Wall energy relaxation in the Cahn-Hilliard model for moving contact lines

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dc.contributor.authorYue, Pengtaoen
dc.contributor.authorFeng, James J.en
dc.contributor.departmentMathematicsen
dc.date.accessed2014-04-04en
dc.date.accessioned2014-04-24T18:34:22Zen
dc.date.available2014-04-24T18:34:22Zen
dc.date.issued2011-01en
dc.description.abstractThe Cahn-Hilliard model uses diffusion between fluid components to regularize the stress singularity at a moving contact line. In addition, it represents the dynamics of the near-wall layer by the relaxation of a wall energy. The first part of the paper elucidates the role of the wall relaxation in a flowing system, with two main results. First, we show that wall energy relaxation produces a dynamic contact angle that deviates from the static one, and derive an analytical formula for the deviation. Second, we demonstrate that wall relaxation competes with Cahn-Hilliard diffusion in defining the apparent contact angle, the former tending to "rotate" the interface at the contact line while the latter to "bend" it in the bulk. Thus, varying the two in coordination may compensate each other to produce the same macroscopic solution that is insensitive to the microscopic dynamics of the contact line. The second part of the paper exploits this competition to develop a computational strategy for simulating realistic flows with microscopic slip length at a reduced cost. This consists in computing a moving contact line with a diffusion length larger than the real slip length, but using the wall relaxation to correct the solution to that corresponding to the small slip length. We derive an analytical criterion for the required amount of wall relaxation, and validate it by numerical results on dynamic wetting in capillary tubes and drop spreading. (C) 2011 American Institute of Physics. [doi:10.1063/1.3541806]en
dc.description.sponsorshipNSF-DMS Contract No. 0907788en
dc.description.sponsorshipPetroleum Research Funden
dc.description.sponsorshipNSERC (Discovery, Accelerator and Strategic grants)en
dc.description.sponsorshipCanadian Foundation for Innovationen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationYue, Pengtao; Feng, James J., "Wall energy relaxation in the Cahn-Hilliard model for moving contact lines," Phys. Fluids 23, 012106 (2011); http://dx.doi.org/10.1063/1.3541806en
dc.identifier.doihttps://doi.org/10.1063/1.3541806en
dc.identifier.issn1070-6631en
dc.identifier.urihttp://hdl.handle.net/10919/47674en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/pof2/23/1/10.1063/1.3541806en
dc.language.isoenen
dc.publisherAIP Publishingen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectliquid-liquid-systemsen
dc.subjectboundary-conditionen
dc.subjectsolid-surfacesen
dc.subjectdynamicsen
dc.subjectinterfaceen
dc.subjecthydrodynamicsen
dc.subjectdisplacementen
dc.subjectkineticsen
dc.subjectflowen
dc.subjectangleen
dc.titleWall energy relaxation in the Cahn-Hilliard model for moving contact linesen
dc.title.serialPhysics of Fluidsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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