Brownian motion of rod-like micelles under flow

Abstract

The dynamics of self-assembling rod-like micelles under both elongational and shear flow have been studied theoretically. For simplicity, a two-dimensional model that is analytically tractable was used; results for three-dimensional systems are also discussed. Simple reaction kinetics were assumed in which two micelles can fuse only if they are collinear. This provides a positive feedback between micellar alignment and growth, which was studied in the regime where micelle–micelle reactions are frequent on the timescale of rotational diffusion. In two dimensions under elongational flow a strong maximum in the mean rod length along the flow axis is predicted. This maximum mean length diverges as a power of the flow rate but does not exhibit an abrupt transition to an aligned ‘gel’ state, in contrast to our earlier results for the three-dimensional system. In two-dimensional shear flow it is shown that the absence of a stable equilibrium direction (in conjunction with Brownian diffusion) also prevents a sharp transition. The existence of a transition in a full three-dimensional shear-flow geometry remains an open theoretical question (although the experimental evidence is in favour); a scaling approach is outlined that should allow this issue to be resolved.