Shear thickening in dilute solutions of wormlike micelles

– A new mechanism is suggested for shear thickening in dilute solutions of wormlike micelles. According to this mechanism, there is an instability above a critical shear rate, γ̇c, by which micelles aggregate to form networks of bundles. We examine the first step of this instability by studying the aggregation of two micelles into a paired bundle. The model predicts that γ̇c is given by the inverse of the time necessary for the two micelles to unbind from each other. The order of magnitude and temperature dependence of the predicted γ̇c are in good agreement with experimental measurements. In addition, the model provides a natural explanation for the observation of coexistence between the shear-induced structure and a dilute phase at fixed shear stress. Introduction. – Many surfactant molecules self-assemble in solution to form long cylindrical micelles. While great progress has been made in understanding the rheological behavior of such systems [1–3], some fundamental problems still remain to be understood. Some of the most intriguing phenomena are the shear thickening and rheopexy observed in a wide class of low-concentration wormlike micellar solutions. These solutions can exhibit a steep increase of the viscosity in shear flow as the shear rate exceeds a critical value, γ̇c, as well as a decrease of the drag in turbulent flow [4–6]. These phenomena are attributed to the formation of a shear-induced structure (SIS) [7–12,20]. The following common characteristics are observed: – Shear thickening occurs in solutions of cylindrical micelles made of cationic surfactants (e.g., CTAB) with a strongly bound counterion (e.g., the salicylate ion Sal−). The counterion typically has a hydrophobic moiety and acts like a co-surfactant [13]. – The shear thickening transition is observed in the dilute regime, where the rodlike micelles are not entangled [8, 11]. – The critical shear rate exhibits an Arrhenius temperature dependence [8, 12, 14, 21]: γ̇c ∝ exp [−E/kBT ], where E is an activation energy. On the theoretical side, shear thickening has been attributed to shear-induced gelation into a network of long micelles [15–18]. In all these theoretical approaches, gelation occurs when the shear rate is high enough to overcome the rotational Brownian diffusion of the rodlike micelles. Thus, they predict a critical shear rate of the order of the rotational diffusion constant of a rod Dr [19]: γ̇c ∼ Dr ∼ kBT πηL3 , (1)