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CHAPTER8

Fundamentalsof MassTransfer

Diffusion is theprocessby which molecules,ions,or othersmallparticlesspon- taneouslymix, moving from regionsof relativelyhigh concentrationinto regionsof lower concentration.This processcan be analyzedin two ways. First, it can be describedwith Fick's law anda diffusioncoeffìcient,a fundamentalandscientificdescriptionusedin the f ì r s t t w o p a r t s o f t h i s b o o k . S e c o n d ,i t c a n b e e x p l a i n e di n t e r m s o f a m a s s t r a n s f e rc o e f - ficient,anapproximateengineeringideathatoftengivesasimplerdescription.It isthis simplerideathat is emphasizedin this part of this book.

Analyzingdiffusionwith masstransfercoefficientsrequiresassumingthatchangesin concentrationarelimitedtothatsmallpartof thesystem'svolumenearitsboundaries.For example,in theabsorptionof onegasinto a liquid, we assumethatall gasesandliquidsare well mixed,exceptnearthegas-liquidinterface.In theleachingof metalby pouringacid overore,weassumethattheacidishomogeneouse,xceptinathinlayernexttothesolidore particles.In studiesof digestion,we assumethatthecontentsof thesmallintestinearewell mixed,exceptnearthevilli attheintestine'swall. Suchananalysisis sometimescalleda "lumped-parametemr odel" to distinguishit from the "distributed-parametemr odel" using diffusioncoefficients.Bothmodelsaremuchsimplerfor dilutesolutions.

If you arebeginninga studyof diffusion,you may havetroubìedecidingwhetherto organizeyour resultsasmasstransfercoefficientsor asdiffusioncoefficients.I havethis troubletoo. Theclichéis thatyou shouldusethemasstransfercoeffìcientapproachif the diffusion occursacrossan interface,but this cliché has many exceptions.Insteadof dependingon the cliché, I believeyou shouldalwaystry both approachesto seewhich is betterfor your own needs.In my own work, I havefound that I often switch from one to theotherasthework proceedsandmy objectivesevolve.

This chapterdiscussesmasstransfercoefficientsfor dilute solutions;extensionsto con- centratedsolutionsaredeferredto Section13.5. In Section8.1, we give a basicdefinition for amasstransfercoefficientandshowhowthiscoefficientcanbeusedexperimentally. I n S e c t i o n 8 . 2 , w e p r e s e n t o t h e r c o m m o n d e f i n i t i o n s t h a t r e p r e s e n ta t h i c k e t o f p r i c k l y a l - ternativesrivaledonly by standardstatesfor chemicalpotentials.Thesevariousdefinitions arewhy masstransferoftenhasa reputationwith studentsof beinga difficult subject.In Section8.3,we list existingcorrelationsof masstransfercoefficients;andin Section8.4, we explainhow thesecorrelationscanbedevelopedwith dimensionalanalysis.Finally,in Section8.5,we discussprocessesinvolvingdiffusionacrossinterfacesa, topicthatleadsto overallmasstransfercoeffìcientsfoundasaveragesof morelocalprocessesT. hislastidea is commonlycalledmasstransferresistancesin series.

8.1 A Definition of Mass Tlansfer Coefficients

The defìnitionof masstransferis basedon empirical argumentslike thoseused in developingFick's law in Chapter2. Imaginewe areinterestedin the transferof mass

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