Similarity equation in non-axisymmetric lamellar eutectic growth

Abstract

The authors extend their previous derivation (1991) of similarity laws in directional solidification of eutectics to general non-axisymmetric growth patterns. This involves mathematical subtleties which are not encountered in the symmetric case. The result explains the observation that numerical solutions describing tilted eutectic growth share the basic similarity property of axisymmetric solutions. They find additional scaling relations of the form lambda approximately V-1/2g(G/V), e.g. for the wavelength lambda of a tilted pattern at fixed tilt angle phi (V is the pulling velocity, G the temperature gradient). Discussing the question of universality of the scaling function g for different distinguished wavelengths, the authors are led to the prediction that the transition to a parity-broken state takes place at roughly twice the selected wavelength of the symmetric pattern for sufficiently large velocities and that the ratio of these wavelengths increases with decreasing velocity.