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 w
ithin 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 dest
roys gel. We recover a re-entrant region in the stress-shear rate curve, wh
ich is only accessible under controlled stress conditions. When the apparen
t shear rate is fixed, the corresponding; stress-shear rate relation is dis
continuous. Our results are in qualitative agreement with the experimental
observations of Pine et al.