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The rippling instability of icicles

Presented by: 
Stephen Morris
Thursday 14th April 2016 - 16:00 to 17:00
INI Seminar Room 1
Co-authors: Jake Wells (Dept. of Physics, University of Toronto, Toronto ON Canada M5S 1A7), Alina Barnett (Dept. of Physics, McMaster University of Toronto, Hamilton ON Canada L8S 4M1), Josh Calafato (Dept. of Physics, University of Toronto, Toronto ON Canada M5S 1A7), Ken Liao (Dept. of Physics, University of Toronto, Toronto ON Canada M5S 1A7), Antony Szu-Han Chen (Southern Alberta Institute of Technology, Calgary AB Canada T2M 0L4), John Ladan (Dept. of Physics, University of Toronto, Toronto ON Canada M5S 1A7)

Icicles are a common ice formation, familiar to anyone who lives in a cold climate. The shape of an icicle emerges from a delicate dance between solidification, hydrodynamics and heat transport. Many, but not all, natural icicles are observed to be decorated around their circumference by ribs or ripples. These features are presumed to be the result of a morphological instability in the growth process of the ice. The sides of an icicle are covered by a thin supercooled water film which flows down their nearly vertical surface. The wavelength of the ripples, which is always found to be near 1~cm, is surprisingly constant, even under diverse growing conditions. A recent detailed study in which hundreds of icicles were grown in controlled laboratory experiments revealed that trace amounts of impurities are required for the formation of the ripples. Icicles grown from distilled water have no ripples. Ripples appear at a remarkably low concentration of impurity, becoming me asurable above a concentration of just 10−3 weight \% of salt. Thereafter, they grow at a rate which is roughly logarithmic in the concentration of the impurity. These effects are not explained by linear stability theory which does not account for impurities.

In this talk, we will discuss our recent experiments in which the concentration and molecular species of the impurity were varied, as well as our progress toward a generalized linear stability analysis of the growing ice surface, which includes the effects of impurities. The theory crucially depends on the boundary conditions on the ice-water interface and the possible presence of a mushy layer near this interface.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons