Alternating Vorticity Bands in a Solution of Wormlike Micelles

We report on structural characterization of vorticity bands formed in a wormlike micellar solution by Rheo–small-angle neutron scattering and video imaging experiments. Below a critical shear stress ${\tau }_c$ in Newtonian and shear-thinning regime, only a minor flow alignment of the micelles is observed. Above ${\tau }_c$, in the shear-thickening regime, alternating transparent and turbid bands are formed. Triggered small-angle neutron scattering shows different anisotropic patterns in both bands indicating strongly aligned structures. By high-speed video imaging, we show that such an alignment of micelles does not correspond to a phase of lower viscosity.

Figure 1

Nonlinear and linear (inset) flow curves for a 40 mM CPyCl-NaSal WM solution and the corresponding SANS intensity maps at rest (0 Pa) and at different elevated shear stresses. The dotted ellipse in the flow curve shows the region where the solution exhibits shear-thickening ($13\le \tau \le 23\mathrm{Pa}$) while the bars indicate the minimum and maximum shear rate during flip-flop motion at constant shear stress. The inset shows the linear flow behavior indicating a Maxwell behavior. Displayed scattering patterns were collected at 6 m detector distance, corresponding to a $q$ range of $0.008-0.06{\AA }^{-1}$. Coordinates $x$, $y$, and $z$ correspond to the flow, velocity gradient, and vorticity directions, respectively. The neutron beam passes through the sample along the velocity gradient $y$ direction.

Figure 2

(a) Formation of vorticity bands in the shear-thickening regime at 21 Pa, as visualized by a high-speed digital video camera. The small white rectangle shows the approximate position of the neutron beam. (b) 2D SANS patterns obtained by triggering the Neutron detector for transparent (left) and turbid (right) regions at a detector distance of 6 m ($0.008\le q\le 0.06{\AA }^{-1}$) (see also Fig. 3).

Figure 3

Scattering intensity $I$ as a function of momentum transfer $q$ for transparent (open symbols) and turbid bands (closed symbols) obtained from triggered measurements. Square symbols represent 20° sector average in vorticity direction and circles represent the same in flow direction. The inset shows the anisotropy factor $A_f$ as a function of shear stress $\tau$. The gray circles are calculated $A_f$ for $\tau <{\tau }_c$ and triangular symbols are for $\tau >{\tau }_c$, i.e., in the vorticity banding regime. Open triangle corresponds to transparent band and closed triangle to the turbid band.

Figure 4

Coupling between structure and flow: time evolution of macroscopic band morphology and the rotation of the inner cylinder of the shear cell. (a) Vorticity bands as seen through the transparent concentric cylinders in the flow-vorticity ($x\mathrm{\text{−}}z$) plane. Images i to v cover one period which is approximately 1 s. The white dotted rectangle shows the area used to extract the average grayscale intensity of the bands and the dotted line in the middle shows the approximate boundary between the bands. The corresponding intensities of the images i–v are shown in (b). (b) Average intensity $I$ of vorticity bands (open squares) and angular position $\theta$ of the inner rotating cylinder of the Couette geometry (closed circles) as a function of time. A higher intensity corresponds to a turbid band and a lower intensity to a transparent one. (c) Average intensity $I$ and angular velocity $\omega =d\theta /dt$ of the rotating tool (closed circles) as a function of time. Regions marked $A$ and $B$ indicate appearance of transparent and turbid bands, where the angular velocity $\omega$ of the tool increases and decreases, respectively.