Flow behaviour of entangled surfactant micelles

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Abstract
Many viscoelastic surfactant solutions contain giant, self-assembled micelles. These can be described as `living polymers', whose chains are subject to reversible scission and recombination. Their dynamics in the entangled regime is accordingly modified from the reptation picture for conventional polymer chains. For rapid scission kinetics, the linear viscoelastic spectrum approaches a single-exponential (Maxwell) behaviour: small departures from this can be measured, and the model used to deduce information both on the micellar kinetics (the lifetime of a typical micelle before breaking) and on the structure (the mean micelle length). These ideas work for several systems, but for others, unreasonable trends for these quantities are found. The most likely reason for this is micellar branching effects, which (as far as the reptation - reaction model is concerned) introduce an effective micellar length equal to the mean distance between branch points. Another possible discrepancy comes from the breakdown of mean-field averaging for the micellar reactions. The reptation - reaction model yields a non-linear constitutive equation which shows a non-monotonic dependence of stress on strain rate, in simple steady shear. This leads one to expect flow instabilities, and (with further assumptions) suggests that steady shear-banded flows should arise, in which macroscopic layers of fluid of different shear rates coexist. Several experimental observations support this general picture, although the same instability could instead lead to wall slip, or unsteady flows.