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Related Experiment Video

Updated: Jun 5, 2026

Characterization of Thermal Transport in One-dimensional Solid Materials

Characterization of Thermal Transport in One-dimensional Solid Materials

Published on: January 26, 2014

Maximal potential energy transport: a variational principle for solidification problems.

A J Wells¹, J S Wettlaufer, S A Orszag

¹Department of Geology and Geophysics, Yale University, New Haven, Connecticut 06520, USA.

Physical Review Letters

|January 15, 2011

Summary

This summary is machine-generated.

Chimney spacing in mushy layers optimizes material transport by maximizing energy removal. Below a critical spacing, chimneys collapse, showing hysteresis between flow and no-flow states.

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Area of Science:

Materials Science
Fluid Dynamics
Thermodynamics

Background:

Mushy layers form during alloy solidification, featuring channels called chimneys.
Chimneys are crucial for transporting material via buoyancy effects.
Observed experimental coarsening of chimney spacing suggests an optimization process.

Purpose of the Study:

To numerically analyze mechanisms controlling chimney spacing in 2D mushy layers.
To test the hypothesis that spacing optimizes material transport and energy removal.
To investigate the relationship between chimney spacing, solute flux, and material transport.

Main Methods:

Numerical analysis of two-dimensional mushy layers during binary alloy solidification.
Investigating the role of buoyancy-driven convection within chimneys.
Examining the influence of mush Rayleigh number on solute flux and chimney dynamics.

Main Results:

Optimal solute flux increases with the mush Rayleigh number.
A critical chimney spacing exists below which chimneys collapse.
Hysteresis observed between chimney convection and no-flow states.

Conclusions:

Chimney spacing adjusts to optimize material transport and potential energy removal.
The dynamics of this dissipative system appear governed by a variational principle.
Results provide insight into the control mechanisms of solidification processes.