Nonequilibrium scale selection mechanism for columnar jointing

Nonequilibrium scale selection mechanism
for columnar jointing

Proceedings of the National Academy of Science, 106, 387 (2009).

Lucas Goehring [1],
L. Mahadevan [2]
and Stephen W. Morris [3]

[1] BP Institute for Multiphase Flow, University of Cambridge, Madingley Road, Cambridge, UK CB3 0EZ

[2] School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA 02138

[3] Department of Physics, University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.

Crack patterns in laboratory experiments on thick samples of drying cornstarch are geometrically similar to columnar joints in cooling lava found at geological sites such as the Giant's Causeway. We present measurements of the crack spacing from both laboratory and geological investigations of columnar jointing, and show how these data can be collapsed onto a single master scaling curve. This is due to the underlying mathematical similarity between theories for the cracking of solids induced by differential drying or by cooling. We use this theory to give a simple quantitative explanation of how these geometrically similar crack patterns arise from a single dynamical law rooted in the nonequilibrium nature of the phenomena. We also give scaling relations for the characteristic crack spacing in other limits consistent with our experiments and observations, and discuss the implications of our results for the control of crack patterns in thin and thick solid films.


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