Deborah Number

Ed LaChapelle in McCarthy, Alaska, 2005
Ed LaChapelle in McCarthy, Alaska, 2005

panta rheiEverything flows. If your perspective is right, you see the motion.

Ed Lachapelle introduced quite a few of us to the Deborah Number, while talking about glaciology and about politics out by his shed in McCarthy, where he was splitting firewood.

The Deborah Number is a dimensionless number, often used in rheology to characterize the fluidity of materials under specific flow conditions. It was originally proposed by Markus Reiner, a professor at Technion in Israel, inspired by a verse in the Bible, stating “The mountains flowed before the Lord” in a song by prophetess Deborah (Judges 5:5). It is based on the premise that given enough time even the hardest material, like mountains, will flow. Thus the flow characteristics is not an inherent property of the material alone, but a relative property that depends on two fundamentally different characteristic times.

Formally, the Deborah number is defined as the ratio of the relaxation time characterizing the time it takes for a material to adjust to applied stresses or deformations , and the characteristic time scale of an experiment (or a computer simulation) probing the response of the material. It incorporates both on the elasticity and viscosity of the material. The smaller the Deborah number, the material behaves more fluid like with an associated Newtonian viscous flow. At higher Deborah numbers, the material behavior changes to non-Newtonian regime, increasingly dominated by elasticity, reaching solid like behavior with very high Deborah numbers.

See Markus Reiner. “The Deborah Number.” Physics Today 17 (1964): 62.

For more about Ed LaChapelle, including his essay, “The Ascending Spiral,” which discusses the Deborah Number and much else, see the retrospective on his life in The Avalanche Review April, 2007.

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An ongoing inquiry into change and stability in nature, politics and ourselves, by Ben Shaine