Abstract
The potential theoretic methods developed recently at NRL for solving the diffusion equation are applied to the free-boundary problem which describes lamellar solidification in binary eutectic systems. By using these techniques, the original free-boundary problem is reduced to a set of coupled nonlinear integro-differential equations which when solved yield the shape of the solid/liquid interface and the solute concentration on the interface. A simplified version of the general integro-differential equations is derived by assuming that (1) the solute diffusion length is large compared with the lamellar spacing, and (2) the solid/liquid interface is approximately isothermal. Numerical solutions to the approximate equations are obtained and are utilized to assess the effect of interface curvature on the interfacial solute concentrations, and to check the new theory for consistency with experiment.
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