Oscillation superimposed on steady shearing: Measurements and predictions for wormlike micellar solutions

Measurements are made of the viscoelastic properties of a wormlike micellar solution undergoing steady shearing. The wormlike micellar solution has a clearly defined Maxwell response in oscillation. The features (for example, the plateau of the elastic modulus, G ′ , and the peak of the viscous modulus, G ″ ) are extremely well defined, allowing the differences in elastic properties brought about by steady-shearing to be easily discerned. An important feature of the solution studied is that it displays a plateau-like region with almost constant shear stress over a range of steady shear rates. We find that as the steady shear rate is increased: (i) G ′ becomes negative at low frequencies; (ii) the plateau value of G ′ decreases; (iii) the frequency at which the plateau value of G ′ is reached shifts to higher frequencies; (iv) the width of the G ″ peak decreases; (v) the position of the G ″ peak shifts to higher frequencies; and (vi) the height of the G ″ peak increases then decreases. The constitutive equations of Bautista et al. [J. Non-Newtonian Fluid Mech. 80, 93–113 (1999)] and Boek et al. [J. Non-Newtonian Fluid Mech. 126, 39–46 (2005)] were used to fit and predict bulk rheology measurements. Neither model predicts the observed rise in normal stress, despite fitting the plateau region in the shear-stress versus shear-rate curve. It proved difficult to predict transient shear stress data when both increases and decreases in the shear rate were considered. The features found in combined steady and oscillatory flow are predicted qualitatively but not quantitatively. In particular, the reduction of the plateau of G ′ is predicted to occur only at much higher shear rates than found experimentally. We also note that the commercial software controlling the rheometer does not interpret the raw data correctly in the regime where G ′ is negative.