Table Of ContentSpringerBriefs in Applied Sciences and Technology
Thermal Engineering and Applied Science
SeriesEditor
FrancisA.Kulacki,UniversityofMinnesota,USA
Forfurthervolumes:
http://www.springer.com/series/10305
Seshasai Srinivasan • M. Ziad Saghir
Thermodiffusion in
Multicomponent Mixtures
Thermodynamic, Algebraic,
and Neuro-Computing Models
123
SeshasaiSrinivasan M.ZiadSaghir
DepartmentofMathematics DepartmentofMechanical
andStatistics andIndustrialEngineering
McMasterUniversity RyersonUniversity
Hamilton,Ontario Toronto,Ontario
Canada Canada
ISSN2191-530X ISSN2191-5318(electronic)
ISBN978-1-4614-5598-1 ISBN978-1-4614-5599-8(eBook)
DOI10.1007/978-1-4614-5599-8
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2012950589
©SpringerScience+BusinessMedia,LLC2013
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection
with reviews or scholarly analysis or material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of
this publication or parts thereof is permitted only under the provisions of the Copyright Law of the
Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.
PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations
areliabletoprosecutionundertherespectiveCopyrightLaw.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
While the advice and information in this book are believed to be true and accurate at the date of
publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor
anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with
respecttothematerialcontainedherein.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
To ourfamilies.
Preface
Thesubtleandintricatephenomenonofthermodiffusionisevidentinseveralfacets
of life and nature. However, it is still not understood very well and there is a
lackofasinglesourcethatdealsexclusivelywiththisphenomenon.Consequently,
a newcomer in the field of thermodiffusion has to fend for himself through the
researcharticlesthatarescatteredallovertheengineeringandpuresciencejournals.
Inanefforttoaddressthisshortfall,thistextisanattempttoofferacomprehensive
starting point by presenting the current theoretical/computational approaches to
studythermodiffusion.
In writing this book it has been assumed that there is little or no prior
understandingoftheprinciplesofthermodiffusion.Inlayingdownthefoundations
ofthermodiffusion,thebookdiscussesthecurrenttheoreticalframeworkstostudy
this fascinating phenomenon. Additionally, studies employing these theories are
presented for the reader to understand the drawbacks/advantages of the various
expressions that quantify thermodiffusion. A separate list of references is also
includedattheendofeachchapterforfurtherreading.
Apart from serving as a reference text for the professionals in the fields of
chemistry, mechanical engineering, reservoir engineering as well as materials
science, this book is also an excellent guide for the postdoctoral researchers and
graduatestudentsinthisfield.
Inpreparingthiswork,weareindebtedtoourfellowresearchersinthescientific
communitywhose studies have helped us shape our understandingof the subject.
Specialthankstothemembersofourresearchgroup,graduatestudentsinparticular,
fortheircontributionstothisfascinatingfield.
Hamilton,Canada SeshasaiSrinivasan
Toronto,Canada M.ZiadSaghir
vii
Contents
1 Introduction .................................................................. 1
1.1 Background:DefinitionandHistory ................................... 1
1.2 RelevanceofThermodiffusion ......................................... 2
1.3 StudiesinThermodiffusion............................................. 2
1.4 FoundingPrinciplesofThermodiffusionFormalisms................. 3
1.5 TheSubtleNatureofThermodiffusion:TheUndesirable
ConvectiveForces....................................................... 5
1.6 TopicsofThisBook .................................................... 6
References..................................................................... 7
2 ThermodiffusionModels.................................................... 11
2.1 LinearNonequilibriumThermodynamicTheory...................... 11
2.1.1 PhenomenologicalEquations .................................. 12
2.2 Method1:ThermodiffusionModelsBasedonLNETTheory........ 13
2.2.1 TheNetHeatofTransport...................................... 15
2.2.2 EquationofState................................................ 15
2.2.3 BinaryLiquidMixtures ........................................ 21
2.2.4 TernaryLiquidMixtures ....................................... 29
2.3 Method2:SimpleAlgebraicExpressionstoQuantify
Thermodiffusion ........................................................ 32
2.3.1 LiquidHydrocarbonMixtures ................................. 32
2.3.2 LiquidPolymerMixtures....................................... 38
2.3.3 ColloidalMixtures.............................................. 40
2.4 Method3:NeurocomputingModelstoStudyThermodiffusion...... 43
2.4.1 WhatareNeuralNetworks?.................................... 43
2.4.2 WhyArtificialNeuralNetworks?.............................. 45
2.4.3 TheoreticalFormalisms ........................................ 45
References..................................................................... 53
ix
x Contents
3 ApplicationofLNETModelstoStudyThermodiffusion................ 57
3.1 LiquidHydrocarbonMixtures.......................................... 57
3.1.1 BinaryHydrocarbonMixtures ................................. 57
3.1.2 TernaryHydrocarbonMixtures ................................ 58
3.2 LiquidAssociatingMixtures ........................................... 59
3.3 DilutePolymerMixtures ............................................... 59
3.4 MoltenMetalMixtures ................................................. 61
3.5 EffectoftheEquationofState ......................................... 62
References..................................................................... 64
4 CFDStudiesinThermodiffusion........................................... 65
4.1 Introduction ............................................................. 65
4.2 ProblemSetupandGoverningEquations.............................. 66
4.2.1 SourceTermsinMomentumEquation ........................ 68
4.3 CaseStudies............................................................. 70
4.3.1 CaseA:Methane–n-Butane–n-DodecaneMixture............ 70
4.3.2 CaseB:Water–IsopropanolMixture........................... 71
4.4 RelevanceofAccurateDensityandViscosityModels................ 73
4.4.1 DensityCalculations............................................ 73
4.4.2 ViscosityCalculations.......................................... 75
References..................................................................... 76
5 ApplicationofAlgebraicCorrelationstoStudyThermodiffusion ..... 77
5.1 BinaryLiquidMixtures................................................. 77
5.1.1 Binaryn-AlkaneMixtures...................................... 77
5.1.2 BinaryPolymerMixtures....................................... 79
5.1.3 BinaryColloidalMixtures...................................... 80
5.2 TernaryMixtures........................................................ 82
References..................................................................... 85
6 ApplicationofNeurocomputingModelstoStudyThermodiffusion ... 87
6.1 NeuralNetworkStudiesinThermodiffusion.......................... 87
6.1.1 ThermodiffusioninBinaryLiquidMetals..................... 87
6.1.2 ThermodiffusioninBinaryLiquidHydrocarbonMixtures... 92
6.2 SensitivityandDiversityoftheParameters............................ 97
6.3 ComparisonwithOtherApproachestoStudyThermodiffusion...... 99
6.3.1 BinaryMoltenMetalMixtures................................. 99
6.3.2 Binaryn-AlkaneMixtures...................................... 100
6.4 ConcludingRemarks.................................................... 101
6.4.1 ExtensiontoMulticomponentSystems........................ 101
6.4.2 SmallDatabaseSize............................................ 101
References..................................................................... 102
Index............................................................................... 105
