Morphological instability of the solid-liquid interface in crystal growth under supercooled liquid film flow and natural convection airflow

TL;DR

This paper investigates how natural convection airflow influences the formation of ripples on icicles, extending previous models that ignored airflow to better understand the morphological instability of ice-water interfaces.

Contribution

It introduces a theoretical model incorporating natural convection airflow to analyze its effect on ripple wavelength during ice growth.

Findings

Airflow significantly affects ripple formation on icicles.

Ripple wavelength remains nearly constant despite airflow variations.

Extended model aligns better with observed icicle ripple patterns.

Abstract

Ring-like ripples on the surface of icicles are an example of morphological instability of the ice-water interface during ice growth under supercooled water film flow. The surface of icicles is typically covered with ripples of about 1 cm in wavelength, and the wavelength appears to be almost independent of external temperature, icicle radius, and volumetric water flow rate. One side of the water layer consists of the water-air surface and growing ice is the other. This is one of the more complicated moving phase boundary problems with two interfaces. A recent theoretical work [K. Ueno, Phys. Rev. E 68, (2003) 021603] to address the underlying instability that produces ripples is based on the assumption of the absence of airflow around icicles. In this paper, we extend the previous theoretical framework to include a natural convection airflow ahead of the water-air surface and consider whether the effect of natural convection airflow on the wavelength of ripples produced on an ice surface is essential or not.