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Related Experiment Video

Updated: May 2, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

Stability of a directional solidification front in subdiffusive media.

Mohammad Abu Hamed¹, Alexander A Nepomnyashchy²

¹Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel and Department of Mathematics, The college of Sakhnin-Academic College for Teacher Education, Sakhnin 30810, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 4, 2014

Summary

Crystal growth instability in alloys is affected by anomalous diffusion, deviating from normal Brownian motion. This study generalizes the Mullins-Sekerka criterion for directional solidification under anomalous diffusion conditions.

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Last Updated: May 2, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

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Published on: February 22, 2018

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Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

Published on: May 15, 2017

Area of Science:

Materials Science
Solidification Physics
Non-equilibrium Thermodynamics

Background:

Crystal growth efficiency is often limited by morphological instability.
This instability arises from a feedback loop between interface deformation and solute diffusion.
Normal diffusion models assume Brownian motion, but anomalous diffusion occurs in complex media.

Purpose of the Study:

To investigate the impact of anomalous diffusion on directional solidification fronts.
To generalize the Mullins-Sekerka stability criterion for anomalous diffusion scenarios.
To derive a nonlinear evolution equation describing interface cellular structures.

Main Methods:

Linear stability analysis of a moving planar solidification front.
Derivation of a generalized stability criterion.
Asymptotic analysis to obtain a nonlinear evolution equation.

Main Results:

A generalized Mullins-Sekerka stability criterion for anomalous diffusion was obtained.
A Sivashinsky-type nonlinear evolution equation governing interface cellular structures was derived.
The study demonstrates how anomalous diffusion modifies solidification front stability.

Conclusions:

Anomalous diffusion significantly impacts crystal growth stability.
The derived generalized criterion and evolution equation provide new tools for understanding alloy solidification.
This work extends classical solidification theory to include memory effects from anomalous diffusion.