Deborah number

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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 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:

De = \frac{t_c}{t_p}

Where tc refers to the characteristic timeframe and tp refers to the timeframe of the phenomenon.

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