Linear stability analysis of the solidification of a supercooled liquid in a half-space

The instability of the solidifying front of a supercooled liquid in a half-space is investigated by introducing a small disturbance at the solid–liquid interface. A relationship between the thermal properties of the material and the disturbance growth rate is obtained using the heat balance equation at the interface, including the effects of surface curvature on the equilibrium temperature. The heat balance equation is solved numerically and compared to the analytical solution obtained by neglecting the effects of surface curvature. The results show that the thermal gradients increase the growth rates of disturbances at the solid–liquid interface and that the effect of surface curvature results in a decrease in the disturbance growth rates. Further analysis shows that marginal stability occurs in both the longer wavelength and capillary regions.