Hydrodynamic boundary conditions for one-component liquid-gas flows on non-isothermal solid substrates

Handle URI:
http://hdl.handle.net/10754/600254
Title:
Hydrodynamic boundary conditions for one-component liquid-gas flows on non-isothermal solid substrates
Authors:
Xu, Xinpeng; Liu, Chun; Qian, Tiezheng
Abstract:
Recently, liquid-gas flows related to droplets, bubbles, and thin films on solid surfaces with thermal and wettability gradients have attracted widespread attention because of the many physical processes involved and their promising potential applications in biology, chemistry, and industry. Various new physical effects have been discovered at fluid-solid interfaces by experiments and molecular dynamics simulations, e.g., fluid velocity slip, temperature slip (Kapitza resistance), mechanical-thermal cross coupling, etc. There have been various models and theories proposed to explain these experimental and numerical observations. However, to the best of our knowledge,a continuum hydrodynamic model capable of predicting the temperature and velocity profiles of liquid-gas flows on non-isothermal, heterogeneous solid substrates is still absent. The purpose of this work is to construct a continuum model for simulating the liquid-gas flows on solid surfaces that are flat and rigid, and may involve wettability gradients and thermal gradients. This model is able to describe fluid velocity slip, temperature slip, and mechanical-thermal coupling that may occur at fluid-solid interfaces. For this purpose, we first employ the diffuse interface modeling to formulate the hydrodynamic equations for one-component liquid-gas flows in the bulk region. This reproduces the dynamic van der Waals theory of Onuki [Phys. Rev. Lett., 94: 054501, 2005]. We then extendWaldmann's method [Z. Naturforsch. A, 22: 1269-1280, 1967] to formulate the boundary conditions at the fluid-solid interface that match the hydrodynamic equations in the bulk. The effects of the solid surface curvature are also briefly discussed in the appendix. The guiding principles of our model derivation are the conservation laws and the positive definiteness of entropy production together with the Onsager reciprocal relation. The derived model is self-consistent in the sense that the boundary conditions are mathematically demanded by the bulk equations. A finite difference scheme is presented for numerically solving the model system. We show that some widely used boundary conditions can actually be recovered by taking appropriate limits. We also point out that the framework presented here for modeling two-phase flows on solid surfaces, from bulk equations to boundary conditions, is in a form that can be readily generalized to model other fluid-solid interfacial phenomena. © 2012 International Press.
Citation:
Liu C, Qian T, Xu X (2012) Hydrodynamic boundary conditions for one-component liquid-gas flows on non-isothermal solid substrates. Communications in Mathematical Sciences 10: 1027–1053. Available: http://dx.doi.org/10.4310/cms.2012.v10.n4.a1.
Publisher:
International Press of Boston
Journal:
Communications in Mathematical Sciences
KAUST Grant Number:
SA-C0040; UK-C0016
Issue Date:
2012
DOI:
10.4310/cms.2012.v10.n4.a1
Type:
Article
ISSN:
1539-6746; 1945-0796
Sponsors:
We would like to thank P. Sheng and X.-P. Wang for helpful discussions. This publication is based on work partially supported by Award No. SA-C0040/UK-C0016, made by King Abdullah University of Science and Technology (KAUST), and Hong Kong RGC grant No. 603510. X. Xu was also supported by the Nano Science and Technology Program of HKUST.
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Full metadata record

DC FieldValue Language
dc.contributor.authorXu, Xinpengen
dc.contributor.authorLiu, Chunen
dc.contributor.authorQian, Tiezhengen
dc.date.accessioned2016-02-28T08:00:06Zen
dc.date.available2016-02-28T08:00:06Zen
dc.date.issued2012en
dc.identifier.citationLiu C, Qian T, Xu X (2012) Hydrodynamic boundary conditions for one-component liquid-gas flows on non-isothermal solid substrates. Communications in Mathematical Sciences 10: 1027–1053. Available: http://dx.doi.org/10.4310/cms.2012.v10.n4.a1.en
dc.identifier.issn1539-6746en
dc.identifier.issn1945-0796en
dc.identifier.doi10.4310/cms.2012.v10.n4.a1en
dc.identifier.urihttp://hdl.handle.net/10754/600254en
dc.description.abstractRecently, liquid-gas flows related to droplets, bubbles, and thin films on solid surfaces with thermal and wettability gradients have attracted widespread attention because of the many physical processes involved and their promising potential applications in biology, chemistry, and industry. Various new physical effects have been discovered at fluid-solid interfaces by experiments and molecular dynamics simulations, e.g., fluid velocity slip, temperature slip (Kapitza resistance), mechanical-thermal cross coupling, etc. There have been various models and theories proposed to explain these experimental and numerical observations. However, to the best of our knowledge,a continuum hydrodynamic model capable of predicting the temperature and velocity profiles of liquid-gas flows on non-isothermal, heterogeneous solid substrates is still absent. The purpose of this work is to construct a continuum model for simulating the liquid-gas flows on solid surfaces that are flat and rigid, and may involve wettability gradients and thermal gradients. This model is able to describe fluid velocity slip, temperature slip, and mechanical-thermal coupling that may occur at fluid-solid interfaces. For this purpose, we first employ the diffuse interface modeling to formulate the hydrodynamic equations for one-component liquid-gas flows in the bulk region. This reproduces the dynamic van der Waals theory of Onuki [Phys. Rev. Lett., 94: 054501, 2005]. We then extendWaldmann's method [Z. Naturforsch. A, 22: 1269-1280, 1967] to formulate the boundary conditions at the fluid-solid interface that match the hydrodynamic equations in the bulk. The effects of the solid surface curvature are also briefly discussed in the appendix. The guiding principles of our model derivation are the conservation laws and the positive definiteness of entropy production together with the Onsager reciprocal relation. The derived model is self-consistent in the sense that the boundary conditions are mathematically demanded by the bulk equations. A finite difference scheme is presented for numerically solving the model system. We show that some widely used boundary conditions can actually be recovered by taking appropriate limits. We also point out that the framework presented here for modeling two-phase flows on solid surfaces, from bulk equations to boundary conditions, is in a form that can be readily generalized to model other fluid-solid interfacial phenomena. © 2012 International Press.en
dc.description.sponsorshipWe would like to thank P. Sheng and X.-P. Wang for helpful discussions. This publication is based on work partially supported by Award No. SA-C0040/UK-C0016, made by King Abdullah University of Science and Technology (KAUST), and Hong Kong RGC grant No. 603510. X. Xu was also supported by the Nano Science and Technology Program of HKUST.en
dc.publisherInternational Press of Bostonen
dc.subjectFluid-solid interfaceen
dc.subjectLiquid-gas phase transitionen
dc.subjectOne-component two-phase flowen
dc.subjectWall slipen
dc.titleHydrodynamic boundary conditions for one-component liquid-gas flows on non-isothermal solid substratesen
dc.typeArticleen
dc.identifier.journalCommunications in Mathematical Sciencesen
dc.contributor.institutionDepartment of Mathematics, Pennsylvania State University, University Parken
dc.contributor.institutionNano Science and Technology (NSNT) Program, Hong Kong University of Science and Technologyen
kaust.authorQian, Tiezhengen
kaust.grant.numberSA-C0040en
kaust.grant.numberUK-C0016en
kaust.grant.fundedcenterKAUST-HKUST Micro/Nanofluidic Joint Laboratoryen
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