Flow-induced gelation of living (micellar) polymers

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Abstract
We consider the effect of shear velocity gradients on the size (L) of rodlike micelles in dilute and semidilute solution. A kinetic equation is introduced for the time‐dependent concentration of aggregates of length L, consisting of ‘‘bimolecular’’ combination processes L+L’ →(L+L’) and ‘‘unimolecular’’ fragmentations L→L’+(L−L’). The former are described by a generalization (from spheres to rods) of the Smoluchowski mechanism for shear‐induced coalesence of emulsions, and the latter by incorporating the tension‐deformation effects due to flow. Steady‐state solutions to the kinetic equation are obtained, with the corresponding mean micellar size (L̄) evaluated as a function of the Peclet number P, i.e., the dimensionless ratio of flow rate γ̇ and rotational diffusion coefficient Dr. For sufficiently dilute solutions, we find only a weak dependence of L̄ on P. In the semidilute regime, however, an apparent divergence in L̄ at P≂1 suggests a flow‐induced first‐order gelation phenomenon.