Viscoelastic model , liquid-state

An important and sometimes overlooked feature of all linear viscoelastic liquids that follow a Maxwell response is that they exhibit anti-thixo-tropic behaviour. That is if a constant shear rate is applied to a material that behaves as a Maxwell model the viscosity increases with time up to a constant value. We have seen in the previous examples that as the shear rate is applied the stress progressively increases to a maximum value. The approach we should adopt is to use the Boltzmann Superposition Principle. Initially we apply a continuous shear rate until a steady state... 

While the Choi and Schowalter [113] theory is fundamental in understanding the rheological behavior of Newtonian emulsions under steady-state flow, the Palierne equation [126], Eq. (2.23), and its numerous modifleations is the preferred model for the dynamic behavior of viscoelastic liquids under small oscillatory deformation. Thus, the linear viscoelastic behavior of such blends as PS with PMMA, PDMS with PEG, and PS with PEMA (poly(ethyl methacrylate))at <0.15 followed Palierne s equation [129]. From the single model parameter, R = R/vu, the extracted interfacial tension coefficient was in good agreement with the value measured directly. However, the theory (developed for dilute emulsions) fails at concentrations above the percolation limit, 0 > (p rc 0.19 0.09. 

At very short times this simplifies to elastic behaviour. Then at t = r, the stress is 1/e of its value at steady state, where it is cr= 77/, i.e. purely steady-state viscous behaviour. The start-up of real viscoelastic liquids may need to be modelled using a number of Maxwell elements. However, for most realistic experiments using this kind of test, the response quickly enters the non-linear region since the strain is continually increasing. 

The relaxation of the primary normal stress difference after cessation of steady-state flow at strain rate 7 can also be expressed in terms of linear viscoelastic properties by these models. For example, in terms of the relaxation spectrum, the rubberlike liquid theory of Lodge ° provides ... 

Validity of the linear stress-optical rule points at the dominant role of the network forces in pol3mier melts. The Lodge equation of state can be interpreted on this basis. We introduced the equation empirically, as an ap>-propriate combination of properties of rubbers with those of viscous liquids. It is possible to associate the equation with a microscopic model. Since the entanglement network, although temporary in its microscopic structure, leads under steady state conditions to stationary viscoelastic properties, we have to assume a continuous destruction and creation of stress-bearing chain sequences. This implies that at any time the network will consist of sequences of different ages. As long as a sequence exists, it can follow all imposed deformations. 

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