Linear and non-linear analyses on the onset of miscible viscous fingering in a porous medium

The onset of miscible viscous fingering in porous media was analyzed theoretically. The linear stability equations were derived in the self-similar domain, and solved through the modal and non-modal analyses. In the non-modal analysis, adjoint equations were derived using the Lagrangian multiplier t...

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Bibliographic Details
Published in:The Korean journal of chemical engineering 2018, 35(7), 220, pp.1423-1432
Main Authors: Ryoo, Won Sun, Kim, Min Chan
Format: Article
Language:English
Subjects:
Biotechnology
Catalysis
Chemistry
Chemistry and Materials Science
Computer simulation
Industrial Chemistry/Chemical Engineering
Materials Science
Mathematical analysis
Miscibility
Modal analysis
Nonlinear analysis
Porous media
Self-similarity
Stability analysis
Transport Phenomena
화학공학
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Summary:The onset of miscible viscous fingering in porous media was analyzed theoretically. The linear stability equations were derived in the self-similar domain, and solved through the modal and non-modal analyses. In the non-modal analysis, adjoint equations were derived using the Lagrangian multiplier technique. Through the non-modal analysis, we show that initially the system is unconditionally stable even in the unfavorable viscosity distribution, and there exists the most unstable initial disturbance. To relate the theoretical predictions with the experimental work, nonlinear direct numerical simulations were also conducted. The present stability condition explains the system more reasonably than the previous results based on the conventional quasi-steady state approximation.
ISSN:0256-1115
1975-7220
DOI:10.1007/s11814-018-0046-4