IntroductionThereleaseofadrugfromadiffusiona lmatrixhasbeeninvestigatedbyvariousresearch ersfordifferentconditions(1').Thedrugloadin ginmatrixmaybeaboveorbelowitssaturationleve l.Ifabove,leachingdrugfromthematrixwillresu ltintWoregionsdividedbyasharpinterfaceandth econcentrationinreleasedregionmaybeproporti onaltothedistanceandkeepatserrationinunrele asedregion.Ifbelow,theconcentrationinthewho lematriXdecreasescontinuouslywithtime.Manyt heoreticalmodelshavebeenreportedforthesetWo casesinordertodescribethediffusionpropertie sofcontrolledreleasedevices.However,mostoft hemhavebeenlimitedtotheassumptionofsteady-s tatediffusion.Forexample,Higuchiusedthisass umptionaswellasmatrixdiffusionassumptiontop roposeasquaretakerootreleaserelationship(') forsuper-saturationcase.Wealsodiscussedthec asesofsub-saturationloadingwithorwithoutaco atinginthepre.1viouswork(s~,).Inthispaper,w econtinuethediscussionforthecaseofsuper-sat urationloadingwithoutasteady-statediffusion assumption.Inconsideringthisuniqueperforman ce,themathematicalanalysiswasgenerallycarri edout,testedwiththeexperimentaldatafrom5-Fu /EVALmatfixsystemandcomparedwiththeearliest andwidelyacceptedHiguchi'smodel(1).Experime ntalTheexperimentaldetailscanbereferredtoou rpreviouswork(v~).ItshouldbepointedoUtthatt hemodelparametersC,,solubilityofthedruginth ematrix,andD.,diffusioncoefficientofthedrug inthematrix,weredeterminedas7.815mg.cm-'and 2.78xl0-8cmZ's-l(',,),respectively.Mathemat icalanalysisAdrugwasdissolveduniformlyinasl abmatrixwiththickness,L.'Thedrugloading(C,) wasaboveitssaturationlevel(C,)'Thematrixwas thenimmersedinawell-stirredmediumofvolumeV. .Thustheboundarylayermightbeassumedtobenegl igible.Drugconcentrationinthematrixandextra ctionmediumwererepresentedbyC,,,(t)andC.(t) ,respectively.Diffusivityofdruginthematrixw asrepresentedbyD,.andassumedtobeconstant.As chematicdrawingofthiscaseisshowninFig.1.The basicmasstransferequationforthematrixisasfo llowstWiththeinitialandtheboundarycondition s,theaboveequationcanbesolvedbyLaplacetrans formindimensionlessformsusingthetermsdefine dasbelow:'tTheproceduresforthesolutionsarea nalogoustothoseinourpreviouswork(s,6)andthe resultsareasfollowsiwhere,A(Pn)=argoncosPn+ (4+Ka)sinPn(5)andanarethenon-zerorootsofequ ation(6)ffiPnsinfinW.cosPn=0(6)Thecumulativ ereleasefraction,F,,isdefinedasfollowsbased ontheinitialdrugloadingfIntegratingtheabove equation,withtheassumptionthatreleasedistan ceL,isconstantatadesignatedtimet,yieldsThec aseofaperfectsinkmaybeobtainedbyset-tingthe volumeofextractionmediumtobeinfinite,i.e.,V ,-co,andthustheresultsaresimplifiedasfollow sfWherePnarethenon-zerorootsofequationsinpn =0.ResultsandDiscussionForthecaseofCd>C,,th einterfacialresistancebetweenthematrixandth emediummightbeassumedtobenegligiblebecauset hedisperseddrugparticlesexistedinthematrixb eforethecompletedepletion.Andthusthevolumeo fextractionmediumhadlittleaffectonreleasepr ocessexceptonthetimeofattainingthereleaseeq uilibrium.Foraconventionalexperimentalcondi tion,suchasthematfixwitha2cmindiameterand0. 01cminthicknessreleasingintothemediumof25ml ,thevolumetricratioV,exceededavalueof796.It isobviousthatthepoleequation(8)hasnearlythe samesolutionasthatinthecaseofaperfectsinkaf terasubstitutionofthiscomparativelylargeV,v alueandasmallK.value(about0.6intheconcerned system).Therefore,inthispaper,onlythecaseof aperfectsinkisdiscussed.Tofindthesolutionso fthemodelsasdescribedabove,itisofgreatimpor tancetocalculatethevariationofreleasedistan ceL,withtime.Fromthematerialsbalance,wehave Combiningthedimensionlessvariablesandequati on(ga),wecanobtainThisequationcouldbesimpli fiedasHiguchi'smodel(1)forasteadystaterelea seprocessItiseasytosolveequation(12)byRunge -Kuttamethodforthereleasedistanceatanytimep oint,andthusthecumulativereleasefractionsca nbecarriedoutwiththeindependentlydetermined parameters.Thetheoreticalfractionswerecalcu latedateachtimepointandcomparedwiththeexper imentalonesandthosecalculatedbyHiguchi'smodelsinFigs.Za~dwherethedrugloadingwas15.5,50,123.6and210mg.cm-'respectively,allofwhichwerehigherthanthesolubility7.815mg.cm-'.Thes
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