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arXiv · 2412.07654

On the shape of ice stalagmites

Daniel Papa·Christophe Josserand·Caroline Cohen
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Abstract

The growth of ice stalagmites obtained by the solidification of impacting droplets on a cooled substrate ($-50^{\circ}$C to $-140^{\circ}$C) is investigated experimentally. It is shown that for any combination of substrate temperature and drop discharge, there is a critical height above which unfrozen water accumulates at the stalagmite's tip, drips and develops into fingers that give a star-shape to the stalagmite. Both the vertical growth and the radial growth of the stalagmite are discussed through the Stefan problem and mass scaling arguments respectively. Finally, a phase diagram that presents the stalagmite aspect ratio in function of the main control parameters is proposed.

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Daniel Papa, Christophe Josserand, Caroline Cohen. 2024-12-10. On the shape of ice stalagmites. https://arxiv.org/abs/2412.07654

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