On the role of confinement on solidification in pure materials and binary alloys

Abstract

We use a phase-field model to study the effect of confinement on dendritic growth, in a pure material solidifying in an undercooled melt, and in the directional solidification of a dilute binary alloy. Specifically, we observe the effect of varying the vertical domain extent (δ) on tip selection, by quantifying the dendrite tip velocity and curvature as a function of δ, and other process parameters. As δ decreases, we find that the operating state of the dendrite tips becomes significantly affected by the presence of finite boundaries. For particular boundary conditions, we observe a switching of the growth state from 3D to 2D at very small δ, in both the pure material and alloy. We demonstrate that results from the alloy model compare favorably with those from an experimental study investigating this effect.

Acknowledgement

The authors gratefully acknowledge support for this work from NASA under Grant NAG 8-1657, and from the National Science Foundation under Grant DMR 01-21695. We thank Jun-Ho Jeong and Navot Israeli for their significant contributions in the development and implementation of the adaptive grid algorithm which made this study possible, and the Computational Science and Engineering program at UIUC for availing us their computing facilities.