Distinguishing Shear Banding from Shear Thinning in Flows with a Shear Stress Gradient

Shear banding of complex fluids, including wormlike micelles (WLMs), involves spontaneous separation of a flow field into regions with distinct velocity gradient upon shear, and is typically attributed to mechanical instability due to a non-monotonic constitutive curve. The detailed signatures of steady state banding, including an apparent stress plateau between lower and upper critical shear rates as well as the simple “lever rule” followed by the location of the interface between bands, have been thoroughly studied for narrow gap Taylor-Couette flows that approximate simple shear. However, geometries with significant spatial gradients in the shear stress (e.g., large gap Taylor-Couette flows) can produce banding-like features, even when the fluid possesses a monotonic constitutive curve. This raises important fundamental questions. Most importantly, how does shear banding manifest in geometries with significant stress gradients, and how do we identify whether a fluid is truly shear banding, as opposed to strongly shear thinning?

Here, we report a model-free approach to experimentally distinguish shear banding from strong shear thinning, and apply it to rheological and flow velocimetry measurements on WLMs in a Taylor-Couette device with systematically varying curvature (i.e., the ratio of gap size to cylinder radius). The method, which involves numerical analysis of various derivatives of the velocity profile, is verified through one-dimensional flow calculations using fluids with non-monotonic and monotonic constitutive curves. We then apply the method to experimental data obtained through high-resolution velocimetry measurements. In both simulation and experiment, we find that shear banding WLMs exhibit several distinctive features in the velocity profile, whose presence and quantitative behavior are relatively insensitive both to the applied shear rate and the degree of curvature of the flow geometry. By contrast, the shear thinning WLMs exhibit features that are strongly dependent on the geometry and applied shear rate. Our results provide a clear, unambiguous criterion for identifying shear banding in complex fluids.