Chamber music: Difference between revisions

Revision as of 00:15, 27 January 2014

The Deborah number (De) 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. The flow characteristics are not inherent properties of the material alone, but a relative property which depends on two fundamentally different characteristic times.

Formally, the Deborah number is defined as the ratio of the relaxation time characterizing the time it takes for a material to adjust to applied stresses or deformations, and the characteristic time scale of an experiment (or a computer simulation) probing the response of the material. It incorporates both the elasticity and viscosity of the material. At lower Deborah numbers, the material behaves in a more fluidlike manner, with an associated Newtonian viscous flow. At higher Deborah numbers, the material behavior enters the non-Newtonian regime, increasingly dominated by elasticity and demonstrating solidlike behavior.^[1]^[2]

The equation is thus:

\mathrm {De} ={\frac {t_{\mathrm {c} }}{t_{\mathrm {p} }}}

where t_c refers to the stress relaxation time (sometimes called the Maxwell relaxation time), and t_p refers to the time scale of observation.

History

It was originally proposed by Markus Reiner, a professor at Technion in Israel, inspired by a verse in the Bible, stating "The mountains flowed before the Lord" in a song by prophetess Deborah (Judges 5:5).

Time-Temperature Superposition

The Deborah Number is particularly useful in conceptualizing the Time–temperature superposition principle. Time-Temperature superposition has to do with altering experimental time scales using reference temperatures to extrapolate on the temperature-dependent mechanical properties of polymers. A material at low temperature with a long experimental or relaxation time behaves like the same material at high temperature and short experimental or relaxation time if the Deborah number remains the same. This can be particularly useful when working with materials which relax on a long time scale under a certain temperature. The practical application of this idea arises in the Williams–Landel–Ferry equation. Time-temperature superposition avoids the inefficiency of measuring a polymer’s behavior over long periods of time at a specified temperature by utilizing the Deborah Number.^[3]

References

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J.S. Vrentas, C.M. Jarzebski, J.L. Dudda (1975) "A Deborah number for diffusion in polymer-solvent systems", AIChE Journal 21(5):894–901, weblink to Wiley Online Library.

Template:NonDimFluMech

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↑ The Deborah Number
↑ Rudin, Alfred, and Phillip Choi. The Elements of Polymer Science and Engineering. 3rd. Oxford: Academic Press, 2013. Print. Page 221.

[1] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

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15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

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[2] The Deborah Number

[3] Rudin, Alfred, and Phillip Choi. The Elements of Polymer Science and Engineering. 3rd. Oxford: Academic Press, 2013. Print. Page 221.

[1]

[2]

[3]

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+The '''Deborah number''' ('''De''') 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. The flow characteristics are not inherent properties of the material alone, but a relative property which depends on two fundamentally different characteristic times.
+Formally, the Deborah number is defined as the ratio of the [[relaxation time]] characterizing the time it takes for a material to adjust to applied stresses or deformations<!-- characterizing the intrinsic fluidity of a material: THIS WILL BE A CIRCULAR EXPLANATION-->, and the characteristic time scale of an experiment (or a computer simulation) probing the response of the material. It incorporates both the elasticity and viscosity of the material. At lower Deborah numbers, the material behaves in a more fluidlike manner, with an associated Newtonian viscous flow. At higher Deborah numbers, the material behavior enters the non-Newtonian regime, increasingly dominated by elasticity and demonstrating solidlike behavior.<ref>{{citation|first=M. |last=Reiner |year=1964|journal=Physics Today|volume =17|issue= 1| page= 62 |title=The Deborah Number|doi=10.1063/1.3051374}}</ref><ref>[http://rrc.engr.wisc.edu/deborah.html The Deborah Number]</ref>
+The equation is thus:
+:<math> \mathrm{De} = \frac{t_\mathrm{c}}{t_\mathrm{p}}</math>
+where ''t''<sub>c</sub> refers to the [[Stress relaxation|stress relaxation time]]  (sometimes called the Maxwell relaxation time), and ''t''<sub>p</sub> refers to the time scale of observation.
+<!--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 (like the Voigt or [[Kelvin material|Kelvin model]]) that are viscous on short time scales but solid on the long term.-->
+'''History'''
+It was originally proposed by [[Markus Reiner]], a professor at [[Technion – Israel Institute of Technology|Technion]] in [[Israel]], inspired by a verse in the [[Bible]], stating "The mountains flowed before the Lord" in a song by prophetess [[Deborah]] ([[Book of Judges|Judges]] 5:5).
+'''Time-Temperature Superposition'''
+The Deborah Number is particularly useful in conceptualizing the [[Time–temperature superposition]] principle. Time-Temperature superposition has to do with altering experimental time scales using reference temperatures to extrapolate on the temperature-dependent mechanical properties of [[polymers]]. A material at low temperature with a long experimental or [[relaxation time]] behaves like the same material at high temperature and short experimental or relaxation time if the Deborah number remains the same. This can be particularly useful when working with materials which relax on a long time scale under a certain temperature. The practical application of this idea arises in the [[Williams–Landel–Ferry equation]]. Time-temperature superposition avoids the inefficiency of measuring a polymer’s behavior over long periods of time at a specified temperature by utilizing the Deborah Number.<ref>Rudin, Alfred, and Phillip Choi. The Elements of Polymer Science and Engineering. 3rd. Oxford: Academic Press, 2013. Print. Page 221.</ref>
+==References==
+{{reflist}}
+* J.S. Vrentas, C.M. Jarzebski, J.L. Dudda (1975) [http://onlinelibrary.wiley.com/doi/10.1002/aic.690210510/abstract "A Deborah number for diffusion in polymer-solvent systems"], [[AIChE]] Journal 21(5):894&ndash;901, weblink to Wiley Online Library.
+{{NonDimFluMech}}
+[[Category:Dimensionless numbers of fluid mechanics]]
+[[Category:Fluid dynamics]]

Chamber music: Difference between revisions

Revision as of 00:15, 27 January 2014

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