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The Deborah number is a dimensionless number, used in rheology to characterize how "fluid" a material is. Even some apparent solids "flow" if they are observed long enough; the origin of the name, coined by Prof. Markus Reiner, is the line "The mountains flowed before the Lord" in a song by prophetess Deborah recorded in the Bible (Judges 5:5).
Formally, the Deborah number is defined as the ratio of a relaxation time, characterizing the intrinsic fluidity of a material, and the characteristic time scale of an experiment (or a computer simulation) probing the response of the material. The smaller the Deborah number, the more fluid the material appears.
The equation is thus:
where tc refers to the relaxation time scale and tp refers to the time scale of observation.
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