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 coalescence 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 (LBAR) evaluated as a function of the Peclet number P, i.e., the dimensionless ratio of flow rate-gamma and rotational diffusion coefficient D(r). For sufficiently dilute solutions, we find only a weak dependence of LBAR on P. In the semidilute regime, however, an apparent divergence in LBAR at P congruent-to 1 suggests a flow-induced first-order gelation phenomenon.