Deborah number 

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.1

The equation is thus:

\mathrm{De} = \frac{t_\mathrm{c}}{t_\mathrm{p}}

where tc refers to the relaxation time scale and tp refers to the time scale of observation.

Reference

  1. ^ M. Reiner (1964) Physics Today volume 17 no 1 page 62 The Deborah Number
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Dimensionless numbers in fluid dynamics
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