dorsal/arxiv
View SchemaViscous fingering of miscible slices
| Authors | Anne De Wit, Yann Bertho, Michel Martin |
|---|---|
| Categories | |
| ArXiv ID | physics/0508080 |
| URL | https://arxiv.org/abs/physics/0508080 |
| DOI | 10.1063/1.1909188 |
| Journal | Phys. Fluids 17, 054114 (2005) |
Abstract
Viscous fingering of a miscible high viscosity slice of fluid displaced by a lower viscosity fluid is studied in porous media by direct numerical simulations of Darcy's law coupled to the evolution equation for the concentration of a solute controlling the viscosity of miscible solutions. In contrast with fingering between two semi-infinite regions, fingering of finite slices is a transient phenomenon due to the decrease in time of the viscosity ratio across the interface induced by fingering and dispersion processes. We show that fingering contributes transiently to the broadening of the peak in time by increasing its variance. A quantitative analysis of the asymptotic contribution of fingering to this variance is conducted as a function of the four relevant parameters of the problem i.e. the log-mobility ratio R, the length of the slice l, the Peclet number Pe and the ratio between transverse and axial dispersion coefficients $\epsilon$. Relevance of the results is discussed in relation with transport of viscous samples in chromatographic columns and propagation of contaminants in porous media.
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"abstract": "Viscous fingering of a miscible high viscosity slice of fluid displaced by a\nlower viscosity fluid is studied in porous media by direct numerical\nsimulations of Darcy\u0027s law coupled to the evolution equation for the\nconcentration of a solute controlling the viscosity of miscible solutions. In\ncontrast with fingering between two semi-infinite regions, fingering of finite\nslices is a transient phenomenon due to the decrease in time of the viscosity\nratio across the interface induced by fingering and dispersion processes. We\nshow that fingering contributes transiently to the broadening of the peak in\ntime by increasing its variance. A quantitative analysis of the asymptotic\ncontribution of fingering to this variance is conducted as a function of the\nfour relevant parameters of the problem i.e. the log-mobility ratio R, the\nlength of the slice l, the Peclet number Pe and the ratio between transverse\nand axial dispersion coefficients $\\epsilon$. Relevance of the results is\ndiscussed in relation with transport of viscous samples in chromatographic\ncolumns and propagation of contaminants in porous media.",
"arxiv_id": "physics/0508080",
"authors": [
"Anne De Wit",
"Yann Bertho",
"Michel Martin"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1063/1.1909188",
"journal_ref": "Phys. Fluids 17, 054114 (2005)",
"title": "Viscous fingering of miscible slices",
"url": "https://arxiv.org/abs/physics/0508080"
},
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