Experiments on the formation of rippled icicles Ph.D. thesis, Unpublished, Jan. 2023. John Ladan Department of Physics, University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.

Icicles are a common sight during winter weather, hanging from rooftops, railings and other structures from which water drips. The long slender shape of an icicle develops through a highly non-equilibrium process in which supercooled water flows down its surface, partially freezing along the way. This is an example of "wet ice growth". The growth rate is dictated by how quickly latent heat released by freezing can be transported away from the ice surface. The cooling of the liquid is greater at the tip, causing the tip to grow faster, leading its elongated form.

Many icicles are observed to have a rippled pattern along their length with a near universal wavelength of 9 mm. Rippled icicles often have a foggy appearance with small bubbles visible in the interior. While measurements of icicle ripples date back to at least 1933, the mechanism through which they form has eluded physicists. It has previously been shown that the existence and amplitude of ripples depends on the presence of impurities in the source water, but no existing model for icicle ripples includes impurities. The problem of how icicle ripples form in the presence of impurities is the focus of this thesis. A pre-existing model for the rippling instability was extended to include physical effects of impurities. A linear stability analysis was performed on this model, and found that it did not predict ripples. The stability of the model is not sensitive to changes in concentration, so it is unlikely that such a model will ever agree with experiment.

In order to better understand the role of impurities in wet ice formation, we grew icicles using various chemical species as the impurity for concentrations between 0 - 43.9 mMol/kg. The changes in morphology from impurities were only affected by the molar concentration, showing that icicle ripples are a colligative phenomenon, depending only on the number of molecules.

One of the impurities used was sodium fluorescein, a fluorescent dye that fluoresces when dissolved in water. The liquid flowing down the surface of icicles was observed directly using this dye. Contrary to previous models, we find that the ice is incompletely wetted by the liquid phase, and that the whole process is much more stochastic than has been previously assumed. In addition, the presence of impurities modifies the wetting properties of the ice surface, while the emerging topography interacts with the liquid distribution.

Using the fluorescent dye, we also observed the location of impurities trapped inside of icicles. All of the impurities are found inside small spherical inclusions. The inclusions are organized into chevron patterns aligned with the peaks of the ripples. Within the chevrons, a substructure of layered crescent-shaped structures is observed, suggestive of cyclic wetting and freezing. We also examine the crystal grain structure of laboratory icicles, with and without impurities. These observations must inform any successful model of an impurity-driven rip- pling instability. Our results have general implications for the morphological evolution of many natural, gravity-driven, wet ice growth processes.

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The Experimental Nonlinear Physics Group / Dept. of Physics / University of Toronto / 60 St. George St. Toronto, Ontario, Canada, M5S 1A7.