= Full thermal stability of a travelling solidification front
{title2=$\sigma=(V-2\kappa\Gamma\alpha^2/\Delta T)Q-V^2/(2\kappa)$}
Retaining perturbation thermal diffusion gives
$$
Q=\sqrt{\alpha^2+V^2/(4\kappa^2)+\sigma/\kappa},
\qquad r_s=Q-V/(2\kappa),\quad r_l=-Q-V/(2\kappa).
$$
The displaced interfacial <temperature> and <Stefan condition> give the displayed implicit <dispersion relation>. In the capillarity-free limit its growing branch is exactly $\sigma=V\alpha$, which checks the limits of the <small-wavelength thermal approximation for a solidification front>.
Back to article page
