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Freezing, Outside-In

March 9, 2017

While my childhood was influenced in many ways by Walt Disney's creations, I now try to avoid all things Disney, since I object to that company's advocacy of perpetual copyright. As a child of the 1950s, I watched Disney's Davy Crockett, and the Mars exploration episodes of Walt Disney Presents. I also enjoyed watching Annette Funicello , a native of my home town of Utica, New York, on The Mickey Mouse Club.

One Christmas ritual of my family is our watching an old VHS tape of Christmas-themed Disney cartoons entitled, "A Walt Disney Christmas." The earliest cartoon on this tape is the 1932 Santa's Workshop. Although I found a copy of this cartoon on YouTube, I believe that it's still under copyright after all these years. The term for a 1934 copyright, barring other circumstances, is presently 95 years. The cartoon is notable in the unusual sense that it contains fleeting racial and ethnic stereotypes, most of which have been removed in later releases.

The Disney animated films, especially the so-called "Disney Princess" films are wildly popular, since they entertain both children and their parents and grandparents. There's been an attempt to recast these films to make them attractive to boys in addition to girls. Thus, recent films such as the 2010 Tangled and 2013 Frozen, aren't titled after a female character, and they feature many action sequences.

A Princess of Mars book cover, 1917A public domain princess.

Cover of a 1917 edition of A Princess of Mars by Edgar Rice Burroughs.

I enjoyed reading all the Barsoom books of Burroughs, but I never read any Tarzan.

(Cover art by Frank E. Schoonover, via Wikimedia Commons.)

While the magical aspects of Frozen are fiction, there is some respect for the physics of ice and the freezing of water; notably, the idea that ice can be created out of water in the air to blanket the Kingdom of Arendelle. However, as pointed out in a paper by Aaron Goldberg of McMaster University, the physics of this movie fails when you consider the energy required to freeze all that water.[1]

Since the Hans Christian Andersen "Snow Queen" fairy tale on which the movie is based has the Norwegian fjord, Nærøyfjord, as the frozen locale, Goldberg calculated that about 1011 kilograms of water are involved. A Carnot cycle refrigerator, the most efficient heat engine, would require 5.8 x 1015 joules to freeze that much water into ice. This is about a hundred times the energy released in the Hiroshima atomic bomb. Writes Goldberg,

"This immense number puts Elsa's power into perspective, implying either that the Snow Queen has enormous strength, or that Disney underestimated the ramifications of their animated fantasy."[1]

The Snow Queen is one feminist that you wouldn't want to rile!

The Snow Queen by William Heath Robinson, 1913The Snow Queen, a 1913 illustration by William Heath Robinson (1872-1944).

(Via Wikimedia Commons.)

It comes as no surprise to a crystal grower like me that ice tends to nucleate on atmospheric particles, since large, technologically useful, crystals are grown on smaller seed crystal substrates. The world's deserts inject about 1012 grams of dust into the atmosphere annually.[2] Atmospheric water can exist for days in a supercooled state at very low temperatures, even below -33°C, without changing into ice, but a few particles of dust can transform a cloud of water to ice.[3]

A research team from the Karlsruhe Institute of Technology (Eggenstein-Leopoldshafen, Germany), University College London (London, UK), and the Universität Heidelberg (Heidelberg, Germany) has recently published a study of ice nucleation on potassium-feldspar, KAlSi3O8, a common mineral dust present in the atmosphere.[2-4]
Potassium feldspar (US Geological Survey)Potassium-feldspar, KAlSi3O8.

(United States Geological Survey image, via Wikimedia Commons.)

Feldspar is unusually effective as a substrate for ice nucleation, and this study showed that ice preferentially nucleates at a high rate on surface defects on the feldspar. Nucleation was found to be most favorable on the (100) crystal planes of feldspar, which are not exposed as facets on natural feldspar. This plane, however, is exposed at steps, cracks, and cavities on other facets.[2-3]

Water is unusual among liquids, since it expands when it solidifies to ice, rather than shrink as other liquids do when they solidify. Ice is about 9% larger in volume than the water from which it forms, since ice consists of a hydrogen-bonded array of water molecules, and this forced arrangement of the molecules results in a larger volume.

A team of scientists from the University of Twente (Enschede, the Netherlands), Tsinghua University (Beijing, China), and the Max Planck Institute for Dynamics and Self-Organization (Göttingen, Germany) has just published a study in which they looked at the consequences of this expansion on the dynamics of a drop of water freezing from the outside-in.[5] This study uses high speed video analysis to show how the self-confinement of the expanding inner solid by the outer rigid ice shell is resolved.

Previous studies have revealed two interesting features of this process. First, an ice spicule appears on the droplet surface; and, second, the droplets explode and fly apart into pieces. Such explosions can explain the shapes of the larger ice particles in clouds and hailstone nuclei.[5].

To perform these experiments, the research team placed small droplets of clean, degassed water on a glass slide, coated with a super-hydrophobic layer of candle soot, in a vacuum chamber. This allowed spherical droplets to cool by evaporative cooling in vacuum, and a final supercooled temperature of about -7°C was achieved by placement and control of thermal reservoirs. The final chamber pressure was 340 ± 10 Pa, which is the equilibrium vapor pressure at that temperature. Ice nucleation was accomplished by touching with the tip of silver iodide crystal. Silver iodide crystals are lattice-matched to ice, and this explains their ability to rapidly nucleate ice.[5]

Water droplet freezing ouside-in, then exploding
Water droplet freezing ouside-in, then exploding. A - Ice nucleation at the drop surface; B - Formation of the ice shell; C - An ice spicule emerges from the shell, and grows (D) as the shell cracks and vapor cavities form; E - The cavities have completely healed; F - The spicule tip explodes, emitting splinters at about 3.5 meters per second; I - Final explosion with fragment velocities of 1.5 m/s. The scale bar is 1 mm. (Portion of fig. 2 from Ref. 5.[5])

Details of droplet freezing are seen in the above figure. The ice shell forms in a few tens of milliseconds, then a frozen spicule is ejected, forced out by the increased pressure. The spicule grows in length to about a droplet diameter, and when it stops growing, the internal droplet pressure increases. The droplet shell undergoes numerous cracking and crack-healing cycles; and, finally, after two seconds, the droplet explodes.[5]

The research team developed a mathematical model of the process based on the material and thermophysical properties of ice. The model shows that the fragment velocity for millimeter-sized droplets is independent of the droplet size and depends only on the bulk modulus of water and the tensile stress of the ice. Surface tension becomes important for smaller droplets, and it's predicted that water droplets of radius below 50 micrometers won't explode.[5]

References:

  1. Aaron Goldberg, "Powering Disney's Frozen with a Carnot refrigerator," Journal of Interdisciplinary Science Topics, vol. 3, February 19, 2014. A PDF file can be found here.
  2. Alexei Kiselev, Felix Bachmann, Philipp Pedevilla, Stephen J. Cox, Angelos Michaelides, Dagmar Gerthsen, and Thomas Leisner, "Active sites in heterogeneous ice nucleation—the example of K-rich feldspars," Science, vol. 355, no. 6323 (January 27, 2017), pp. 367-371, DOI: 10.1126/science.aai8034.
  3. Benjamin J. Murray, "Cracking the problem of ice nucleation," Science, vol. 355, no. 6323 (January 27, 2017), pp. 346-347, DOI: 10.1126/science.aam5320.
  4. Understanding how ice crystals form in clouds, London Centre for Nanotechnology, January 27, 2017.
  5. Sander Wildeman, Sebastian Sterl, Chao Sun, and Detlef Lohse, "Fast dynamics of water droplets freezing from the outside-in," arXiv, January 24, 2015.

Permanent Link to this article

Linked Keywords: Childhood; Walt Disney; The Walt Disney Company; Copyright Term Extension Act; perpetual copyright; 1950s; Davy Crockett (miniseries); Mars exploration; Walt Disney anthology television series; Walt Disney Presents; Annette Funicello; Utica, New York; The Mickey Mouse Club; Christmas; ritual; family; VHS tape; cartoon; anta's Workshop (film); YouTube; copyright; racial and ethnic stereotypes; animation; animated film; Disney Princess; child; children; parent; grandparent; rebranding; recast; boy; girl; Tangled; Frozen (2013 film); public domain; princess; book cover; A Princess of Mars; Edgar Rice Burroughs; Barsoom; Tarzan; Frank E. Schoonover; Wikimedia Commons; cold and ice manipulation; magical aspect; fiction; physics; ice; freeze; freezing; water; atmosphere of Earth; air; Kingdom of Arendelle; scientific literature; paper; McMaster University; energy; Hans Christian Andersen; The Snow Queen; fairy tale; Norway; Norwegian; fjord; Nærøyfjord; kilogram; Carnot cycl; refrigerator; efficiency; efficient; heat engine; joule; Hiroshima atomic bomb; feminism; feminist; rile; William Heath Robinson (1872-1944); crystal growth; crystal grower; nucleation; nucleate; technology; technological; crystal; seed crystal; substrate; desert; gram; dust; supercooling; supercooled state; cryogenics; very low temperature; celsius; °C; cloud; research; Karlsruhe Institute of Technology (Eggenstein-Leopoldshafen, Germany); University College London (London, UK); Universität Heidelberg (Heidelberg, Germany); potassium-feldspar; mineral; United States Geological Survey; feldspar; crystallographic defect; surface defect; Miller index; (100) crystal plane; facet; liquid; volume; hydrogen bond; hydrogen-bonded; molecule; scientist; University of Twente (Enschede, the Netherlands); Tsinghua University (Beijing, China); Max Planck Institute for Dynamics and Self-Organization (Göttingen, Germany); dynamics; drop; machine vision; high speed video analysis; solid; stiffness; rigid; spindle; spicule; explosion; explode; hailstone; nucleus; experiment; Henry's law; degass; microscope slide; glass slide; super-hydrophobic layer; candle; soot; vacuum chamber; sphere; spherical; enthalpy of vaporization; evaporative cooling; thermal reservoir; pressure; pascal; Pa; equilibrium vapor pressure; silver iodide; crystal structure; lattice-match; water; droplet; splinter; meters per second; velocity; scale bar; milliseconds; diameter; mathematical model; materials property; thermophysical property; millimeter; independent variable; bulk modulus; tensile stress; surface tension; micrometer.

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