Flow instabilities in circular Couette flow of wormlike micelle solutions with a reentrant flow curve

TL;DR

This study numerically investigates flow instabilities in inertialess circular Couette flow of wormlike micelle solutions with reentrant flow curves, revealing complex finger-like structures and the stability of vorticity banding.

Contribution

It introduces a reactive rod model (RRM-R) to simulate flow instabilities and captures the development of finger-like structures and vorticity banding in wormlike micelle solutions.

Findings

Reentrant flow curves lead to mixed flow behaviors causing complex instabilities.

Initial 3D finger-like structures originate from 2D instabilities.

Vorticity bands are linearly stable in narrow-gap Couette flow.

Abstract

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, JNNFM 295 (2021) 104606], 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.