The Deborah Number

During a recent informal writer’s meeting in McMurdo, a scientist and writer (Jack) from the New Harbor foraminifera study asked us if we’d ever heard of “the Deborah Number.” As I recall, we’d been talking about time.

No one had — so another member of the group (Bill) did some digging. Turns out the Deborah Number is a term used by scientists who are studying FLOW (plastics, hydrocolloids), DEFORMATION, etc. This little area of physics which deals with “the mechanics of continuous media” or continua is called “Rheology.” The term rheology itself is based on the Heraclitus phrase: “everything flows.”

The Deborah number is called a “nondimensional number” and can be expressed as:
D = time of relaxation / time of observation.

In rheological terms, Antarctica’s glaciers and the polar ice plateau and the Ross ice shelf are all flowing — projects like TAMDEF tell us that the land itself is flowing in places, just very slowly. Interestingly, this relates to the Deborah number. This tidbit is a bit odd, but strangely thought-provoking, so I am including the following explanation from Marcus Reiner:

Prophetess Deborah sang, “The mountains flowed before the Lord.” When… the Bible was translated into English, the translators, who had never heard of Heraclitus, translated the passage as “The mountains melted before the Lord”- and so it stands in the authorized version. But Deborah knew two things. First, that the mountains flow, as everything flows. But, secondly, that they flowed before the Lord, and not before man, for the simple reason that man in his short lifetime cannot see them flowing, while the time of observation of God is infinite…. The difference between solids and fluids is then defined by the magnitude of D. If your time of observation is very large, or, conversely, if the time of relaxation of the material under observation is very small, you see the material flowing. On the other hand, if the time of relaxation of the material is larger than your time of observation, the material, for all practical purposes, is a solid.
(-M. Reiner, Physics Today, 1964)

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