Time Dependence in Flow and the Boltzmann Superposition Principle

2 Time Dependence in Flow and the Boltzmann Superposition Principle 

The application of a shear rate to a linear viscoelastic liquid will cause the material to flow. The same will happen to a pseudoplastic material and to a plastic material once the yield stress has been exceeded. The stress that would result from the application of the shear rate would not necessarily be achieved instantaneously. The molecules or particles will undergo spatial rearrangements in an attempt to follow the applied flow field. 

Viscosity / viscosity / increases Viscosity ( viscosity reduces 

Simplistically one could visualise the molecules or particles in that sample either 

Whilst the flow curves of materials have received widespread consideration, with the development of many models, the same cannot be said of the temporal changes seen with constant shear rate or stress. Moreover we could argue that after the apparent complexity of linear viscoeleastic systems the non-linear models developed above are very poor cousins. However, it is possible to introduce a little more phenomenological rigour by starting with the Boltzmann superposition integral given in Chapter 4, Equation (4.60). This represents the stress at time t for an applied strain history  

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