Pattern formation in crystal growth under parabolic shear flow II

TL;DR

This paper investigates the mechanisms behind wavy pattern formation during ice growth on inclined surfaces, highlighting the role of restoring forces and phase differences in interface stability, distinct from classical diffusion-driven instabilities.

Contribution

It introduces a new mechanism involving phase differences and restoring forces that explains morphological stability in ice growth, expanding beyond traditional Mullins-Sekerka theory.

Findings

Restoring forces influence interface stability through phase differences.

A new instability mechanism differs from Mullins-Sekerka instability.

Stability depends on the interplay between heat flux and interface fluctuations.

Abstract

Wavy pattern of ice with a specific wavelength occurs during ice growth from a thin layer of undercooled water flowing down the surface of icicles or inclined plane. In the preceding paper [K. Ueno, Phys. Rev. E {\bf 68}, 021603 (2003)], we have found that restoring forces due to gravity and surface tension is a factor for stabilization of morphological instability of the solid-liquid interface. However, the mechanism for the morphological instability and stability of the solid-liquid interface has not been well understood. In the present paper, it is shown that a phase difference between fluctuation of the solid-liquid interface and distribution of heat flux at the deformed solid-liquid interface, which depends on the magnitude of the restoring forces, is a cause of the instability and stability of the interface. This mechanism is completely different from the usual Mullins-Sekerka instability due to diffusion and stabilization due to the Gibbs-Thomson effect.