Pattern formation in crystal growth under parabolic shear flow

TL;DR

This paper investigates how shear flow and restoring forces like gravity and surface tension influence the stability and pattern formation of crystal growth interfaces, explaining observed icicle surface patterns.

Contribution

It introduces a new stabilizing effect from restoring forces in crystal growth under shear flow, distinct from the Gibbs-Thomson effect.

Findings

Restoring forces stabilize long wavelength interface modes.

A 1 cm wavelength pattern explains icicle surface waves.

Flow and restoring forces influence pattern formation.

Abstract

Morphological instability of the solid-liquid interface occuring in a crystal growing from an undercooled thin liquid being bounded on one side by a free surface and flowing down inclined plane is investigated by a linear stability analysis under shear flow. It is found that restoring forces due to gravity and surface tension is important factor for stabilization of the solid-liquid interface on long length scales. This is a new stabilizing effect different from the Gibbs-Thomson effect. A particular long wavelength mode of about 1 cm of wavy pattern observed on the surface of icicles covered with thin layer of flowing water is obtained from the dispersion relation including the effect of flow and restoring forces.