SCIENCE: The point of icicles
EcoPolis
The point of icicles
======================================
Contemplating some of nature's cool creations is always fun. Now a team
of scientists from The University of Arizona in Tucson has figured out
the physics of how drips of icy water can swell into the skinny spikes
known as icicles.
Deciphering patterns in nature is a specialty of UA researchers Martin
B. Short, James C. Baygents and Raymond E. Goldstein. In 2005, the team
figured out that stalactites, the formations that hang from the
ceilings of caves, have a unique underlying shape described by a
strikingly simple mathematical equation.
However, stalactites aren't the only natural formations that look like
elongated carrots. Once the researchers had found a mathematical
representation of the stalactite's shape, they began to wonder if the
solution applied to other similarly shaped natural formations caused by
dripping water.
So the team decided to investigate icicles. Although other scientists
have studied how icicles grow, they had not found a formula to describe
their shape.
Surprisingly, the team found that the same mathematical formula that
describes the shape of stalactites also describes the shape of icicles.
"Everyone knows what an icicle is and what it looks like, so this
research is very accessible. I think it is amazing that science and
math can explain something like this so well. It really highlights the
beauty of nature," Short said.
The finding is surprising because the physical processes that form
icicles are very different from those that form stalactites. Whereas
heat diffusion and a rising air column are keys to an icicle's growth,
the diffusion of carbon dioxide gas fuels a stalactite's growth.
Short, a doctoral candidate in UA's physics department, Baygents, a UA
associate professor of chemical and environmental engineering, and
Goldstein, a UA professor of physics and the Schlumberger Professor of
Complex Physical Systems at the University of Cambridge in England,
published their article, "A Free-Boundary Theory for the Shape of the
Ideal Dripping Icicle," in the August 2006 issue of Physics of Fluids.
The National Science Foundation funded the research.
As residents of cold climates know, icicles form when melting snow
begins dripping down from a surface such as the edge of a roof. For an
icicle to grow, there must be a constant layer of water flowing over
it.
The growth of an icicle is caused by the diffusion of heat away from
the icicle by a thin fluid layer of water and the resulting updraft of
air traveling over the surface. The updraft of air occurs because the
icicle is generally warmer than its surrounding environment, and thus
convective heating causes the air surrounding the icicle to rise. As
the rising air removes heat from the liquid layer, some of the water
freezes, and the icicle grows thicker and elongates.
"At first, we focused only on the thin water layer covering the icicle,
just like we did with stalactites," said Short. "It was only later that
we examined the layer of rising air, which is technically more correct.
Strangely though, both methods lead to the same mathematical shape for
icicles."
The resulting shape turns out to be described by the same mathematical
equation that describes stalactites. One could call it the Platonic
form.
The team wanted to compare the predicted shape to real icicles. Because
icicles are scarce in Tucson, the scientists naturally turned to the
Internet. They were able to compare pictures of actual icicles with
their predicted shape.
The team found that it doesn't matter how big or small the actual
icicles were, they could all fit to the shape generated by the
mathematical equation.
"Fundamentally, just like in the early stalactite work, it's a result
that implies that the shape of an icicle, at least in its ideal,
pristine form, ought to be described by this mathematical equation. And
we found, examining images of icicles, that it is a very good fit,"
senior author Goldstein said.
The team's next step will be to solve the problem of how ripples are
formed on the surfaces of both stalactites and icicles.
###
This news release was prepared by Ryan Krug for the UA's Office of
University Communications.
Researcher contact information:
Martin B. Short
520-621-6786
msh...@physics.arizona.edu
Raymond E. Goldstein
+44 (0)1223 337908
R.E.Go...@damtp.cam.ac.uk
Related website:
Ray Goldstein
www.damtp.cam.ac.uk/user/gold
(Source: University of Arizona)