Original paper
Mathematical revision of Korzhinskii's theory of infiltration metasomatic zoning
Guy, Bernard
European Journal of Mineralogy Volume 5 Number 2 (1993), p. 317 - 340
55 references
published: Apr 19, 1993
manuscript accepted: Nov 23, 1992
manuscript received: Aug 19, 1991
DOI: 10.1127/ejm/5/2/0317
Abstract
Abstract The application of the model of chromatography to metasomatism is formulated in the classical work of Korzhinskii (1970). Although this model may not be readily applied to dissolution-precipitation phenomena, it provides a general understanding of the structure of some transport + reaction problems. However, several mathematical points are not correctly treated in Korzhinskii's work and the purpose of the paper is to present a mathematical revision of the model. The problem of the appearance of the composition discontinuities that define the metasomatic zoning needs to be assessed when arbitrary initial conditions are chosen; the precise evolution of discontinuities may then be studied. The nature of the mathematical functions that are the solution of the problem must also be defined: a function that admits discontinuities is not an "ordinary" function and a new mathematical framework is necessary; the mathematical solutions may then be multiple and, in addition to the initial equation of mass balance, a new condition must be written in order to select the solution that has a physical meaning. This allows one to assess the appearance and stability of sharp fronts from a thermodynamical point of view and to predict the location of the fronts on the isotherm. As a consequence the role of diffusion in infiltration metasomatism may be discussed in a new way and appears as related to scale: the composition changes may be considered as sharp fronts when compared to larger systems. Lastly, within this new framework, appropriate numerical simulations are possible, that possess the property of a good stability in the discontinuities. The revised model may also provide qualitative insights into processes where differential movements between a solid and a pervading aqueous fluid or magma are obtained, and whenever there is a tendency to local chemical equilibrium. While sharp fronts are well known to exist in hydrothermal deposits, one must envisage the possibility of evolutions leading to their existence in other contexts and on other scales, both in magmatic and sedimentary rocks
Keywords
chromatography • hyperbolic problems • metasomatism • infiltration • discontinuities • entropy condition