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

Abstract

Ringlike 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, 021603 ͑2003͔͒ 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.

Linear stability analysis of ice growth under supercooled water film driven by a laminar airflow

“…[29][30][31] Therefore, herein we perform a linear stability analysis for ice growth under a supercooled water film driven by a laminar airflow, taking into account the effect of interaction between the air and water flows on the ice growth conditions. There is a significant difference between the current and previous works [15][16][17][18][19] as follows. Our previous works featured a gravity-driven water flow, and the shape of the water-air interface was determined by the action of gravity and surface tension only.…”

“…As shown in Eq. ͑29͒ herein, h 0 and u la are functions of x. k is the amplitude of the water-air interface disturbance, and f a , f l , g a , g l , H a , H l , and H s are dimensionless amplitudes of disturbed parts of the stream function , pressure p, and temperature T. In the following, quasistationary approximation is used for the disturbed fields as in previous papers, [15][16][17][18][19] and we assume that the undisturbed part of temperature gradient within the ice does not exist, hence T s = T sl ͑T sl = 0°C for pure water͒.…”

“…Equations ͑31͒ and ͑32͒ are the same form as those in a previous paper, 19 but the value of Ḡ a‫ء‬ is different. In Eqs.…”

“…18 We extended the above theoretical framework to include natural convection airflow around icicles. 19 It was found that the enhancement of the rate of latent heat loss from the water-air interface to the surrounding air due to airflow caused the amplification rate of the ice-water interface disturbance to increase. However, the wavelength of ice ripples was not significantly affected by the airflow.…”

“…19 However, when wind speed is large, the wind drag at the water-air interface also drives the water film. For example, the combination of two driving mechanisms due to gravity and wind drag produces a variety of aufeis ͑also referred to as icings͒ morphologies with various surface features.…”