Transient evolution of flow profiles in a shear banding wormlike micellar solution: experimental results and a comparison with the VCM model

Heterogeneity-induced retraction in viscoelastic fluids following cessation of flow

Complex fluids including colloidal suspensions, microgels, and entangled wormlike micelles (WLMs) can develop heterogeneous flow regions under imposed steady shear. In some of these systems, the evolution to this flow state from rest is accompanied by flow reversal - when a portion of the fluid moves opposite to the imposed flow direction. Flow reversal was proposed to occur in shear startup when (1) the fluid has significant elasticity, and (2) the flow becomes heterogeneous immediately following the stress overshoot [McCauley et al., J. Rheol., 2023, 67, 661-681]. To verify this hypothesis, a new method is developed for measuring flow heterogeneity. Upon cessation of the imposed flow, elasticity and flow heterogeneity cause retraction of the fluid, which is quantified with particle tracking velocimetry. Flow is stopped at key times during shear startup in two systems: a gel-like WLM that exhibits flow reversal before heterogeneous flow and a viscoelastic, fluid-like WLM that does not. The degree of flow heterogeneity is inferred from the shape and magnitude of velocity profiles measured during retraction. Flow heterogeneity develops earlier in gel-like WLMs - supporting the proposed flow reversal criteria. For comparison, heterogeneous Couette flows described with the upper-convected Maxwell or Germann-Cook-Beris models are analyzed. These theoretical flow problems confirm that stark differences in rheological properties across the flow geometry can cause significant fluid retraction and reproduce key features of the experimentally observed retraction. This new method can be used to extract quantitative information about spatially heterogeneous flows in viscoelastic complex fluids, whether or not flow reversal occurs.

Kinetics of shear banding flow formation in linear and branched wormlike micelles

We investigate the flow evolution of a linear and a branched wormlike micellar solution with matched rheology in a Taylor-Couette (TC) cell using a combination of particle-tracking velocimetry, birefringence, and turbidity measurements. Both solutions exhibit a stress plateau within a range of shear rates. Under startup of a steady shear rate flow within the stress plateau, both linear and branched samples exhibit strong transient shear thinning flow profiles. However, while the flow of the linear solution evolves to a banded structure at longer times, the flow of the branched solution transitions to a curved velocity profile with no evidence of shear banding. Flow-induced birefringence measurements indicate transient birefringence banding with strong micellar alignment in the high shear band for the linear solution. The transient flow-induced birefringence is stronger for the branched system at an otherwise identical Wi. At longer times, the birefringence bands are replaced by a chaotic flow reminiscent of elastic instabilities. Visualization of the flow-induced turbidity in the velocity gradient-vorticity plane reveals quasi-steady banding with a turbidity contrast between high and low shear bands in the linear solution. However, the turbidity evolves uniformly within the gap of the TC cell for the branched solution, corroborating the non-banded quasi-steady velocimetry results. Finally, we show that while elastic instabilities in the linear solution emerge in the high shear band, the flow of branched solution at high Wi becomes unstable due to end effects, with growing end regions that ultimately span the entire axial length of the TC cell.

Effect of chain scission on flow characteristics of wormlike micellar solutions past a confined microfluidic cylinder: a numerical analysis

Flow past a microfluidic cylinder confined in a channel is considered as one of the benchmark problems for the analysis of transport phenomena of complex fluids. Earlier experiments show the existence of an elastic instability for the flow of a wormlike micellar solution in this model system after a critical value of the Weissenberg number in the creeping flow regime (G. R. Moss and J. P. Rothstein, J. Non-Newtonian Fluid Mech., 2010, 165, 1505-1515; Y. A. Zhao et al., Soft Matter, 2016, 12, 8666-8681; S. J. Haward et al., Soft Matter, 2019, 15, 1927-1941). This study presents a detailed numerical investigation of this elastic instability in this model system using the two-species VCM (Vasquez-Cook-McKinley) constitutive model for the wormlike micellar solution. Inline with the experimental trends, we also observe the existence of a similar elastic instability in this flow once the Weissenberg number exceeds a critical value. However, we additionally find that the elastic instability in this model geometry is greatly influenced by the breakage and reformation dynamics of the wormlike micelles. In particular, the onset of such an elastic instability is delayed or even may be completely suppressed as the micelles become progressively easier to break. Furthermore, this elastic instability is seen to be associated with the elastic wave phenomena which has been recently observed experimentally for polymer solutions. The present study reveals that the speed of such an elastic wave increases non-linearly with the Weissenberg number similar to that seen in polymer solutions.