Quantitative Approaches to Model Viscoelasticity

Example 15.3 Thermocouples and Pitot tubes (used to measure flowrate based on differential pressures) inserted in a flowing stream of a viscoelastic fluid often give erroneous results. Explain. 

Solution. When a viscoelastic fluid in steady-state flow (De — 0) encounters a probe, it must make a sudden (De 0) jog to get around 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 unobstructed stream. 

Example 15.4 (This is believed due to Professor A.B. Metzner and has probably been verified by TV s Mythbusters team.) A paper cup containing water is placed on a tree stump. A 0.22-caliber bullet fired at the cup passes cleanly through, leaving the cup sitting on the stump. The water is replaced by a dilute polymer solution in a second cup. This time, the bullet knocks the cup 25 ft beyond the stump. Explain. 

Expressed in terms of the time-dependent relaxation modulus Gr(t), the response is 

FIGURE 15.10 Generalized Maxwell model for material response to shear. Note that the model can also be used to show the response to extensional stress, a. 

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