Particle-fluid mass transfer in multiparticle systems at low Reynolds numbers

The problemofmasstransferbetweenactivesolidparticlesandafluidinmultiparticlesystemsis examinedwithafocusonthestagnantandthelowReynoldsnumbercases.Thisproblemhasattracted significantattentionwithregardtooperationoffixedandfluidizedbeds.Itisrecognizedthatdifferent Sherwoodnumberscanbedefineddependingonthechoiceofthereferenceconcentrationdifference (drivingforce).Aneffective Sh has oftenbeenusedtoanalyzeexperimentaldatabasedonanoverall concentrationdifferenceacrossthebed.Alocal Sh can alsobeintroducedbasedonaconcentration differenceclosetotheactiveparticle.However,theuseofthesetwodifferentSherwoodnumbers impliesadifferentimplementationofthemassbalanceequations. The massbalanceequationsarehereanalyticallysolvedbothunderstagnantandnon-stagnant conditionsinamultiparticlesystemundersuitablesimplifyingassumptions.Equationsfortheeffective and localSherwoodnumbersarederivedforthegeneralcaseandfortheasymptoticlimits.Allowance is givenforthevariationofbedvoidageandvolumefractionofactiveparticlesinthebed.Itisshown that thelocal Sh only dependsongeometricalandfluid-dynamicsconsiderationsandaccordinglyhasa generalvalidity.Onthecontrary,theeffective Sh also dependsontheassumptionsmadeinderivingthe mass balanceequationsacrossthebed(e.g.,fluidplugflow).Theuseofthelocal Sh is therefore suggested. Resultsshowthatfor Re-0 thelimitingvalueofthelocal Sh is alwaysafinitenumber,whilethe effective Sh tendstozerolinearlywith Re. Itisshownthatthisresultissimplyaconsequenceofthe plug flowassumptionmadeinthebedmassbalance.Thegeneralexpressionsderivedherecompare very welltoexperimentaltrendsforthecasesoflargeReynoldsnumbersandoffewisolatedactive spheres immersedinabedofinertparticles,wheremostofthereportedexperimentaldatagather. Unfortunately,forthemostcontroversialcaseofverylow Re in bedsmadeentirelyofactiveparticlesno reliabledataappearstobeavailabletochecktheaccuracyoftheexpressions.