Deborah number

Physical key figure
Surname	Deborah number
Formula symbol	${\displaystyle {\mathit {De}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {De}}={\frac {t_{\mathrm {c} }}{t_{\mathrm {p} }}}}$
${\displaystyle t_{\mathrm {c} }}$ Relaxation time ${\displaystyle t_{\mathrm {p} }}$ Observation time
Named after	Debora song
scope of application	Viscoelasticity of fluids

The Deborah number ( symbol :) is a dimensionless number of rheology . It describes the time dependence of the viscoelastic behavior of a fluid as the ratio of its relaxation time to the observation time : ${\displaystyle {\mathit {De}}}$ ${\displaystyle t_{\mathrm {c} }}$ ${\displaystyle t_{\mathrm {p} }}$

${\displaystyle {\mathit {De}}={\frac {t_{\mathrm {c} }}{t_{\mathrm {p} }}}.}$

In the simplest case, the relaxation time would be that from a Maxwell model of the fluid. The "observation time" can e.g. B. the inverse of a shear rate or the frequency of a mechanical excitation can be understood.

The smaller the Deborah number, the more fluid the fluid appears.

history

The inventor of the Deborah number, the Israeli rheologist Markus Reiner , referred to a passage from the Debora song : The mountains poured out before the Lord, Sinai before the Lord, the God of Israel. ( Judgment 5.5  EU ) Accordingly, the mountains are in motion in the face of God, while to human observers they appear to be solid.

Individual evidence

1. ^ M. Reiner (1964) Physics Today , Vol. 17, No. 1, p. 62: The Deborah Number

literature

• John M. Dealy: Weissenberg and Deborah numbers - their Definition and Use , 2010 Rheology Bulletin 79 (2), p. 14