Self-similar shear thickening behavior in CTAB/$NaSal$ surfactant solutions

The effect of salt concentration $Cs$ on the critical shear rate $γ̇c$ required for the onset of shear thickening and apparent relaxation time $λ$ of the shear-thickened phase has been investigated systematically for dilute Cetyl-trimethylammonium bromide/sodium salicylate solutions. Experimental data suggest a self-similar behavior of $γ̇c$ and $λ$ as functions of $Cs$⁠. Specifically, $γ̇c∼Cs−6$ whereas $λ∼Cs6$ such that an effective Weissenberg number $We≡λγ̇$ for the shear-thickened phase is only weakly dependent on $Cs$⁠. A procedure has been developed to collapse the apparent shear viscosity versus shear rate data obtained for various values of $Cs$ into a single master curve. The effect of $Cs$ on the elastic modulus and mesh size of the shear-induced gel phase for different surfactant concentrations is discussed. Experiments performed using different flow cells (Couette and cone-and-plate) show that $γ̇c$⁠, $λ$ and the maximum viscosity attained are geometry independent. The elastic modulus of the gel phase inferred indirectly by employing simplified hydrodynamic instability analysis of a sheared gel-fluid interface is in qualitative agreement with that predicted for an entangled phase of living polymers. A qualitative mechanism that combines the effect of $Cs$ on average micelle length and Debye parameter with shear-induced configurational changes of rod-like micelles is proposed to rationalize the self-similarity of shear induced structure formation.