(422i) Instabilities of Dilute Wormlike Micelle Solutions in 2D and 3D Circular Couette Flows

Dilute surfactant solutions that form wormlike micelles (WLMs) have been shown to exhibit remarkable drag reduction at levels comparable to some of the most widely used polymer solutions; these WLM solutions further benefit from being self-assembling in nature and can thus recover from mechanical degradation, such as that in high shear regions, which is a known drawback of using polymer solutions as drag-reducing agents. WLM solutions also display a range of interesting flow dynamics including both shear-thickening and -thinning, a reentrant (i.e. multivalued) flow curve, and a number of instabilities in shear and extensional flows. Notably, these solutions can display a vorticity banding instability in circular Couette flow (CCF) that manifests as stacked bands along the vorticity axis, where adjacent bands support distinct shear stresses.

In this study, we present on computational results of a model for dilute WLM solutions – the reformulated reactive rod model (RRM-R) – in 2D and 3D circular Couette flows. The RRM-R, which treats WLMs as rigid, Brownian rods that can fuse and rupture in flow, has shown strong agreement with experimental observations of steady and transient WLM solution rheology and is well-suited for CFD simulations. We perform direct numerical simulations in 2D and 3D circular Couette flows and focus on critical conditions for viscoelastic and elastic instability formation, paying close attention to parameter regimes in which the RRM-R predicts a reentrant flow curve (a necessary condition for vorticity banding). Upon forcing the flow into unstable regions of the constitutive curve (i.e. dτ₁₂/dγ < 0), we observe an ‘interface-like’ instability in which extreme gradients in the length of micelles (and therefore also the stress and normal stress differences) arise, giving the appearance of a multiphase fluid. We further investigate the origins and mechanisms of this instability by pairing these simulations with a linear stability analysis of the governing RRM-R equations using a Chebyshev pseudospectral method. In comparing our results to experiments, we look at how variations in micelle length and orientation can give rise to the birefringence and turbidity differences observed in experiments. We also investigate the roles that curvature and gap width play in the development of instabilities, finding that increasing curvature tends to destabilize the flow.