Editing Rheology (section)

=== Deborah number ===

{{Main|Deborah number}}

On one end of the spectrum we have an [[inviscid flow|inviscid]] or a simple Newtonian fluid and on the other end, a rigid solid; thus the behavior of all materials fall somewhere in between these two ends. The difference in material behavior is characterized by the level and nature of elasticity present in the material when it deforms, which takes the material behavior to the non-Newtonian regime. The non-dimensional Deborah number is designed to account for the degree of non-Newtonian behavior in a flow.  The Deborah number is defined as the ratio of the characteristic time of relaxation (which purely depends on the material and other conditions like the temperature) to the characteristic time of experiment or observation.<ref name="deb1" /><ref>{{cite journal|last1=Reiner|first1=M.|title=The Deborah Number|journal=Physics Today|volume=17|issue=1|year=1964|pages=62 |doi=10.1063/1.3051374|bibcode = 1964PhT....17a..62R }}</ref> Small Deborah numbers represent Newtonian flow, while   non-Newtonian (with both viscous and elastic effects present) behavior occurs for intermediate range Deborah numbers, and high Deborah numbers indicate an elastic/rigid solid. Since Deborah number is a relative quantity, the numerator or the denominator can alter the number. A very small Deborah number can be obtained for a fluid with extremely small relaxation time or a very large experimental time, for example.
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When the rheological behavior of a material includes a transition from elastic to viscous as the time scale increases (or, more generally, a transition from a more resistant to a less resistant behavior), one may define the relevant time scale as a relaxation time of the material. Correspondingly, the ratio of the relaxation time of a material to the timescale of a deformation is called [[Deborah number]]. Small Deborah numbers correspond to situations where the material has time to relax (and behaves in a viscous manner), while high Deborah numbers correspond to situations where the material behaves rather elastically.<ref>M. Reiner (1964) ''Physics Today'' volume 17 no 1 page 62 ''The Deborah Number''</ref><ref>[http://rrc.engr.wisc.edu/deborah.html The Deborah Number]</ref>
Note that the Deborah number is relevant for materials that flow on long time scales (like a [[Maxwell material|Maxwell fluid]]) but ''not'' for the reverse kind of materials ([[Kelvin–Voigt material]]s) that are viscous on short time scales but solid on the long term.-->