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 timehyphen;dependent concentration of aggregates of lengthL, consisting of lsquo;lsquo;bimolecularrsquo;rsquo; combination processesL+Lrsquo;rarr;(L+Lrsquo;) and lsquo;lsquo;unimolecularrsquo;rsquo; fragmentationsLrarr;Lrsquo;+(Lminus;Lrsquo;). The former are described by a generalization (from spheres to rods) of the Smoluchowski mechanism for shearhyphen;induced coalesence of emulsions, and the latter by incorporating the tensionhyphen;deformation effects due to flow. Steadyhyphen;state solutions to the kinetic equation are obtained, with the corresponding mean micellar size (Lmacr;) evaluated as a function of the Peclet numberP, i.e., the dimensionless ratio of flow rate ggr;dot; and rotational diffusion coefficientDr. For sufficiently dilute solutions, we find only a weak dependence ofLmacr; onP. In the semidilute regime, however, an apparent divergence inLmacr; atPbartil;1 suggests a flowhyphen;induced firsthyphen;order gelation phenomenon.
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