24 Oct

The Deborah number

The Deborah number is a dimensionless (or pure number, like a counting number or pi) used to characterize the fluidity of solid materials.  As long as the following is read as analogy, it matches my Deborah (who’s also named after the Old Testament figure) very very closely.

From the wikipedia page:

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:

 mathrm{De} = frac{t_mathrm{c}}{t_mathrm{p}}

where tc refers to the stress relaxation time (sometimes called the Maxwell relaxation time), and tp refers to the time scale of observation.

Note that the Deborah number is relevant for materials that flow on long time scales (but not for the reverse kind of materials that are viscous on short time scales but solid on the long term).