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Asymptotic behaviour of Stokes flow in a thin domain with amoving rough boundary
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0003-1993-8229
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0003-0799-5285
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0001-8211-3671
2014 (English)In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 470, no 2167, article id 20130735Article in journal (Refereed) Published
Abstract [en]

We consider a problem that models fluid flow in a thin domain bounded by two surfaces. One of the surfaces is rough and moving, whereas the other is flat and stationary. The problem involves two small parameters ε and μ that describe film thickness and roughness wavelength, respectively. Depending on the ratio λ = ε/μ, three different flow regimes are obtained in the limit as both of them tend to zero. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high-frequency roughness regime). The derivations of the limiting equations are based on formal expansions in the parameters ε and μ.

Place, publisher, year, edition, pages
2014. Vol. 470, no 2167, article id 20130735
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-4639DOI: 10.1098/rspa.2013.0735ISI: 000336184600003Scopus ID: 2-s2.0-84901270334Local ID: 29cc4d7b-7c7c-4e3c-9b00-a9bce047ccd3OAI: oai:DiVA.org:ltu-4639DiVA, id: diva2:977513
Note
Validerad; 2014; 20140610 (johsod)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Fabricius, JohnKoroleva, YuliaTsandzana, Afonso FernandoWall, Peter

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