Flow-induced phase transitions in rod-like micelles

The authors study the dynamics of self-assembling rod-like micelles under both shear and elongational flow. They assume a simple reaction scheme in which two micelles can fuse only if they are collinear. This results in a positive feedback mechanism between micellar alignment and growth. They define tau break as the reaction time for a typical micelle and tau rot as its rotational diffusion time. They consider both the limiting case of tau break > tau rot. By matching these limiting results they are able to make some predictions for the general case. In elongational flow they predict a gelation transition, at some critical flow rate, to a phase of extremely long rods which are fully aligned with the flow axis. It is shown that these rods can be of a length which is very much greater than the mean micellar length in the absence of flow but which is still stable with respect to the tension produced in a flow. It is found that the analogous transition in shear flow is absent although the mean micellar size near the flow axis is still expected to increase sharply at high flow rates. The authors briefly discuss the relevance of the calculations to experiments on shear-induced structures in micellar systems.