Shallow cells in directional solidification

The existing theory on two-dimensional transitions (appropriate to thin parallel-plate geometries) is presented in such a way that it is possible to identify easily conditions for the onset of shallow cells. Conditions are given under which succinonitrile-acetone mixtures should undergo supercritical bifurcation in experimentally accessible ranges. These results suggest a means for the quantitative test of the Mullins and Sekerka (1964) model and its weakly nonlinear extensions.