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Film Control to Study Contributions of Waves to Droplet Impact Dynamics on Thin Flowing Liquid Films

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Capillary-wave description of rapid directional solidification.

Alexander L Korzhenevskii¹, Richard Bausch, Rudi Schmitz

¹Institute for Problems of Mechanical Engineering, RAS, Bol'shoi prospekt, V. O. 61, St. Petersburg 199178, Russia.

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

|April 3, 2012

Summary

This study generalizes capillary-wave theory for binary alloy directional solidification, revealing a universal dispersion relation and a differential equation explaining solute banding formation via interface oscillations and Mullins-Sekerka instability.

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Area of Science:

Materials Science
Solidification Physics
Thermodynamics

Background:

Existing capillary-wave models for binary alloy solidification lack comprehensive inclusion of directional solidification processes.
Understanding interface stability is crucial for controlling alloy microstructure and properties.

Purpose of the Study:

To generalize the capillary-wave description for binary alloy solidification to incorporate directional solidification.
To derive a universal dispersion relation for solidification front stability.
To establish a model for solute band formation during solidification.

Main Methods:

Generalization of the capillary-wave theory.
Derivation of a universal dispersion relation for unstable eigenmodes.
Establishment of a differential equation for interface oscillatory motions.

Main Results:

A universal dispersion relation for the unstable eigenmodes of a planar steady-state solidification front was derived.
A differential equation describing oscillatory interface motions was established.
The model provides a limit-cycle scenario for solute band formation, including the Mullins-Sekerka instability.

Conclusions:

The generalized capillary-wave theory offers a unified framework for analyzing solidification front stability.
The derived model successfully explains the formation of solute bands and banded structures.
This work advances the understanding of pattern formation during alloy solidification.