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Mathematics and Mechanics

Russian Academy of Sciences
 Founded
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(Translated from 1958)
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IssuesArchive of Issues2017-3pp.206-213

Archive of Issues

Total articles in the database: 1774
In Russian (): 975
In English (J. Appl. Math. Mech.): 799

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A.A. Afanasyev and E.A. Belyaeva, "The stability of serpentization due to the water flow in a kimberlite pipe," J. Appl. Math. Mech. 81 (3), 206-213 (2017)
Year 2017 Volume 81 Issue 3 Pages 206-213
DOI 10.1016/j.jappmathmech.2017.08.012
Title The stability of serpentization due to the water flow in a kimberlite pipe
Author(s) A.A. Afanasyev (Institute of mechanics, Lomonosov Moscow State University, Moscow, Russia, afanasyev@imec.msu.ru)
E.A. Belyaeva (Institute of mechanics, Lomonosov Moscow State University, Moscow, Russia, eabelyaeva_94@mail.ru)
Abstract A linear analysis of the stability of the course of serpentization, that is, of the exothermic hydration reaction, due to the flow of water in a kimberlite pipe is carried out, taking both the heat conduction and the convective heat transfer by the fluid saturating the pipe rocks into account. It is shown that two different serpentization processes exist: a homogeneous process and an inhomogeneous process associated with a loss of stability by the homogeneous process and a non-uniform reaction rate distribution. Dimensionless similarity parameters that determine the course of the reaction are proposed. It is shown that convective heat transfer promotes a stabilization of the flow and the formation of a homogeneous serpentinite distribution. Other conditions being equal, an increase in the convective heat flux leads to an increase in the wavelengths of the unstable perturbations and to a decrease in their amplitude. A critical value of the flow rate exists, and, when this is exceeded, instability does not develop and serpentinization takes place under homogeneous conditions.
Received 30 November 2016
Link to Fulltext http://www.sciencedirect.com/science/article/pii/S0021892817300783
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