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dc.contributor.authorXu, Xinpeng
dc.contributor.authorThiele, Uwe
dc.contributor.authorQian, Tiezheng
dc.date.accessioned2016-02-28T07:59:50Z
dc.date.available2016-02-28T07:59:50Z
dc.date.issued2015-02-04
dc.identifier.citationXu X, Thiele U, Qian T (2015) A Variational approach to thin film hydrodynamics of binary mixtures. J Phys: Condens Matter 27: 085005. Available: http://dx.doi.org/10.1088/0953-8984/27/8/085005.
dc.identifier.issn0953-8984
dc.identifier.issn1361-648X
dc.identifier.pmid25651053
dc.identifier.doi10.1088/0953-8984/27/8/085005
dc.identifier.urihttp://hdl.handle.net/10754/600242
dc.description.abstractIn order to model the dynamics of thin films of mixtures, solutions, and suspensions, a thermodynamically consistent formulation is needed such that various coexisting dissipative processes with cross couplings can be correctly described in the presence of capillarity, wettability, and mixing effects. In the present work, we apply Onsager's variational principle to the formulation of thin film hydrodynamics for binary fluid mixtures. We first derive the dynamic equations in two spatial dimensions, one along the substrate and the other normal to the substrate. Then, using long-wave asymptotics, we derive the thin film equations in one spatial dimension along the substrate. This enables us to establish the connection between the present variational approach and the gradient dynamics formulation for thin films. It is shown that for the mobility matrix in the gradient dynamics description, Onsager's reciprocal symmetry is automatically preserved by the variational derivation. Furthermore, using local hydrodynamic variables, our variational approach is capable of introducing diffusive dissipation beyond the limit of dilute solute. Supplemented with a Flory-Huggins-type mixing free energy, our variational approach leads to a thin film model that treats solvent and solute in a symmetric manner. Our approach can be further generalized to include more complicated free energy and additional dissipative processes.
dc.description.sponsorshipThis work is supported by Hong Kong RGC Grant No 604013. T Qian and U Thiele would like to thank the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge for the Research Program 'Mathematical Modelling and Analysis of Complex Fluids and Active Media in Evolving Domains' in which this work was initiated.
dc.publisherIOP Publishing
dc.subjectbinary mixtures
dc.subjectcapillarity
dc.subjectliquid thin films
dc.subjectliquidsolid interfaces
dc.subjectmodeling
dc.subjectwettability
dc.titleA Variational approach to thin film hydrodynamics of binary mixtures
dc.typeArticle
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.identifier.journalJournal of Physics: Condensed Matter
dc.contributor.institutionDepartment of Mathematics, Hong Kong University of Science and Technology, Clear Water BayKowloon, Hong Kong
dc.contributor.institutionInstitut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm Klemm Str. 9Münster, Germany
dc.contributor.institutionCenter of Nonlinear Science (CeNoS), Westfälische Wilhelms Universität Münster, Corrensstr. 2Münster, Germany
kaust.personQian, Tiezheng
kaust.grant.fundedcenterKAUST-HKUST Micro/Nanofluidic Joint Laboratory
dc.date.published-online2015-02-04
dc.date.published-print2015-03-04


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