The effect of marangoni convection on fibrous monotectic growth

Directional solidification of monotectic alloys can lead, under certain conditions of growth velocity and temperature gradient in the melt, to composite microstructures with a rodlike appearance. For a theoretical description, most often the Jackson and Hunt model of rod eutectic growth is used. A relation between the mean rod distance R and the solidification velocity v, similar to eutectics, is generally observed in experiments. A comparison between theory and experiments always led to discrepancies not yet fully resolved. In the approach presented here, we propose an additional mode of mass transport ahead of the monotectic solidification front, namely, Marangoni convection. The main difference between monotectic and eutectic solidification seems to be the liquid phase state of the (rod) L2 phase growing simultaneously within a nearly perfectly pure solid matrix. We assume that the thermocapillary effect causes convection at the interface of the fibrous liquid phase. This Marangoni convection induces a flow field in the matrix and has an influence on the solute transport if the fluid flow Peclet number is large enough. First, an analytical model is described using a suitably modified convective diffusion equation for the concentration field; and, second, a numerical model is presented. The main result of both models is a new functional relation between fiber spacing and solidification velocity being explicitly dependent on the temperature gradient ahead of the solidification front.