In this work, we numerically investigate flow instabilities of inertialess circular Couette flow of dilute wormlike micelle solutions. Using the reformulated reactive rod model (RRM-R) (Hommel and Graham, 2021), which treats micelles as rigid Brownian rods undergoing reversible scission and fusion in flow, we study the development and behavior of both vorticity banding and finger-like instabilities. In particular, we focus on solutions that exhibit reentrant constitutive curves, in which there exists some region where the shear stress, $\tau$, has a multivalued relation to shear rate, $\dot{\gamma }$. We find that the radial dependence of the shear stress in circular Couette flow allows for solutions in which parts of the domain lie in the region of the flow curve where $\partial \tau /\partial \dot{\gamma }>0$, while others lie in the region where $\partial \tau /\partial \dot{\gamma }<0$; this mixed behavior can lead to complex flow instabilities that manifest as finger-like structures of elongated and anisotropically-oriented micelles. In 3D simulations we find that the initial instability is 2D in origin, and 3D finger-like structures arise through the axial instability of 2D sheets. Finally, we show that the RRM-R can capture vorticity banding in narrow-gap circular Couette flow and that vorticity bands are linearly stable to perturbations.

在这项工作中，我们对稀蠕虫状胶束溶液的无惯性圆形库埃特流的流动不稳定性进行了数值研究。使用重新制定的反应棒模型 (RRM-R)（Hommel 和 Graham，2021），将胶束视为在流动中经历可逆分裂和融合的刚性布朗棒，我们研究了涡度带和指状不稳定性的发展和行为。特别是，我们专注于表现出重入本构曲线的解决方案，其中存在剪应力的某些区域，$\tau$，与剪切速率具有多值关系，$\dot{\gamma }$。我们发现，圆形库埃特流中剪切应力的径向相关性允许解决其中部分域位于流动曲线区域中的情况，其中$\partial \tau /\partial \dot{\gamma }>0$，而其他的则位于该区域$\partial \tau /\partial \dot{\gamma }<0$; 这种混合行为可能导致复杂的流动不稳定性，表现为细长且各向异性取向的胶束的指状结构。在 3D 模拟中，我们发现初始不稳定性源自 2D，而 3D 指状结构是通过 2D 片材的轴向不稳定性产生的。最后，我们证明 RRM-R 可以捕获窄间隙圆形库埃特流中的涡度带，并且涡度带对于扰动是线性稳定的。