Instabilities in rapid directional solidification under weak flow.

Area of Science:

• Materials Science
• Solidification Physics
• Thermodynamics

Background:

• Directional solidification of binary alloys involves complex interfacial phenomena.
• Nonequilibrium thermodynamics, including speed-dependent segregation coefficients and liquidus slopes, influences solidification pathways.
• Attachment kinetics and interfacial energy play crucial roles in instability formation.

Purpose of the Study:

• To investigate the impact of weak imposed boundary-layer flow on steady cellular (mode S) and pulsatile (mode P) instabilities during rapid alloy solidification.
• To analyze how flow modifies the characteristics of these instabilities, such as their propagation, stability, and spatial structure.
• To develop a theoretical framework, using perturbation methods, to describe these flow-induced changes across different flow magnitudes.

Main Methods:

• Application of regular perturbation theory in powers of the flow magnitude |V|.
• Utilizing a modified expansion in powers of V^(1/3) near critical points where neutral curves cross.
• Development of a uniform composite expansion valid for all small |V| to capture the behavior of instabilities under flow.

Main Results:

• For small |V|, mode S transitions from a steady state to a traveling instability.
• The imposed flow exhibits a dual effect on mode S stability, stabilizing it for low surface energies and destabilizing it for high surface energies.
• Mode P instability is promoted by the flow, with its critical wave number shifting from zero to nonzero, introducing spatial structure.
• Flow-induced changes in mode P frequencies depend on the wave number, increasing for large wave numbers and decreasing for small ones.

Conclusions:

• Weak boundary-layer flow significantly alters the nature and stability of interfacial instabilities during rapid alloy solidification.
• The study provides a comprehensive theoretical understanding of flow effects on both cellular and pulsatile modes, crucial for controlling microstructure.
• The developed perturbation methods offer a robust framework for analyzing flow-interface interactions in various solidification scenarios.