Radial Viscous Fingering in Case of Poorly Miscible Fluids

The displacement of a viscous fluid from an annular Hele-Shaw cell with a source of finite radius by a less viscous one is investigated. A special case of poorly miscible fluids is considered when corresponding dimensionless criteria—capillary and Peclet numbers—both tend to infinity. Brinkman model...

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Bibliographic Details
Published inTransport in porous media Vol. 124; no. 2; pp. 495 - 508
Main Author Logvinov, Oleg A.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.09.2018
Springer Nature B.V
Subjects
Brinkman model
Civil Engineering
Classical and Continuum Physics
Computational fluid dynamics
Criteria
Displacement
Earth and Environmental Science
Earth Sciences
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Hydrology/Water Resources
Industrial Chemistry/Chemical Engineering
Linear analysis
Mathematical models
Miscibility
Peclet number
Viscous fluids
Hele-Shaw cell
Brinkman model
Radial fingering
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Summary:The displacement of a viscous fluid from an annular Hele-Shaw cell with a source of finite radius by a less viscous one is investigated. A special case of poorly miscible fluids is considered when corresponding dimensionless criteria—capillary and Peclet numbers—both tend to infinity. Brinkman model which additionally takes into account small viscous forces in a plane of the cell is used to describe the displacement process. Linear analysis shows a stabilizing effect of viscous forces and reveals a geometrical similarity criterion, namely the ratio of the interface’s radius to the gap between the cell’s plates. The displacement patterns, obtained numerically under Brinkman model, are very sensitive to the discovered criterion. The comparison with available experimental data is acceptable.
ISSN:0169-3913
1573-1634
DOI:10.1007/s11242-018-1081-7