The oscillatory response of real systems

The most general overall G, G response of real examples of structured liquids is shown in figure 12. The exact values of the moduli and their position in the frequency domain will of course vary, but the indicated overall quahtative behaviour is usually seen if data is available over a wide-enough frequency range. A number of specific regions can often be differentiated, namely 

If the range of testing is artificially extended by using different temperatures (the so-called time/ temperature superposition principle), then for many materials, it is often possible to see all the regions described by superimposing the data using suitable shift factors, see Ferry [9]. 

We will now show various practical examples of viscoelastic behaviour in oscillatory flow. 

1 Viscous erminal region - simple Maxwell behaviour 

There are two specific examples of liquids that often show simple MaxweU-like behaviour within the normal measuring range (lO - 10 Hz), with the expected shapes of the G and G curves and a single relaxation time, viz. associative-thickener-type polymers (see chapter 16 for details) and worm-like surfactant micellar systems, otherwise known as threadlike or rod-like micelles (linear or branched). (The latter are also called living polymers because if they break imder large stresses, they can reform under conditions of rest or low stress (see chapter 18).) The typical response of such a system is shown in figure 14, where a representative relaxation time would be around 1 s, see [10]. 

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