Shear banding and flow instabilities in wormlike micelles: Modelling and mechanisms – A review

Worm-like micelles (WLMs) are dynamic, self-assembling supramolecular structures that exhibit complex viscoelastic behaviour due to their ability to undergo reversible scission, fusion, branching, and sequence rearrangement. This review provides a comprehensive analysis of recent theoretical advances in modelling WLM rheology, from classical reptation–scission theories to modern stochastic simulations and multi-scale population-balance frameworks. A central challenge addressed is the rheological indistinguishability of competing models under linear conditions, which renders inverse modelling ill-posed and necessitates the integration of experimental data, such as cryogenic transmission electron microscopy (cryo-TEM), small-angle neutron scattering (SANS), and flow birefringence, to constrain theoretical predictions. The article further explores the limitations of conventional models in capturing nonlinear responses, including shear banding and extensional strain hardening, and emphasizes the need for spatially resolved, structurally informed constitutive equations. Emerging tools, including neural networks and hybrid modular frameworks, are identified as promising solutions for bridging microscopic rearrangement dynamics with macroscopic flow behaviour. Ultimately, the development of predictive, physically grounded WLM models will be essential for advancing applications in formulation science, smart materials, and industrial processing.