A phenomenological model for shear-thickening in wormlike micelle solutions

– We present a simple phenomenological model to describe shear-thickening in a wormlike micelle solution. The solution is assumed to undergo a reaction above a critical shear stress, to form a gel-like phase. There is no flow within this “gel” phase, and it is insoluble in the solution. The amount of gel in the system is determined by a competition between a stress-dependent reaction rate, which creates gel, and a constant breakage rate, which destroys gel. We recover a re-entrant region in the stress-shear rate curve, which is only accessible under controlled stress conditions. When the apparent shear rate is fixed, the corresponding stress-shear rate relation is discontinuous. Our results are in qualitative agreement with the experimental observations of Pine et al. Introduction. – Solutions of wormlike micelles show novel non-linear rheology. Shearthinning wormlike micelle solutions are known to “shear-band” [1] such that macroscopic phases with different shear rates coexist within the same system. These observations have been attributed to a multi-valued stress constitutive relation for the solution [2]. Thus, different shear rates can correspond to the same stress such that the average shear rate of the system is held constant. Another class of wormlike micelle solutions, however, show shear-thickening behavior [3]. Pine et al. [4] have found that the sudden viscosity increase that occurs upon shearing these solutions is concomitant with the growth of a new phase. This phase is difficult to characterize structurally, but is not known to exist under equilibrium conditions, and appears to possess the mechanical properties of a gel. The experiments are carried out in a Couette rheometer, with either the outer or inner cylinder rotating and the other cylinder stationary. Dramatically (∗) E-mail: [email protected] c © EDP Sciences j. l. goveas et al.: model for shear-thickening inwormlikemicelle solutions 707