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22. Two different mathematical schemes for solving chemical dissolution-front instability problems in fluid-saturated rocks

Author

Zhao, ChongBin, Hobbs, Bruce, and Ord, Alison

Abstract

Chemical dissolution-front instability (CDFI) problems usually involve multiple temporal and spatial scales, as well as multiple processes. A key issue associated with solving a CDFI problem in a fluid-saturated rock is to mathematically establish a theoretical criterion, which can be used to judge the instability of a chemical dissolution-front (CDF) propagating in the fluid-saturated rock. This theoretical paper deals with how two different mathematical schemes can be used to precisely establish such a theoretical criterion in a purely mathematical manner, rather than in a numerical simulation manner. The main distinguishment between these two different mathematical schemes is that in the first mathematical scheme, a curved surface coordinate system is used, while in the second mathematical scheme, a planar surface coordinate system is employed. In particular, all the key mathematical deduction steps associated with using these two different mathematical schemes are described and discussed in great detail. The main theoretical outcomes of this study have demonstrated that (1) two different mathematical schemes under consideration can produce exactly the same theoretical criterion; (2) the main advantage of using the first mathematical scheme is that the interface conditions at the curved interface between the downstream and upstream regions can be easily described mathematically; (3) the main advantage of using the second mathematical scheme is that the first-order perturbation equations of the CDFI problem can be easily described in a purely mathematical manner.

Published
2024
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32. Introduction

Author

Zhao, Chongbin, Hobbs, Bruce E., Ord, Alison, Ord, Alison, Hobbs, Bruce E., and Zhao, Chongbin

Published
2009
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33. Entropic Bounds for Multi-Scale and Multi-Physics Coupling in Earth Sciences

Author

Regenauer-Lieb, Klaus, Karrech, Ali, Chua, Hui Tong, Poulet, Thomas, Veveakis, Manolis, Wellmann, Florian, Liu, Jie, Schrank, Christoph, Gaede, Oliver, Trefry, Mike G., Ord, Alison, Hobbs, Bruce, Metcalfe, Guy, Lester, Daniel, Abarbanel, Henry, Series editor, Braha, Dan, Series editor, Érdi, Péter, Series editor, Friston, Karl, Series editor, Haken, Hermann, Series editor, Jirsa, Viktor, Series editor, Kacprzyk, Janusz, Series editor, Kaneko, Kunihiko, Series editor, Kirkilionis, Markus, Series editor, Kurths, Jürgen, Series editor, Nowak, Andrzej, Series editor, Reichl, Linda, Series editor, Schuster, Peter, Series editor, Schweitzer, Frank, Series editor, Sornette, Didier, Series editor, Thurner, Stefan, Series editor, Dewar, Roderick C., editor, Lineweaver, Charles H., editor, Niven, Robert K., editor, and Regenauer-Lieb, Klaus, editor

Published
2014
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34. Non-Linear Thermo-Mechanics of Folding in Geomaterials

Author

Paesold, Martin K., Karrech, Ali, Dodwell, Tim, Regenauer-Lieb, Klaus, Bassom, Andrew P., Ord, Alison, Hobbs, Bruce E., Blondel, Philippe, Series editor, Reitner, Joachim, Series editor, Stüwe, Kurt, Series editor, Trauth, Martin H., Series editor, Yuen, David A., Series editor, Pardo-Igúzquiza, Eulogio, editor, Guardiola-Albert, Carolina, editor, Heredia, Javier, editor, Moreno-Merino, Luis, editor, Durán, Juan José, editor, and Vargas-Guzmán, Jose Antonio, editor

Published
2014
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41. Introduction

Author

Zhao, Chongbin, Hobbs, Bruce E., Ord, Alison, Hutter, Kolumban, editor, Zhao, Chongbin, Hobbs, Bruce E., and Ord, Alison

Published
2008
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49. First Steps Towards Modeling a Multi-Scale Earth System

Author

Regenauer-Lieb, Klaus, Poulet, Thomas, Siret, Delphine, Fusseis, Florian, Liu, Jie, Gessner, Klaus, Gaede, Oliver, Morra, Gabriele, Hobbs, Bruce, Ord, Alison, Muhlhaus, Hans, Yuen, David A., Weinberg, Roberto, Rosenbaum, Gideon, Bhattacharji, S., editor, Neugebauer, H. J., editor, Reitner, J., editor, Stüwe, K., editor, Friedman, Gerald M., editor, Seilacher, Adolf, editor, and Xing, Huilin

Published
2009
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50. Non-equilibrium Thermodynamics, Thermomechanics, Geodynamics

Author

Regenauer-Lieb, Klaus, Hobbs, Bruce, Ord, Alison, Yuen, Dave A., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Rangan, C. Pandu, editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Shi, Yong, editor, van Albada, Geert Dick, editor, Dongarra, Jack, editor, and Sloot, Peter M. A., editor

Published
2007
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