Extensional Flow of Wormlike Micellar Solutions

by Cromer, M.J., Cook, L.P. and McKinley, G.H.

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 resultof 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 Maxwelland Giesekus models under equivalent kinematic boundary conditions.