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1、OntheTransitionbetweenaWettingFilmandaCapillaryMeniscusF.RENK,P.C.WAYNER,JR.,ANDG.M.HOMSYWestvaco,Laurel,Maryland20810,DepartmentofChemicalEngineering,RensselaerPolytechnicInstitute,Troy,NewYork12181,andDepartmentofChemicalEngineering,StanfordUniversity,Stanford,Califo
2、rnia94305ReceivedJanuary13,1978;acceptedMay18,1978Theshapeofahorizontalmeniscuswhichisinfluencedbothbycapillarityandbyanadsorbedthinfilmisdetermined.Anexactsolutionisobtainedwhichclearlyshowsthefeaturesofatransitionbetweenacurvedmeniscusandanadsorbedfilm.Themethodofmat
3、chedasymptoticexpansionsisusedtoelucidatemanyofthedetailsofthetransitionlayer,itshorizontalthickness,andthequestionofapparentcontactangle.INTRODUCTIONthattheprofileshapeinthetransitionre-gionmaybeusedasaprobeoftheformIthaslongbeenrecognizedthatamenis-andmagnitudeofthef
4、orcesactingonathincuscanexistinthermodynamicequilibriumfilm.Morerecently,inworkcloselyparal-withanadsorbedorfreeliquidfilm.Theseleledbyourown,Deryaginetal.(2)havesituationsareofinterestinthe"microscopicreportedsolutionstothecombinedcapil-film"techniqueforstudyingforces
5、inthinlary-thinfilmproblemforthecaseofahori-films(1),incapillarycondensation(2,3),inzontalcapillarytube.Theresultsclearlyproblemsinvolvingdynamicmenisci,andinshowthetransitionregionasbeingconfinedevaporationatameniscuswhichwetsatosmallhorizontalextent,andnumericalheate
6、dsolid(4,5).Whilethetreatmentofevaluationsofthesolutionsindicatethatmultilayeradsorptiononsurfaces,onthethetransitionzoneincreaseswithincreasingonehand,andthedescriptionofstaticthicknessoftheadsorbedfilmandwithmenisciwithprescribedcontactangle,ondecreasingcapillarypres
7、sure.Thesetheother,arebothwelldeveloped,thereauthors(2,7)andothers(10)havediscussedseemstobelittletheoryavailablewhichtherelationbetweentheapparentcontactdescribesthecombinedmechanisms.Theangleandthetransitionregion,andthecon-problemwasrecognizedsometimeagobyceptualdif
8、ficultiesthatariseinattemptingtoDeryagin(6),whodevelopedtheideaofadefineandmeasureanequilibriumcontacttransitionregio