Viscous or Elastic Response The Deborah Number

Response will appear elastic at high Deborah numbers (De 1) and viscous at low Deborah numbers (De 0). 

Consider, for example, the creep response of the four-parameter model (Rgure 15.8). For this model, a logical choice for Xc would be the time constant for its Voigt-Kelvin component, r]2/G2- For De1 (t Xc), the Voigt-Kelvin element and dashpot 1 will be essentially immobile, and the response will be due almost entirely to spring 1, that is, almost purely elastic. For De 0 Xc), the instantaneous and retarded elastic 

Modifications of the devices described in Chapter 14 can also be used to obtain information on the material s elastic response. For example, if the stress is suddenly removed from a rotational viscometer, the creep recovery or elastic recoil of the material can be followed. This provides a value of Xc for the material. 

Example 3. Thermocouples and Pitot tubes inserted in a flowing stream of a viscoelastic fluid often give erroneous results. Explain. 

Solution. When a viscoelastic fluid in equilibrium flow (De 0) encounters a probe, it must make a sudden (De 1) jog to get arount it The retarded elastic response mechanisms simply cannot respond fast enough in the immediate vicinity of the probe, which for all practical purposes behaves as if it were covered with a solid plug. What is measured, therefore, is not characteristic of the fluid in an imobstructed stream. 

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