Cellular growth near absolute stability
- 1 December 1988
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 38 (16) , 11452-11460
- https://doi.org/10.1103/physrevb.38.11452
Abstract
We derive a strongly nonlinear evolution equation for the interface of a directionally solidified binary alloy when surface energies are large. This equation includes interfacial acceleration and the nonlinear effects of surface tension. Bifurcation analysis on this equation reveals that planar interfaces immediately develop three-dimensional structure, and, when the segregation coefficient is near unity, stable hexagonal solutions are found.Keywords
This publication has 16 references indexed in Scilit:
- Modified asymptotic approach to modeling a dilute-binary-alloy solidification frontPhysical Review B, 1988
- Formation of deep grooves in directional solidificationPhysical Review B, 1988
- Anisotropic interface kinetics and tilted cells in unidirectional solidificationJournal of Crystal Growth, 1987
- Directional solidification with buoyancy in systems with small segregation coefficientPhysical Review B, 1986
- Cellular interface morphologies in directional solidification. The one-sided modelPhysical Review B, 1984
- Instabilities and pattern formation in crystal growthReviews of Modern Physics, 1980
- Finite bandwidth, finite amplitude convectionJournal of Fluid Mechanics, 1969
- Distant side-walls cause slow amplitude modulation of cellular convectionJournal of Fluid Mechanics, 1969
- Stability of a Planar Interface During Solidification of a Dilute Binary AlloyJournal of Applied Physics, 1964
- On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 1. The basic behaviour in plane Poiseuille flowJournal of Fluid Mechanics, 1960