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1、journalotMEMBRANESCIENCEELSEVIERJournalofMembraneScience100(1995)33-38OnliquiddiffusionAdolphFickZiirich,SwitzerlandAfewyearsagoGrahampublishedanextensivestratumbetweenthehorizontalplanesatxandx+dxinvestigationonthediffusionofsaltsinwater,inwhich(inwhichtheconcentrationisy)ther
2、ewillpass,duringhemoreespeciallycomparedthediffusibilityofdiffer-anelementoftimedt,intotheimmediatesuperjacententsalts.Itappearstomeamatterofregret,however,stratum,boundedbythehorizontalplanesx+dxandthatinsuchanexceedinglyvaluableandextensivex+2dx(inwhichtheconcentrationy+dy/dx
3、dxpre-investigation,thedevelopmentofafundamentallaw,vails),aquantityofsalt=-Q.k.dy/dxdt,inwhichfortheoperationofdiffusioninasingleelementofQsignifiesthesurfaceofthestratum,andkaconstantspace,wasneglected,andIhavethereforeendeavoureddependentuponthenatureofthesubstances.Itisevi-
4、tosupplythisomission.dentthatavolumeofwaterequaltothatofthesaltItwasquitenaturaltosuppose,thatthislawforthepassessimultaneouslyoutoftheupperstratumintothediffusionofasaltinitssolventmustbeidenticalwithlower.that,accordingtowhichthediffusionofheatinacon-Exactlyaccordingtothemode
5、lofFourier'smathe-ductingbodytakesplace;uponthislawFouriermaticaldevelopmentforacurrentofheat,wecanobtainfoundedhiscelebratedtheoryofheat,anditisthesamefromthisfundamentallawforthediffusion-current,thewhichOhmappliedwithsuchextraordinarysuccess,differentialequationtothediffusio
6、nofelectricityinaconductor.According6y6t-[62y(~-d-fdQ6y_)tothislaw,thetransferofsaltandwateroccurringinaunitoftime,betweentwoelementsofspacefilledwithdifferentlyconcentratedsolutionsofthesamesalt,mustwhenthesectionQofthevesselinwhichthecurrentbe,caeterisparibus,directlyproporti
7、onaltothediffer-takesplaceisafunctionofitsheightabovethebottom.enceofconcentration,andinverselyproportionaltotheIfthesectionbeconstant(i.e.thevesselcylindricalordistanceoftheelementsfromoneanother.prismatic),thedifferentialequationbecomessimpli-Inmathematicallanguagethismaybeth
8、usfiedtoexpressed:--Inavolumeofsaltsolution,letthecon-
