Scaling laws and instabilities in electric field-enhanced smelting and refining of steel

摘要

In electric field-enhanced smelting of iron from slag, liquid iron formation at the cathode exhibits a Mullins-Sekerka in-stability, leading to the growth of fingers and enhancing the reaction rate. However, the liquid state of the growing iron phase leads to the expression of this instability that is qualitatively different from the classical example of growth of dendrites in solidification. As the molten iron fingers grow into the slag, there is a surface tension-induced instability that leads to breakup into droplets, and this breakup is accelerated by the higher inward Lorentz force in the narrower regions due to higher current density. And if growth is directed downward, there is a buoyancy instability due to the higher density of iron than slag. These instabilities and their scaling behavior are treated analytically, and compared qualitatively with experimental measurements of finger size.