindrical,brick,andspherical nanoparticles.Eliasetal. [5,6] conductedaseriesofapplication-basedexperimentalstudies,where theyinvestigatedtheeffectofparticleshapeontheoverallheattransfercoefficientfortheheat exchangers.Theyreportedthatthecylindricalnanoparticlesperformedsignificantlybettercomparedtootheroptions.Atthispointitisnotpossibletoderiveaconcreteconclusionaboutthe effectsofthenanoparticleshapeonthermalconductivityofthenanofluids;itneedsfurther consideration.
Inclusionofmorethanonenanoparticletothebasefluidimprovesthephysicalpropertiesof theblend.Generally,thehybridnanofluidsdemonstratesuperiormaterialpropertiescomparedtoa
FIGURE1.2
Theclassificationofthenanoparticlesgenerallyusedincolloidaldispersionsandschematicrepresentationof single-andtwo-stepnanofluidspreparation.
AdaptedfromQ.Lin,Z.Ning,F.Yanhui,M.E.Efstathios,Z.Gaweł,J.Dengwei,etal.,Areviewofrecentadvancesinthermophysical propertiesatthenanoscale:fromsolidstatetocolloids,Phys.Rep.843(2020)1 81
basefluidandasubsetofunitarynanofluidblend.Itisimportanttonotethattheselectionofthe nanoparticlesplayanimportantrole [7 10].Forinstance,thethermalconductivitygapbetween thenanoparticlesplaysakeyroleforthermalconductivityoftheresultinghybridnanofluid [10]. Nabiletal. [9] reportedthecomparisonofthreedifferenthybridnanofluids:TiO2-SiO2/water-EG, Al2O3-G/water,andMWCBT-Fe3O4/water.Thehighestthermalconductivityratioenhancement wasobservedfortheTiO2-SiO2/waterhybridnanofluid.Thiswasbecauseasahybridnanoparticle coupleTiO2 andSiO2 areclosertoeachotherintheirthermalconductivitycomparedtotheother couples.
Themathematicalmodelsforsuspensionsdonotaccuratelyestimatethephysicalpropertiesof nanofluidblends.Forthatreason,intheliterature,therearealargenumberofmodelsforthephysicalpropertiesofnanofluidsthatprocurewidevariationintheirestimates.Someofthesemodels employpolynomialfits,neuralnetworkalgorithms,ortheBuckinghamPitheoremtorelatethe propertiestonondimensionalgroups.Forinstance,themathematicalmodelstopredictthenanofluidviscosityhaveevolvedovertheyears,resultinginawiderangeofdifferentmodelswithdifferentcapabilitiesandlimitations.InitiallytheEinsteinmodelwasmodifiedfornanofluids,where theNewtoniancolloidviscosityisafunctionofconcentrationonly [11,12].Saitoetal. [13],
Brinkmanetal. [14],andFrankelandAcrivos [15] proposedmodifiedmodelswithimprovements inconcentrationrangeandparticlesizerangewithdistributionconstraints,wheretheexpression fortheviscosityisstillafunctionoftheconcentration [13 15].JangandChoi [16] reportedthat forsmallerparticlesize,thenanoparticleBrownianmotionbecomesmoreprominent,thusconvectionbecomesdominantatnanosize [16].ThenanoparticlesizeanddensitywithBrownianmotion featuresareincludedsimultaneouslybythemodelofMasouminetal. [12].Clustersizeeffectis takenintoaccountbythemodelofHosseini [17] andthenanolayerthicknesseswithaverageparticleradiusarealsoapartofthisformulation [17].Onecommonobservationforthesemorerecent modelsisthatthemathematicalexpressionscontainempiricalcoefficientsthatneedtobedeterminedexperimentally.Theproposedmodelscannotbedirectlyappliedineverysituation;theyare uniquemodelswithstrictconstraints.Foreachnanoblendwithaspecificconcentration,temperature,andpHintervalthereisaspecificexpressioninthemathematicalmodelforadesiredmaterial property.Thishighlightstheurgentneedforthedevelopmentofageneralizedmodeltoobtainthe materialpropertiesofthenanofluids.Thiscouldonlybepossiblewithaclearunderstandingofthe masstransfermechanismsofnanofluids.Thesemechanismsincludethediffusionandconvection phenomena,wheretheformerisduetogradientoftheconcentrationandthelatterisduetothe fluidmotion.
1.1.1 Massdiffusionofnanofluids
Theresultsfordiffusivecharacteristicsofnanofluidsreportedintheliteraturecanshowdissimilar trendsforthesamenanoparticle/basefluidblend.Forexample,animprovementinmassdiffusivity isreportedforincreasingconcentrationoftheAl3O2/waternanofluid [18,19].Forthesamecolloidalmixture,areductionindiffusivitywasreported [20,21].Additionally,Ozturketal. [22] reportednosignificantchangeindiffusivitywithconcentration.Fangetal. [23],reported26times morediffusiveCu/waternanofluidcomparedtothebasefluid,especiallyatlowerconcentrations [23].Theseconflictingobservationsrevealtheneedforfurtherinvestigations.
Intheliteraturethemassdiffusionenhancementinnanofluidsismostlylinkedtotherandom dynamicmotionofthenanoparticles,whichisalsoknownasBrownianmotion.ThelocalconvectionduetoBrownianmotionofthenanoparticlesenhancesthethermalconductivityinnanofluids morethantheclassicalconductiontheoriescanforesee.Asignificantmassdiffusionenhancement innanofluidscomparedtobasefluidsisreportedbyseveralresearchers [18,23 27].Themass transferandtheheattransferaretwoanalogousprocesses.Themassdiffusivityaugmentationin nanofluidsisthereasonfortheenhancedthermalconductivityofthenanofluid [18].Terhaniand Kelishami [27,28] investigatedthemasstransferofdifferentnanoparticlemassfractionsthrougha supportednanoliquidmembrane [27].Theyconstructedtheirmodelbyassumingincompressible flowwithoutchemicalreactionsandviscousdissipationforananoparticlemassfractionmuchless than1,whichmakestheblendadilutecolloidalmixture.Usingthetemperatureandconcentration analogytheyformedthefollowingnondimensionalgroups:thePrandtlnumberandtheNusselt numberfortheheattransfer;andtheSchmidtnumberandSherwoodnumberforthemasstransfer ofananofluid(see Table1.1).Theconstantsintheeffectivediffusivityexpression, Dnf,provided in Table1.1 are c 5 146, m1 5 0.523, m2 5 0.011,and m3 5 1.83 [28].Theyalsoconcludedthat Brownianmotionenhancedthemasstransferandnanoparticlesimprovedtheconvectionmass transfer;however,furtherconcentrationaugmentationreversedtheimprovementeffects [27].Ina
Table1.1Thenondimensionalgroupsforheatandmasstransfer.
HeattransferMasstransfer
Prandtlnumber
recentstudy,Machrafi [29] introducedanewmechanismofnanoparticledispersionbyapplying theporousflowprinciplesandthechemicalpotentialformulawhichprovidedagoodagreement withtheexperimentaldata.Thisstudyshowedthattheclassicalfreeenergymixingformulationis notappropriatetoexplainthemoleculardynamicsofnanoparticledispersions.Bydefiningachemicalpotentialbaseforboththedensityandtheporousmediumdescription,wherethebasefluiddiffusesacrosstheparticles,abetteragreementwiththeexperimentaldataisobtained [29]
Inadditiontothemicromotionofthefluid,theconcentrationplaysanimportantroleinthe massdiffusion,wherethegradientoftheconcentrationdifferenceisthedrivingforceforthemass transfer.Gerardietal. [20] experimentallyinvestigatedaluminawaternanofluids.Theirresultsare inconflictwiththemicroconvectiontheorypresentedinthepreviousstudies,whereanincreasein bothmassandheattransferisexpectedwithanincreasingconcentration.Theyreportedasignificantdecayinself-diffusioncoefficientofthenanoparticlesforincreasingaluminaconcentration [20].TuranovandTolmachev [30] experimentallyinvestigatedthesilica waternanofluidsforvolumetricconcentration ϕ # 0.3%andcomparedfourdifferentsilicananoparticleswithincreasing particlediameters [30].Theyreportedforallconcentrationsandnanosilicadiametersthesolvent self-diffusioncoefficientshowedareductionandtheenhancementinthethermalconductionwas modest,whichissimilartothefindingsofGerardietal.’sstudy [20].TuranovandTolmachev [30] suggestedthatthediffusiondecreaseoccurredduetowatercoatingthenanoparticles;whereasthey explainedthemoderateconductivityenhancementwiththeheattransferresistanceattheinterface ofthenanoparticleandwatermolecules [30].
1.1.2 Convectivemasstransferofnanofluids
Convectivemassandheattransferisobservedinnatureandengineeringapplicationsrangingfrom atmosphericandoceaniccirculations,heatingofbuildingstocoolingofelectronicdevices.Itis dominantinabsorptionprocesses,membranesystems,andextractionsystems.Duringmultiphase reactions,suchasfermentation,hydrogenationreactions,andwatertreatment,themasstransfer fromgasphasetoliquidovertheinterfacehasamajorrole.Theinterfacesizeaswellastheconcentration,theparticlesize,andthetemperatureaffectthismasstransfer.Nosignificanteffecton heatandmasstransferratesisobservedwithincreasingbuoyancyratio.
Olleetal.reportedanenhancementintheoxygenabsorptionofwaterwithmagneticnanoparticles. Theyreportedanimprovementinmasstransfercoefficientuptosixtimescomparedtothebasefluidand forbothdynamicandquiescentconditions.Theincreaseingas liquidinterfacebynanoparticleadditionis responsibleforthisincreasewithastrongdependencyontemperature.Kimetal. [31] investigatedthe
