Extensional flow of wormlike micellar solutions

We consider the inhomogeneous extensional response of a new constitutive model, the VCM model [Vasquez, et al., 2007. A network scission model for wormlike micellar solutions I: model formulation and homogeneous flow predictions. J. Non-Newt. Fluid Mech. 144, 122–139] that has been developed to describe concentrated solutions of wormlike micelles. The time dependent numerical analysis is carried out in a simplified slender filament formulation appropriate for transient elongational flows of complex fluids. The simulations show that, beyond a critical extension rate, elongating filaments of a micellar fluid described by the VCM model exhibit a dramatic and sudden rupture event as a result of the scission of the entangled wormlike chains. The computations capture many of the features of the high-speed rupture process observed experimentally [Bhardwaj, et al., 2007. Filament stretching and capillary breakup extensional rheometry measurements of viscoelastic wormlike micelle solutions. J. Rheol. 51, 693–719] in filament stretching experiments with wormlike micelle solutions. The highly localized rupture predicted by the VCM model and the corresponding evolution in the tensile force within the filament is contrasted with the familiar and more gradual necking responses predicted by the upper convected Maxwell and Giesekus models under equivalent kinematic boundary conditions.