Viscoelastic Liquids in Stirred Vessels ± Part I: Power Consumption in Unaerated Vessels By Isabelle Seyssiecq*, Adama TolofoudyØ, HervØ Desplanches ,and Yves Gaston-Bonhomme Differentshear-thinningandelasticfluids(STEfluids)havebeenstirredunderunaeratedconditions,invesselsequippedwith Rushtondiscturbines.TheirpowerconsumptionhasbeenevaluatedoverawiderangeofstirringratesandtheirMetzner-Otto constant(k s )hasbeenmeasured.Acorrelationhasthenbeenproposedtopredict k s valuesforaRushtonturbineoperatingin non-Newtoniansolutions.PowercurvesofSTEfluidshavebeendrawnandcomparedwithreferencecurves(Newtonian,shear- thinninginelasticandelasticwithconstantshearviscosityfluids).TheSTEfluidshavethusbeendividedintotwocategories.The STEfluidsofthefirstcategory(STEIfluids),whichareconcentratedviscoussolutionsofpolymers(guar,CMC)reducingthe powerconsumptionatthebeginningofthetransitionalregionandconnectingwiththeNewtonianreferenceathigherReynolds numbers.Incontrast,STEsolutionsofthesecondcategory(STEIIfluids),whicharesolutionsofdragreducingpolymers(PAA), arelessviscousandmoreelastic.Theyreducethepowerconsumptionattheendofthetransitionalregionanddonotconnect withtheNewtonianreference,atleastuntilRe=6000.Ageneralcorrelationhasfinallybeenproposedtomodelthepowercurve ofSTEfluidsstirredbyaRushtonturbinefromthelaminartotheturbulentregions,asafunctionoftheirelasticity. 1Introduction Most of the fluids generally encountered in the chemical, food or cosmetic industries are rheologically complex. In particular, high polymer solutions are known to exhibit a viscoelasticbehavior,whichmayconsiderablyaffecttheflow patternsandthetransportprocesses[1].Asanexample,inthe case of a pipe flow, the presence of elasticity leads to the existenceofadragreduction,knownastheªTomseffectº.In the case of a stirred vessel, which is one of the most widely spread contactors in the chemical and associated industries, theeffectsofafinitepositivefirstnormalstressdifferencein viscoelasticmediaarequalitativelyremarkable.Forinstance, whenaverticalrodpartlyimmersedinaviscoelasticliquidis rotated about its axis, the fluid climbs up the rod. This ªWeissenberg effectº is also called ªinverted vortexº. More generally, it is well known that the elastic component can strongly interfere with current chemical processes, such as mixing,heatormasstransfers. Fromaquantitativepointofview,areviewoftheliterature devoted to the effects of the elastic component on those transport processes reveals that the results are most of the timenotconsistentfromonestudytoanother.Asanexample, ifweconsideramixingprocessundergoingsimultaneousheat transfer, it has been shown in numerous works that the viscoelasticityhasastrongeffectonbothpowerconsumption, heat or mass transfer coefficients and mixing times ([1±4]. However, the intensity but also the sense of this effect may varyfromonestudytoanother,notablydependingontheflow regime(laminar,transitionalorturbulent),thetypeofelastic fluid used (shear-thinning and elastic one or constant shear viscosity elastic one), and the configuration of the whole vessel. As a consequence, if the question of the effect of elasticityontransportprocesseshasbeenwidelystudiedinthe literature, it should be underlined that, at least from a quantitativepointofview,theavailabledataarenoteasyto compare. It finally comes that it is not easy to find a simple correlation for chemical engineers, allowing scale-up and accounting for the effect of the elastic component on hydrodynamics,powerconsumptionandheatormasstransfer inprocesses,suchasmixing. In this context, the present study has been devoted to the followingpoints. Usingglycerolandfourdifferentmacromoleculesatvarious concentrations in aqueous solutions, seventeen fluids with various rheological behavior (Newtonian, shear-thinning inelastic (ST), shear-thinning elastic (STE) or elastic with constantshearviscosity(Bogerfluids))havebeenobtained. These fluids have first been characterized from a rheolog- ical point of view. A natural time quoted t no deduced from rheological oscillatory measurements has been chosen to account for the elasticity of each solution, while the shear- thinning index (n) has been chosen to represent the shear- thinningcomponent.Theelasticitylevelofeachfluidhasbeen evaluatedbyintroducingthenaturaltimet no inadimension- lesselasticitynumberdenotedasEl o . Power consumption measurements have then been per- formed, using two stirred vessels equipped with Rushton turbinesofsizes(d)correspondingtoaratiod/Dof1/3or1/2. MeasurementshavefirstbeenachievedinNewtonianmedia todeterminethereferenceforotherexperiments.Onthebasis ofthemodel(foratwo-bladedimpeller)ofNagata etal. [5],a correlation has been proposed to model the power curve of Newtonian fluids stirred with a Rushton turbine, from the laminartotheturbulentregion.Bogerelasticfluidshavealso beenusedintheReynoldsnumberrangeof1to300,tomake anattempttoseparatetheeffectofelasticityfromtheshear- Chem. Eng. Technol. 2003, 26,11 DOI: 10.1002/ceat.200301689 Ó 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1155 ± [*] Prof. Dr.-Ing. H. Desplanches (deceased), Dr.-Ing. I. Seyssiecq (isabelle.seyssiecq@univ.u-3mrs.fr), Dr.-Ing. A. TolofoudyØ, Dr.-Ing. Y. Gaston-Bonhomme,EAN/884,UniversitØd'Aix-MarseilleIII,Avenue EscadrilleNormandie-Niemen,F-13397Marseillecedex20,France. Full Paper