A model of miscible liquids in porous media
In this article we study the interaction of two miscible liquids in porous media. The model consists of hydrodynamic equations with the Korteweg stress terms coupled with the reaction-diffusion equation for the concentration. We assume that the fluid is incompressible and its motion is describe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2015-10-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/264/abstr.html |
| _version_ | 1811231692054069248 |
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| author | Karam Allali Vitaly Volpert Vitali Vougalter |
| author_facet | Karam Allali Vitaly Volpert Vitali Vougalter |
| author_sort | Karam Allali |
| collection | DOAJ |
| description | In this article we study the interaction of two miscible liquids in
porous media. The model consists of hydrodynamic equations with the
Korteweg stress terms coupled with the reaction-diffusion equation for
the concentration. We assume that the fluid is incompressible and its
motion is described by the Darcy law. The global existence and
uniqueness of solutions is established for some optimal conditions
on the reaction source term and external force functions.
Numerical simulations are performed to show the behavior of two
miscible liquids subjected to the Korteweg stress. |
| first_indexed | 2024-04-12T10:49:06Z |
| format | Article |
| id | doaj.art-92ef010b284b46c883d6aa064a2abbfa |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T10:49:06Z |
| publishDate | 2015-10-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-92ef010b284b46c883d6aa064a2abbfa2022-12-22T03:36:18ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-10-012015264,110A model of miscible liquids in porous mediaKaram Allali0Vitaly Volpert1Vitali Vougalter2 Univ. Hassan II, Mohammedia, Morocco Univ. Lyon 1, Villeurbanne, France Univ. of Toronto, ON, Canada In this article we study the interaction of two miscible liquids in porous media. The model consists of hydrodynamic equations with the Korteweg stress terms coupled with the reaction-diffusion equation for the concentration. We assume that the fluid is incompressible and its motion is described by the Darcy law. The global existence and uniqueness of solutions is established for some optimal conditions on the reaction source term and external force functions. Numerical simulations are performed to show the behavior of two miscible liquids subjected to the Korteweg stress.http://ejde.math.txstate.edu/Volumes/2015/264/abstr.htmlDarcy approximationKorteweg stressmiscible liquidsporous media |
| spellingShingle | Karam Allali Vitaly Volpert Vitali Vougalter A model of miscible liquids in porous media Electronic Journal of Differential Equations Darcy approximation Korteweg stress miscible liquids porous media |
| title | A model of miscible liquids in porous media |
| title_full | A model of miscible liquids in porous media |
| title_fullStr | A model of miscible liquids in porous media |
| title_full_unstemmed | A model of miscible liquids in porous media |
| title_short | A model of miscible liquids in porous media |
| title_sort | model of miscible liquids in porous media |
| topic | Darcy approximation Korteweg stress miscible liquids porous media |
| url | http://ejde.math.txstate.edu/Volumes/2015/264/abstr.html |
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