A phenomenological model for shear-thickening in wormlike micelle solutions

¹ Department of Chemical Engineering - MS-362, Rice University, 6100 Main Street, Houston, TX 77005, USA
² Department of Chemical Engineering and Materials Department, University of California - Santa Barbara, CA 93106, USA

Received: 7 July 1999
Accepted: 18 October 1999

Abstract

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.