Europhys. Lett, 48 (6), pp. 706-712 (1999)
A phenomenological model for shear-thickening in wormlike micelle solutions
J. L. Goveas 1 and D. J. Pine 2
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 in final form 18 October 1999)
PACS. 83.50Qm - Thixotropy; thickening flows.
PACS. 83.70Hq - Heterogeneous liquids: suspensions, dispersions, emulsions, pastes, slurries, foams, block copolymers, etc.
PACS. 83.20Bg - Macroscopic (phenomenological) theories.
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.
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