Abstract
Reactive waters percolating through a porous medium cause changes in the porosity which, through Darcy’s law, alter the flow. This feedback mechanism can cause instabilities in the shape of the porosity level surfaces. In this note we describe the geological problem in a simplified situation. We model the phenomenon mathematically as a coupled system of nonlinear ordinary-partial differential equations and in a certain limiting case as a moving free boundary problem. We formulate the shape stability problem in this context and summarize our analytical and numerical results to date.
Lecturer and preparer of this report. Work done in collaboration with P. Ortoleva, A. Sen and J. Hettmer.
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References
Auchmuty, G., Chadam, J., Merino, E., Ortoleva, P. and Ripley, E., ‘The Structure and Stability of Moving Redox Fronts’, accepted for publication in SIAM J. Appl. Math. (1985).
Chadam, J., Ortoleva, P. and Sen, A., ‘Reactive Percolation Instabilities’, 34 mimeo. pages, submitted for publication to JIMA (1985).
Chadam, J. and Ortoleva, P., ‘Morphological Transitions’, chap. XIV of Variety and Structure of Chemical Waves, P. Ortoleva et al., Synergetics Series, H. Haken, ed. (1985).
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© 1987 D. Reidel Publishing Company, Dordrecht, Holland
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Chadam, J. (1987). Reaction-Percolation Instability. In: Nicolis, C., Nicolis, G. (eds) Irreversible Phenomena and Dynamical Systems Analysis in Geosciences. NATO ASI Series, vol 192. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4778-8_26
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DOI: https://doi.org/10.1007/978-94-009-4778-8_26
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8620-2
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