多孔介质对流、扩散与导电性.ppt

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1、Diffusion,ElectricalConduction,andFlowinPorousMediaContinuumPercolationTheoryforTruncatedRandomFractalMediaTwoBasicApplicationsofPercolationTheorytoFlowNearPerc.ThresholdGivesscalingofhydraulic,electricalconductivity,airpermeabilitywithdistancefromthresholdmoisturecontent.Conn

2、ectivity/tortuosityFarfromPerc.ThresholdGivesdependenceofsamepropertiesonmoisturecontentthroughdependenceof“bottleneck”poresize.Pore-sizedependenceNOTE:Thesetwoapplicationsarenotindependent(samecriticalpercolationprobabilityforboth)!AndOnetoAccessibility(inHysteresis)Theprobab

3、ilitythatagivensite(orvolume)isconnectedtotheinfiniteclusterabovethepercolationthresholdisgivenbyauniversalfunctionofpercolationtheory.ApplytoRandom(Truncated)FractalModelofPorousMediaWhatisoptimalformofpercolationtheory?Continuum.Whatarerelevantvariables?Criticalvolumefractio

4、n(moisturecontent,air-filledporosity).Whataboutpotentialnon-universalbehavior?Much,thoughnotallbehaviorisuniversal.BasicResultsforSaturationDependenceofPropertiesK(S)pore-sizedistributiondominatesathighsat.,connectivity/tortuosityatlowsat.ElectricalConductivitysimilarAirpermea

5、bilityconnectivity/tortuositydominatesthroughoutSoluteandgasdiffusion,connectivity/tortuositydominatethroughoutConsiderFirstUnsaturatedKonLatticeofTubesAppropriateAnalogyinContinuumPercolationRepresentationResultforK()Resultfrombottleneckpore.Resultfromaverageresistancetoflow

6、overalllargerpores.Noteargumentisnot-t(unless=1)!EffectsofTortuosity,ConnectivityHydraulicConductivityElectricalConductivityt=1.88(3D)=1.28(2D)RequirebothKanddK/dtobecontinuousatunknownx;thisgeneratesprefactorandx.InvicinityoftconductivitymustscaleasHanfordsitedata(Rock

7、holdetal.,1988)Connectivity/tortuosityPore-sizesComparisonswithOtherResultsBalberg,Phil.Mag.1987ifW(g)continuestog=0Butifdistributioncontinuestog=0,thismeansthatsmallestporehaszeroradius.Thatmeansthat=1inRieuandSpositomodeland,yieldsBalbergresultsince,at=1(alsofor)Tofindlim

8、itofvalidityofArchie’slawsetArchie’slawEvaluateatsaturationUs