There are a few aspects of the deborah number that I would like clarified. I understand that conceptually it is the amount of time that it would take for a material to begin to flow under a preset stress or shear rate. However, this brings up a few questions:
1. What is the relaxation time of a material? I read that it is the amount of time it takes for a material, when acted upon by an external stress, to lose the stress received. How does a hookean solid have an infinite relaxation time but a newtonian fluid has a relaxation time of 0?
2. Conceptually, what is the observation time of a material? I.e the denominator you divide the relaxation time by to calculate the deborah number.
3. Can there be many different deborah numbers depending on how you define the observation time, stress, shear rate, or temperature that your material is placed under?
"The mountains flowed before the Lord".
A Hookean solid is a perfect solid, i.e., it does not flow. A Newtonian fluid is a perfect liquid, i.e., it only flows. Between these two behaviors we have the rest of matter. The higher the Deborah number, the closer to a perfect solid. Infinite and zero are just the limits of the range of study.
As you mentioned, the Deborah number depends on the observation time. Water is a fluid, but if you jump into a swimming pool you can hurt yourself like you crash with a solid. This is a matter of observation time, i.e., some fluids behave closer to solids under some circumstances.
"The mountains flowed before the Lord".
A Hookean solid is a perfect solid, i.e., it does not flow. A Newtonian fluid is a perfect liquid, i.e., it only flows. Between these two behaviors we have the rest of matter. The higher the Deborah number, the closer to a perfect solid. Infinite and zero are just the limits of the range of study.
As you mentioned, the Deborah number depends on the observation time. Water is a fluid, but if you jump into a swimming pool you can hurt yourself like you crash with a solid. This is a matter of observation time, i.e., some fluids behave closer to solids under some circumstances.
The definition of Deborah number De is available in the chapter that discusses fundamental or basic rheological concepts in Aroon V. Shenoy, Rheology of Filled Polymer Systems, Kluwer Academic Publishers, Netherlands (1999) and also in A. V. Shenoy and D. R. Saini, Thermoplastic Melt Rheology and Processing, Marcel Dekker Inc., New York (1996).
Deborah number is defined as the ratio of the characteristic time to the time scale of deformation. The characteristic time for any material can always be defined as the time required for the material to reach 63.2% or [1-(1/e)] where e = 2.7174 of the ultimate retarded elastic response to a step change. For a fixed value of the characteristic time, there can be different values of the time scale of deformation and hence there can be many different Deborah number values for the same material. If De > 1.0, elastic effects are dominant while if De < 0.5, viscous effects prevail. For any values other than these two extremes, the material would depict viscoelastic behavior.
I'd highly recommend reading the source of this number, an absolutely joyful essay by Markus Reiner from 1964:
http://scitation.aip.org/content/aip/magazine/physicstoday/article/17/1/10.1063/1.3051374
How to calculate Deborah number numerically,
De = stress relaxation time/time scale of observation
I am doing stress relaxation experiment, and I want to calculate Deborah number. How to calculate stress relaxation time? we cannot wait for months or may be years so that our material is completely relaxed? please help.
The following reference discusses the concept of Deborah number with regards to the glass transition:
Article Aspects of the non-crystalline state
Dear Dr
is a dimensionless number, often used in rheology to characterize the fluidity of materials under specific flow conditions. It is based on the premise that given enough time even a solid-like material will flow.
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