Experiments on the Growth and Form of Icicles
the growth and form
Ph.D. thesis, Unpublished, Oct. 2013.
Antony Szu-Han Chen
Department of Physics,
University of Toronto,
60 St. George St., Toronto, Ontario, Canada M5S 1A7.
Icicles are a ubiquitous and picturesque feature of cold winter weather. Their familiar
form emerges from a subtle interplay between the solidification dynamics of ice and the
gravity-driven flow of the thin water film flowing over their evolving surface. The latent
heat released by freezing is advected by the water film and ultimately carried away by the
surrounding sub-zero air, which is also flowing. Like many processes far from equilibrium,
icicle growth can exhibit nonlinear pattern formation. While scaling theory predicts that
icicles converge to `platonic', self-similar shapes, natural icicles often exhibit regular ripple patterns about their circumference, which are due to a morphological instability. This thesis presents a comprehensive experimental study of icicles that sheds new light on the dynamics of their growth and the origin of their form.
A table-top apparatus was designed and built for the controlled growth of icicles,
under different conditions of temperature, water supply rate, ambient air motion, and
water purity. Image analysis and Fourier methods were used to examine their morphology.
Contrary to theoretical expectations, ripples do not appear on icicles made from pure
water. Instead, ripples grow and travel on icicles made from salt solutions, even at
very low concentrations. The addition of non-ionic surfactant or dissolved gases does
not produce ripples, unless ionic impurities are also present. The ripple wavelength is
independent of time and growth conditions. The ripple amplification rate and traveling
velocity vary weakly with the ionic concentration, as do the tip and radial growth speeds
of the icicle. While the tip and radial growth also depend on the ambient temperature and input mass flux, the ripple dynamics is not correlated with extrinsic conditions. If the
ambient temperature or input mass flux is sufficiently low, the tip growth only advances
for a short period of time before it ceases. After cessation, the shape of the icicle deviates increasingly from self-similarity. The most self-similar icicles are made from pure water with the surrounding air gently stirred, whereas icicles made from impure water in still air tend to grow multiple tips.
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