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Lambdaprobe393●LLLagrangecell—FabredeLagrangedevelopedazinc–airbatterywherethesulfuricaciddroppedslowlythroughacolumninwhichthecarbonelectrodewasplacedanddownontothezincelectrode.Thiswasmadetoincreasethecurrentbyamovementoftheelectrolytesolution,andthusdecreasingtheconcentrationpo-larization.SeealsoDaniellcell,zinc,Zn+/Znelectrodes,Zn+/Zn(Hg)electrodes,zinc–airbatter-ies(cell),andLeclanchécell.Ref.:[i]HauckWP()DieGalvanischenBatterien,AccumulatorenundThermosäulen,ndedn.,Hartleben’sVerlag,WienFSLaitinen,HerbertAugust(Jan.,,OtterTailCounty,Minnesota,USA–Mar.,)OfFinnishheritage,LaitinenstudiedchemistryattheUniversityofMinnesota.HisPh.D.thesis,basedonstudiesunderthedirectionofKolthoffattheUni-versityofMinnesota,wasentitled“AQuantitativeStudyofDiffusionbyElectrolysiswithMicroElectrodes”.WithLingane,HerbLaitinenwasoneofKolthoff’sdisciplesinbringingelectrochemistryinAmericaintotherealmofAnalyticalChemistry.HismostproductiveyearswereduringhisprofessorshipattheUniversityofIllinoisinUrbana,–.Amonghismanyaccomplishmentswerepioneeringstudiesofelectrochemistryintwoverydemandingsolvents:liquidammoniaandfusedsalts.Agenerationofstudentsbenefitedfromhistutelageandinspiration,amongwhomRobertOsteryoungmightbesingledout.FollowinghisretirementfromtheUni-versityofIllinois,LaitinenmovedtoGainesville,wherehecontinuedwithelectrochemicalresearchattheUni-versityofFloridauntilhisdeathin.KBOLamb’sequationquasielasticlightscatteringLambdaprobe—Theso-calledlambdaprobe(lambdasensor)isapotentiometricoxygengassensorthatisusedtomonitorthepartialpressureofoxygenpO(oxy-genconcentration),e.g.,intheexhaustgasofcarsinor-dertocontroltheair/fuelratiothatisgoingtothein-ternalcombustionengine.Theterm“lambda”originatesfromthestoichiometrynumberλwhichdescribesthecompositionoftheair/fuelmixture,asfollows:λ=(mairmfuel)real(mairmfuel)stoichwheremair=massofair,mfuel=massoffuel,subscript“real”indicatestheactualair/fuelratio,andsubscript“stoich”indicatesthestoichiometricair/fuelratio(whichdependsontheexactcompositionofthefuel).Whenλthereisafuelexcessandwhenλthereisanexcessofair.TheLambdaprobegivesaverysteepvolt-agestepatλ=andcanthereforebeusedtodetectthestoichiometrypoint.Tokeepthree-waycatalystsforcarexhaustgasesworkingattheiroptimumafastandpre-cisefeedbackcontrolisnecessarythatguaranteesλ=.TheLambdaprobeconsistsofasolid-stateelectrolyte(yttrium-stabilizedzirconia)thatiscoveredwithporousplatinumelectrodesontheinside()andoutside()(seeFig.).TheLambdaprobeisusuallyshapedlikeasparkingplugwherethesolid-stateelectrolyteformsaclosed-endcylinderthatitinsertedintotheexhaustgas.Theinsideofthecylinderisincontactwithambientairwithacon-stantpartialpressureofoxygen,pO,,andtheoutsideisincontactwiththeexhaustgasinwhichthepartialpres-sureofoxygen,pO,,ismonitoredbymeasuringthepo-tentialdifferencebetweenthetwoplatinumelectrodesLambdaprobe—Figure394Laminarflow●Lwherethefollowingtworeactionstakeplace:O+e−O−cathodereactionO−O+e−anodereactionTheO−ionsaretransportedthroughthesolidelec-trolyte(andalsostabilizedzirconia)atelevatedtem-perature(aboveC).ThemeasuredpotentialofthesensoristhengivenbytheNernstequation:E=E+RTFlnpO,pO,Ref.:[i]GöpelW,HesseJ,ZemelJN()Sensors–Acomprehensivesurvey,vols.and.VCH,WeinheimJBLaminarflow—arisesatlowReynoldsnumberswhenReRecandgenerallyoccurswhenviscousforcesdominate.Itischaracterizedbythesmoothsteadyflowoffluidinparallellayersorlaminae,althougheachlayermaynothavethesamevelocity.Laminarflow—Figure.SchematicoflaminarflowthroughapipeThecharacteristicsoflaminarflowcanallowmath-ematicalpredictionofthesolutionvelocityandthishasledtoarangeofhydrodynamicdeviceswhichuseforcedconvectionasatransportcomponentunderlaminarflowconditions,examplesinclude,therotatingdiskelectrode[i],walljetelectrode[ii],andchannelflowcell(seeflowcell).Refs.:[i]NewmanJ()JElectrochemSoc:;[ii]BrettCMA,OliveiraBrettAM,PereiraJLC()Electroanalysis:AF,SMLaminarflowtoturbulentflowtransition—Whenin-creasingthevelocityoftheflow,atransitionfromlam-inarflowto“rippling”andfinallyto“turbulent”flowwilloccur[i].ThetransitionfromlaminartoturbulentflowisgovernedbythedimensionlessReynoldsnumber.Ref.:[i]LevichVG()Physicochemicalhydrodynamics.Prentice-Hall,EnglewoodCliffsFMLandaufreeenergy—Landaufreeenergyisthefreeen-ergyofthesystemFasafunctionalofanorderparame-terψ(r)characterizingthestateofthesystematfixedval-uesofotherthermodynamicparameters(temperature,pressure,etc.).Beingfirstintroducedforthedescriptionofsecond-orderphasetransitions,itwasthenusedinthetheoryofsuperfluidity,superconductivity,ferromag-netism,etc.,andisknownalsoasLandau–Ginzburgfreeenergy.Inchemistryitisusedinparticularinthetheoryofliquidstate.Theorderparameterψ(r)maybeascalarorvectorfield.Anordinaryscalarvariableξmayplaytheroleofanorderparameterinsomesystems.Landaufreeenergyrepresentsinthiscaseandordinaryfunctionofξ.TheminimumofLandaufreeenergyfunctionalwithrespecttotheorderparameterdeterminestheequilib-riumstateofthesystem.Thedeviationsofthe