Directional solidification cells with grooves for a small partition coefficient.

Abstract

Using the asymptotic matching procedure of Dombre and Hakim, we determine properties of the steady-state cellular structures with deep narrow grooves observed in directional solidification experiments. The method is valid in the experimentally relevant region of small partition coefficient and finite P\'eclet number. An extension of the Scheil equation for the grooves is given, and the importance of conservation in determining the groove closing is pointed out.