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Title: | On an averaged model for immiscible two-phase flow with surface tension and dynamic contact angle in a thin strip | Authors: | LUNOWA, Stephan BRINGEDAL, Carina POP, Sorin |
Issue Date: | 2021 | Publisher: | WILEY | Source: | STUDIES IN APPLIED MATHEMATICS, 147 (1) , p. 84-126 | Abstract: | We consider a model for the flow of two immiscible fluids in a two-dimensional thin strip of varying width. This represents an idealization of a pore in a porous medium. The interface separating the fluids forms a freely moving interface in contact with the wall and is driven by the fluid flow and surface tension. The contact-line model incorporates Navier-slip boundary conditions and a dynamic and possibly hysteretic contact angle law. We assume a scale separation between the typical width and the length of the thin strip. Based on asymptotic expansions, we derive effective models for the two-phase flow. These models form a system of differential algebraic equations for the interface position and the total flux. The result is Darcy-type equations for the flow, combined with a capillary pressure-saturation relationship involving dynamic effects. Finally, we provide some numerical examples to show the effect of a varying wall width, of the viscosity ratio, of the slip boundary condition as well as of having a dynamic contact angle law. | Keywords: | asymptotic expansions;dynamic contact angle;freely moving interface;thin strip;two‐phase flow;upscaled models | Document URI: | http://hdl.handle.net/1942/34097 | ISSN: | 0022-2526 | e-ISSN: | 1467-9590 | DOI: | 10.1111/sapm.12376 | ISI #: | 000640117200001 | Rights: | 2021 Wiley Periodicals LLC | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2022 |
Appears in Collections: | Research publications |
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Stud Appl Math - 2021 - Lunowa - On an averaged model for immiscible two‐phase flow with surface tension and dynamic.pdf | Published version | 1.75 MB | Adobe PDF | View/Open |
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