The instability of thermal and fluid fronts during radial injection in a porous medium

Research output: Contribution to journalArticle

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Abstract

We investigate viscous fingering instabilities of the double-front system which results when fluid is injected into a porous medium containing fluid of a different composition and temperature. We describe a linear stability analysis based on an eigenfunction expansion method which enables us to investigate the structure of the discrete eigenvalue spectrum. We investigate the extent to which the properties of each front contribute to the tendency of the system to become unstable: we find that instabilities on the compositional front dominate because of the high ratio of thermal to solute diffusion. It is difficult for a stable compositional front to stabilize an unstable thermal front; however, this situation can result in a new fingering phenomenon in which the perturbations undergo coupled oscillations of growing amplitude.
Original languageEnglish
Pages (from-to)133-163
Number of pages31
JournalJournal of Fluid Mechanics
Volume508
DOIs
Publication statusPublished - 2004

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Porous materials
injection
Linear stability analysis
Fluids
fluids
Eigenvalues and eigenfunctions
Chemical analysis
solutes
eigenvectors
tendencies
eigenvalues
Temperature
Hot Temperature
perturbation
oscillations
expansion
temperature

Keywords

  • fluid dynamics
  • physics
  • unstable thermal front

Cite this

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The instability of thermal and fluid fronts during radial injection in a porous medium. / Pritchard, D.

In: Journal of Fluid Mechanics, Vol. 508, 2004, p. 133-163.

Research output: Contribution to journalArticle

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AU - Pritchard, D.

PY - 2004

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N2 - We investigate viscous fingering instabilities of the double-front system which results when fluid is injected into a porous medium containing fluid of a different composition and temperature. We describe a linear stability analysis based on an eigenfunction expansion method which enables us to investigate the structure of the discrete eigenvalue spectrum. We investigate the extent to which the properties of each front contribute to the tendency of the system to become unstable: we find that instabilities on the compositional front dominate because of the high ratio of thermal to solute diffusion. It is difficult for a stable compositional front to stabilize an unstable thermal front; however, this situation can result in a new fingering phenomenon in which the perturbations undergo coupled oscillations of growing amplitude.

AB - We investigate viscous fingering instabilities of the double-front system which results when fluid is injected into a porous medium containing fluid of a different composition and temperature. We describe a linear stability analysis based on an eigenfunction expansion method which enables us to investigate the structure of the discrete eigenvalue spectrum. We investigate the extent to which the properties of each front contribute to the tendency of the system to become unstable: we find that instabilities on the compositional front dominate because of the high ratio of thermal to solute diffusion. It is difficult for a stable compositional front to stabilize an unstable thermal front; however, this situation can result in a new fingering phenomenon in which the perturbations undergo coupled oscillations of growing amplitude.

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