  We construct a diffuse-interface model of two-phase solidification that
quantitatively reproduces the classic free boundary problem on solid-liquid
interfaces in the thin-interface limit. Convergence tests and comparisons with
boundary integral simulations of eutectic growth show good accuracy for
steady-state lamellae, but the results for limit cycles depend on the interface
thickness through the trijunction behavior. This raises the fundamental issue
of diffuse multiple-junction dynamics.
