Mode selection in a caricature of eutectic solidification

Abstract

We have studied the problem of mode selection, specifically, selection of the lamellar spacing, in eutectic solidification, by constructing a caricature of a thin-film eutectic solidifying at constant velocity in the presence of a finite temperature gradient and in a slightly noisy environment. Our model incorporates mechanisms which allow termination of substable lamellae and creation of new lamellae by the splitting of lamellae larger than a spacing λ_max. We have studied this model both by a simple analytic approximation and by computer simulation. We find that both the steady state spacing and the regularity of the pattern are sensitively dependent on the ratio λ_max/λ_min, where λ_min is the minimum spacing required for steady state stability. An additional result to emerge from our investigation is that when λ_max becomes less than a critical value, the system apparently undergoes a transition into a chaotic state.