Numerical experiment of cyclic layering in a solidified binary eutectic melt

In shallow magmatic intrusions, a characteristic layering structure (hereafter referred to as cyclic layering) can sometimes be observed. This cyclic layering is caused by double diffusion and crystallization kinetics, and different from what is observed as rhythmic layering caused by gravity. The cyclic layering is visualized as differential weathering in response to the differential stiffness caused by textural variations such as those in the volume fraction, number density, and size of vesicles or crystals. The spacing of layers seems to increase according to a geometric progression, like as in Liesegang bands of a diffusion-precipitation system. In order to understand the development condition for cyclic layering and the characteristics of textural variations, such as the spacing of layering in crystallized multi-component melts by conductive cooling, we carried out a numerical experiment on the 1D crystallization process of a binary eutectic melt. This simulation took into account the cooling from contact with country rock as well as the compositional and thermal diffusion and the kinetics of diffusion-limited crystallization. The governing equations include dimensionless control parameters describing the relative importance of thermal diffusion or compositional diffusion (Lewis number, Le) and the effective latent heat release (Stefan number, St). From the results of the numerical experiments, it was found that the layering develops through eutectic oscillation (compositional and thermal oscillation below the eutectic point), suggesting that the bi-activating condition, whereby both phases cooperatively activate their crystallization rates, is essential for the development of layering. No layering is observed at the margin, and the length of the region with no layering increases exponentially with decreasing St. The amplitude of textural oscillation decreases with decreasing St. Thus, practically no layering develops at small latent heat release. Three types of layering structure or oscillatory profiles of texture are observed (short, long and multiple types), depending mainly on Le. Realistic values of Le and St suggest that natural cyclic layering is the multiple or long type of layering. The common ratios of geometric progressions converge with increasing Le to constants in the range of approximately 1.02-1.05, which is similar to the range of the natural observations. Experiments with no latent heat release by the second-phase simulating vesicles show similar oscillatory behaviors, suggesting that the latent heat release of the first crystallizing phase is an essential factor for the development of vesicle layering.