Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Pattern selection in ternary mushy layers

Published

Author(s)

Daniel M. Anderson

Abstract

We consider finite-amplitude convection in a mushy layer during the primary solidification of a ternary alloy. A previous linear theory identified, for the case of vanishing latent heat, solute rejection and background solidification, a direct mode of convective instability when all the individual stratifying agencies (thermal and two solutal) were statically stabilizing. The physical mechanism behind this instability was attributed to the local-phase-change effect on the net solute balance through the liquid-phase solutal diffusivity. A weakly nonlinear development of this instability is investigated in detail. We examine the stability of two-dimensional roll, and three-dimensional square and hexagonal convection patterns. The amplitude evolution equations governing roll/square and roll/hexagon competition are derived. We find that any of rolls, squares or hexagons can be nonlinearly stable, depending on the relative importance of a number of physical effects as reflected in the coefficients of the amplitude equations. The results for a special case are found to isolate a purely double-diffusive phase-change mechanism of pattern selection. Subcritical behaviour is identified inside the domain of individual static stability.
Citation
Journal of Fluid Mechanics
Volume
825

Keywords

Mushy Layer, Solidification, Ternary Alloy, Weakly-nonlinear stability

Citation

Anderson, D. (2017), Pattern selection in ternary mushy layers, Journal of Fluid Mechanics, [online], https://doi.org/10.1017/jfm.2017.382 (Accessed December 7, 2023)
Created August 24, 2017, Updated September 17, 2020