Shear banding predictions for wormlike micellar systems under a contraction–expansion complex flow

Abstract

This study focuses on computational modeling of shear-banded wormlike micellar solutions (WLM) in a complex planar Couette flow, driven by a moving top plate over a rounded-corner 4:1:4 obstruction. The BMP+_τp model is used, which is constructed within an Oldroyd-B-like form, coupled with a thixotropic fluidity-based structure equation. Solute energy dissipation drives fluid–structure adjustment in a construction–destruction dynamics affected by viscoelasticity. This model reproduces conventional WLM features, such as shear thinning, extensional hardening/softening, viscoelasticity, apparent yield stress, and shear banding, with a bounded extensional viscosity and an N1Shear upturn at high deformation rates. The BMP+_τp characterization for shear banding is based on extremely low solvent fractions and appropriate shear-banding intensity parameters. Flow structure is analyzed through velocity, stress, and fluidity, whereupon banded and non-banded response is contrasted at appropriately selected flow rates. Solutions are obtained with our hybrid fe-fv algorithm, capturing essential shear-banded flow features reported experimentally. For a fluid exhibiting banding, banded solutions are generated at a flow rate within the flow curve unstable branch. In the fully developed simple shear flow regions, a split velocity profile is observed, with different viscosity bands at equal stress levels, enhanced with a shock-capture procedure. Non-banded solutions are derived for the lowest and highest flow rates sampled, located in the stable branches. Within the constriction zone, banded profiles are lost due to the mixed non-homogeneous deformation. Shear-banding fluids display less intense viscosity/stress features, correlated with their relatively stronger shear thinning response. The constriction resistance provokes a pressure-level adjustment, leading to fully developed Couette-like constant values upstream–downstream.