(441h) Instabilities of Dilute Wormlike Micelle Solutions in Circular and Planar 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 circular and planar 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 circular and planar 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). In CCF we look at variations in micelle length and orientation and how these can give rise to the birefringence observed in vorticity banding. We also investigate the role curvature plays in the development of instabilities. We pair these simulations with a linear stability analysis of the governing RRM-R equations using a Chebyshev pseudospectral method to understand the modes and mechanisms of instabilities in these flows.