M6 Non-Newtonian Flow: Melt Rheology

Topic

When this polymer melt is subjected to shear flow, the flow progressively disentangles molecular chains that—at rest—remain intertwined within the "tube" described by another model in this set. The faster the shear flow, the less time these molecular chains have to re-entangle before the flow disentangles them again; consequently, they remain more disentangled, on average, for the duration of the flow. This flow-induced disentanglement results in shear thinning: the melt's viscosity—high at rest when the chains are intertwined—drops as the shear flow increasingly disentangles them.

This overall behavior—ranging from the constant-viscosity plateau exhibited at very low shear rates (where the flow is not yet strong enough to significantly disentangle the chains) to the pronounced shear thinning observed at high shear rates—fits the Carreau-Yasuda model. This is the same model used to describe viscosity variation based on the master curve constructed via oscillatory rheometry (another distinct model in the set); the Carreau-Yasuda model captures, in a single continuous expression, both the low-shear-rate plateau and the high-shear-rate thinning, as well as the gradual transition between the two regimes. Because the constant-viscosity plateau extends to higher shear rates before thinning begins, the Carreau-Yasuda model—when fitted to this full behavior—accordingly places that transition at a higher shear rate. For this reason, the model—introduced via shear thinning and the Carreau-Yasuda fit—allows the steady-shear viscosity of the polymer melt to be linked, through the Cox-Merz relation, to the oscillatory complex viscosity measured via dynamic rheometry (a technique employed by a different model in this set). The Cox-Merz relation equates these two viscosities at numerically equal values ​​of shear rate and angular frequency, thereby enabling the validation of the Carreau-Yasuda model using dynamic rheometry alone, without the need for a separate steady-shear test. The fact that this shear-thinning behavior—driven by a microscopic mechanism of molecular chain disentanglement specific to the polymer melt—shares a mathematical form similar to that of a model describing particle suspensions in a different class of materials (where the underlying microscopic mechanism is necessarily different, even if I do not recall the specific details) means that both models share the same mathematical structure without sharing the same underlying physical cause.

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