Solid-like fracture mechanisms of wormlike micellar solutions flowing around a cylinder with a free surface

Solid-like fracture of viscoelastic wormlike micellar (WLM) solutions flowing around a cylinder with a free surface was investigated experimentally. An open-top rectangular vessel filled with a moderately concentrated cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) solution was translated relative to a stationary vertical cylinder. Rheological characterization confirmed that this fluid exhibits single-relaxation-time Maxwellian shear viscoelasticity as well as pronounced extensional viscoelasticity, characterized by nonlinear strain hardening under accumulated extensional deformation. Free-surface deformation and fracture were visualized using high-speed imaging, while particle image velocimetry and force measurements were used to characterize the flow and stress fields. The Deborah number, defined using the relaxation time, vessel translation speed, and cylinder diameter, was varied over a wide range. Two distinct fracture responses were identified depending on the Deborah number: the transition mode at low $$\text {De}$$ and the fracture mode at high $$\text {De}$$ . In the transition mode, fracture initiates from a cavity entrapped behind the cylinder, with crack initiation delayed beyond the relaxation time despite viscous bulk behavior, followed by rapid downstream propagation. In the fracture mode, cracks originate from a small dent on the free surface within the elastic regime. The critical local Weissenberg number for extensional deformation ( $$\text {Wi}_{xx} \simeq 0.4$$ –0.6) is consistent with values reported for uniaxial extension, even in the presence of substantial shear deformation. These results highlight the roles of free-surface curvature and extensional strain in governing solid-like fracture of WLM solutions.