Multicomponent Diffusion Modelling Applied to the Sudbury Igneous Complex
Multicomponent Diffusion Modelling Applied to the Sudbury Igneous Complex
Abstract ID#: 36769
English Abstract:
Chemical diffusion is an essential transport mechanism for many magmatic processes. Diffusion across interfaces separating liquid layers with initially stable density distributions may engender unstable density distributions leading to rapid homogenization of the layers. We developed a finite difference model to simulate diffusion in a multicomponent silicate melt in order to better understand the evolution and differentiation of igneous systems, in particular, the Sudbury Igneous Complex in Ontario, one of the largest meteorite impact craters on Earth. The Sudbury impact melt was differentiated into norite cumulates, quartz gabbro, and granophyre. Within the granophyre unit, there exists a second layer of quartz gabbro which suggests a reversal in the crystallization sequence. This reversal might be explained as a boundary between two melt bodies, separated by either temperature or composition or both, that must have allowed diffusion-driven chemical exchange.
The diffusion partial differential equation is modelled using the semi-implicit Crank-Nicolson finite difference scheme, which involves spatial discretization and solving a system of equations to advance in time. The diffusion coefficient is a proportionality constant between the molar flux and the concentration gradient. The matrix of diffusion coefficients is called the diffusion matrix and is obtained from empirical experiments on the five-component K20-Na20-Al2O3-SiO2-H2O system. Taking an average composition of the granophyre above the boundary and an average composition of the Copper Cliff offset dikes and projecting them onto the five component system, we ran the model at 1200 degrees at 5000 bar. Preliminary results show an overstable density distribution when the magmas are dry and fingering instabilities when >3 weight percent water is added to the upper layer; however, at approximately 2 weight percent water, the upper layer is able to diffuse stably with the lower layer, allowing the two magma bodies to evolve without being rapidly homogenized by diffusion-driven convection.
The diffusion partial differential equation is modelled using the semi-implicit Crank-Nicolson finite difference scheme, which involves spatial discretization and solving a system of equations to advance in time. The diffusion coefficient is a proportionality constant between the molar flux and the concentration gradient. The matrix of diffusion coefficients is called the diffusion matrix and is obtained from empirical experiments on the five-component K20-Na20-Al2O3-SiO2-H2O system. Taking an average composition of the granophyre above the boundary and an average composition of the Copper Cliff offset dikes and projecting them onto the five component system, we ran the model at 1200 degrees at 5000 bar. Preliminary results show an overstable density distribution when the magmas are dry and fingering instabilities when >3 weight percent water is added to the upper layer; however, at approximately 2 weight percent water, the upper layer is able to diffuse stably with the lower layer, allowing the two magma bodies to evolve without being rapidly homogenized by diffusion-driven convection.