Rheology of Wormlike Micelles: Two Universality Classes

We identify two classes of rheology in solutions of wormlike micellar chains which break reversibly. In ``mean-field'' (MF) systems, new ends created by breaks recombine with other chains and stress relaxes exponentially [M. E. Cates, Macromolecules 20, 2289 (1987)]. By contrast, in ``diffusion-controlled'' (DC) cases, self-recombination dominates and the relaxation process is a L\'evy walk, leading to algebraic short time decay. The long time decay remains exponential, but with a different time scale. Our estimates suggest that current experimental systems include both MF and DC types.