Asymptotic Solutions of Steady Lamellar Eutectic Growth in Directional Solidification for Small Tangent Values of the Contact Angles

Abstract

A system of steady lamellar eutectic growth in directional solidification is considered with the case of small tangent values of the contact angles. The mathematical model is given in the non-dimensional rectangular coordinate system and the uniformly valid asymptotic solutions are obtained based on the method of the asymptotic expansions. The necessary condition for existing asymptotic solutions was obtained. The results indicate that the curvature undercooling and the solute undercooling determined the patterns of the solid–liquid interface. The dimensional average undercooling presents a relationship with eutectic spacing and pulling velocity. It can be seen that the dimensional average undercooling in front of both phases is not equal, and the total average undercooling as a function of the lamellar eutectic spacing exhibits a minimum. The minimum undercooling spacing decreases with an increase in the pulling velocity, which is in good agreement with Jackson and Hunt’s results.

Keywords

• solid–liquid interface
• eutectic system
• asymptotic solution
• matching method