# Pattern formation in crystal growth under parabolic shear flow

Source: [Pattern formation in crystal growth under parabolic shear flow](<https://www.sota2.com/research/paper/68fa26142c2a3760193b6628>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T03:03:27.050Z

Authors: K. Ueno

Published: 2003-06-03T09:10:57.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0306055>)

[PDF](<https://arxiv.org/pdf/cond-mat/0306055.pdf>)