Bimodal distribution of the solid products in a magmatic chamber: Modelling by fractional crystallization and coupling of the chemical exchanges with the differential melt/solid transport |
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| Authors: | Morad Lakhssassi Bernard Guy Eric Touboul Jean-Yves Cottin |
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| Institution: | 1. Centre SPIN (sciences des processus industriels et naturels), École nationale supérieure des mines, UMR CNRS 6524 Magmas et volcans, 158, cours Fauriel, 42023 Saint-Étienne cedex 2, France;2. Équipe Méthodes et modèles mathématiques pour l’industrie, centre G2I (génie industriel et informatique), École nationale supérieure des mines, 158, cours Fauriel, 42023 Saint-Étienne cedex 2, France;3. LTL UMR CNRS 6524 Magmas et volcans, faculté des sciences, université Jean-Monnet-Saint-Étienne, rue du Docteur-P.-Michelon, 42023 Saint-Étienne cedex 2, France |
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| Abstract: | Our aim is to explain the possible bimodality of the compositions of the magmatic rocks of the same province. In order to do so, we present a model for the crystallization of a magmatic chamber, coupling the three phenomena: solidification, sedimentation, chemical reactions between the solid and the liquid. These three phenomena make two independent dimensionless parameters appear: the ratios of the solidification rate to the transport velocity, and of the chemical kinetics to the transport velocity. The model is written for one independent chemical component. It is shown that, for certain values of the dimensionless parameters, the chemical composition of the chamber can present a bimodal distribution, starting from uniform initial conditions. This model shows that the coupling between three elementary phenomena is enough to explain the bimodality, or more generally the appearance of discontinuities of chemical compositions, without making any additional assumption. |
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