多孔介质对流、扩散与导电性ppt课件.ppt

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1、TwoBasicApplicationsofPercolationTheorytoFlowNearPerc.ThresholdGivesscalingofhydraulic,electricalconductivity,airpermeabilitywithdistancefromthresholdmoisturecontent.Connectivity/tortuosityFarfromPerc.ThresholdGivesdependenceofsamepropertiesonmoisturecontentthroughdepend

2、enceof“bottleneck”poresize.Pore-sizedependenceNOTE:Thesetwoapplicationsarenotindependent(samecriticalpercolationprobabilityforboth)!AndOnetoAccessibility(inHysteresis)Theprobabilitythatagivensite(orvolume)isconnectedtotheinfiniteclusterabovethepercolationthresholdisgiven

3、byauniversalfunctionofpercolationtheory.ApplytoRandom(Truncated)FractalModelofPorousMediaWhatisoptimalformofpercolationtheory?Continuum.Whatarerelevantvariables?Criticalvolumefraction(moisturecontent,air-filledporosity).Whataboutpotentialnon-universalbehavior?Much,though

4、notallbehaviorisuniversal.BasicResultsforSaturationDependenceofPropertiesK(S)pore-sizedistributiondominatesathighsat.,connectivity/tortuosityatlowsat.ElectricalConductivitysimilarAirpermeabilityconnectivity/tortuositydominatesthroughoutSoluteandgasdiffusion,connectivity/

5、tortuositydominatethroughoutConsiderFirstUnsaturatedKonLatticeofTubesAppropriateAnalogyinContinuumPercolationRepresentationResultforK()Resultfrombottleneckpore.Resultfromaverageresistancetoflowoveralllargerpores.Noteargumentisnot-t(unless=1)!EffectsofTortuosity,Conne

6、ctivityHydraulicConductivityElectricalConductivityt=1.88(3D)=1.28(2D)RequirebothKanddK/dtobecontinuousatunknownx;thisgeneratesprefactorandx.InvicinityoftconductivitymustscaleasHanfordsitedata(Rockholdetal.,1988)Connectivity/tortuosityPore-sizesComparisonswithOtherRes

7、ultsBalberg,Phil.Mag.1987ifW(g)continuestog=0Butifdistributioncontinuestog=0,thismeansthatsmallestporehaszeroradius.Thatmeansthat=1inRieuandSpositomodeland,yieldsBalbergresultsince,at=1(alsofor)TofindlimitofvalidityofArchie’slawsetArchie’slawEvaluateatsaturationUsepro

8、portionalityofcriticalvolumefractiontoporosity(Hunt,AdWR)Archie’sLawExperimentfindsm=1.86Thompsonetal.,