Deborah number

While I prepared a practical experiment for the first-year students in the unit operation of mixing, I did some reading regarding the dimensional analysis and its historical application in Chemical Engineering. I counted up to 21 dimensionless groups in Coulson's Chemical Engineering (Perry's Handbook shows a few less), out of which 19 bear the name of the author _male author. Only 1 number out of these 19 is named after a woman: Deborah number.

However, I found rather peculiar two aspects: first, that Deborah group was proposed by a man if not two (Marcus Reiner and Eugene C. Bingham _yes, sir, the one  that gives name to Bingham plastics); and second, that its derivation (as a simple ratio between two time magnitudes) comes from religious inspiration, rather than from any dimension analysis.

The story is tastefully told by Reiner himself in the after-dinner of the Fourth International Congress in Rheology held in Providence in August 1963. It is indeed a juicy talk, that suggests me the idea of doing a short film out of it, in a documental collection dedicated to the story of the dimensional numbers, and can be found here (it is a pdf file, so you can save it and print it and keep it).

http://www.cours.polymtl.ca/gch2310/Doc%20supplementaire/Deborah-Rainer.pdf

The points of the story that attracts are many: the meeting between Reiner and Bingham, how the term Continuum Mechanics was despised by a chemist like Bingham, the origin of the term rheology, the confusion with the term theology, the train to Oxford from Paddington Station full of theologians and scholars (actually, I will go to Oxford in a few hours, precisely from Paddington, I should have been in bed a few hours ago already), the beautiful Song of Deborah, apparently one of the oldest parts of the Bible (back to the 12th century before Christ), and the incredible remark of Reiner about the necessity of deriving a dimensionless number:

"But Deborah knew two things. First, that the mountains flow, as everything flows. Second, that they flow before the Lord, and not before the man, for the simple reason that man in his short lifetime cannot see them flowing. We may therefore well define as a non-dimensional number the Deborah number D = time of relaxation / time of observation. The difference between solids and fluids is then defined by the magnitude of D"

Reiner also addressed the teapot effect, about which I shall expand a little further some other time.

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