Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility
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ArticleAuthors
Kou, Jisheng
Sun, Shuyu

KAUST Department
Computational Transport Phenomena LabEarth Science and Engineering Program
Physical Science and Engineering (PSE) Division
Date
2016-05-10Online Publication Date
2016-05-10Print Publication Date
2016-08Permanent link to this record
http://hdl.handle.net/10754/609007
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In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng-Robinson equation of state). Because of partial miscibility, thermodynamic relations are used to model not only interfacial properties but also bulk properties, including density, composition, pressure, and realistic viscosity. As far as we know, this effort is the first time to use diffuse interface modeling based on equation of state for modeling of multi-component two-phase flow with partial miscibility. In numerical simulation, the key issue is to resolve the high contrast of scales from the microscopic interface composition to macroscale bulk fluid motion since the interface has a nanoscale thickness only. To efficiently solve this challenging problem, we develop a multi-scale simulation method. At the microscopic scale, we deduce a reduced interfacial equation under reasonable assumptions, and then we propose a formulation of capillary pressure, which is consistent with macroscale flow equations. Moreover, we show that Young-Laplace equation is an approximation of this capillarity formulation, and this formulation is also consistent with the concept of Tolman length, which is a correction of Young-Laplace equation. At the macroscopical scale, the interfaces are treated as discontinuous surfaces separating two phases of fluids. Our approach differs from conventional sharp-interface two-phase flow model in that we use the capillary pressure directly instead of a combination of surface tension and Young-Laplace equation because capillarity can be calculated from our proposed capillarity formulation. A compatible condition is also derived for the pressure in flow equations. Furthermore, based on the proposed capillarity formulation, we design an efficient numerical method for directly computing the capillary pressure between two fluids composed of multiple components. Finally, numerical tests are carried out to verify the effectiveness of the proposed multi-scale method.Citation
Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility 2016 Journal of Computational PhysicsPublisher
Elsevier BVJournal
Journal of Computational PhysicsAdditional Links
http://linkinghub.elsevier.com/retrieve/pii/S0021999116301103ae974a485f413a2113503eed53cd6c53
10.1016/j.jcp.2016.04.055