The Deborah number

If you consult Wikipedia for the definition of the Péclet number , you’ll find at the bottom of the page a list of all the dimensionless numbers used in fluid dynamics. There are 52 of them, from Archimedes to Womersley. All but two are named after an engineer, scientist, or mathematician. The exceptions are capillary and Deborah.

The Deborah of the dimensionless number is the fourth judge or ruler mentioned in the Book of Judges. After foretelling the Israelites’ victory over the Canaanites in chapter 4, she sings a hymn of victory in chapter 5. As translated in the 1769 King James version, verses 3–5 read as follows:

Deborah’s vivid image of mountains turning to liquid evidently inspired Marcus Reiner. In August 1963 he gave an after-dinner speech at the Fourth International Congress on Rheology, which was held in Providence, Rhode Island. After noting that “flowed” is closer than “melted” to the original Hebrew, he pointed out that mountains do indeed flow—even when not smitten by God—provided one observes them on a time scale of divine length. Reiner went on to define the Deborah number, D:

The Deborah number isn’t the only term that Reiner originated. In the same speech, which was reproduced in Physics Today‘s January 1964 issue, Reiner recounted how he and Eugene Bingham challenged themselves in 1928 to come up with a name for a new and growing field that encompassed plastic flow and colloid chemistry. The name they chose, rheology, comes from the Greek word rheo (ρεω), which means “to flow.”

The name must have caught on quickly. The Society of Rheology formed the following year.