Numerical and experimental verification of a theoretical model of ripple formation in ice growth under supercooled water film flow

Abstract

Abstract. Little is known about morphological instability of a solidification front during the crystal growth of a thin film of flowing supercooled liquid with a free surface: for example, the ring-like ripples on the surface of icicles. The length scale of the ripples is nearly 1 cm. Two theoretical models for the ripple formation mechanism have been proposed. However, these models lead to quite different results because of differences in the boundary conditions at the solid-liquid interface and liquid-air surface. The validity of the assumption used in the two models is numerically investigated and some of the theoretical predictions are compared with experiments.

Hydrodynamically locked morphogenesis in karst and ice flutings

“…Past theoretical works have explained the formation of icicles by pure water falling films (e.g. Ueno et al 2010), but the recent experimental findings by Chen & Morris (2013) have questioned whether pure water is able to trigger icicle formation. The experiments in fact required the presence of dissolved salts in order to see appreciable instabilities.…”

“…When coupled to heat conservation equations and an interface evolution law (i.e. the Stefan condition), this equation allowed the stability analysis of icicles (Ueno et al 2010) and ice ripples (Camporeale & Ridolfi 2012b) to be developed theoretically. Some doubts have been raised by Chen & Morris (2013) on the validity of the former theory that we will comment on later, in § 3.4.…”

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

“…Finally, upward ripple motion at about half speed of the mean growth rate of icicle radius was observed experimentally as theoretically predicted, but downward traveling ripples were not observed. 7 In the previous theoretical models, [3][4][5][6][7] ice was covered with a supercooled water layer and there was no airflow around icicles. The latent heat released at the ice-water interface was assumed to be transferred in the air by thermal diffusion through the water layer.…”

“…[3][4][5][6][7] A stability analysis for the ice-water interface disturbance was developed based on heat flow in the water and atmosphere, and thin film water flow dynamics. From the initial model, it was found that the ripple wavelength is determined from =2h 0 Pe l / ␣ max , and that the ripples should move down the icicle.…”

Sculpting of Rocks by Reactive Fluids

“…Icicles are stalactites, where ripples decorate the surface as for their limestone analogue (Fig. 4.17b and Ueno et al, 2010). Spectacular dissolution scallops form on the walls of melt water tunnels in glaciers, just as in the analogous karst setting, and rillenkarst is a familiar sight on melting glaciers and ice cubes in drinks (Fig.…”