Characterization of superimposed instabilities in the planar extensional flow of viscoelastic fluids

Abstract

We simulate the isothermal, incompressible, time-dependent flow of Boger fluids, using the FENE-CR constitutive model, in the optimized shape cross-slot extensional rheometer [Haward et al., Phys. Rev. Lett. 109, 128301 (2012)]. We uncover a family of predominantly elastic instabilities resulting from the interaction of stationary asymmetric and time-dependent flow transitions. The superposition of these instabilities, with varying degrees of relative amplitude, produces five distinct flow regimes which are classified by their elasticity, suggesting that the dynamic system is situated in the vicinity of a triple point in the inertia-elasticity-viscosity parameter space. A detailed characterization of the various associated modes of instability is provided. Spectral analysis of the first component of the velocity vector suggests that the flow regimes featuring loss of birefringence strand integrity become chaotic and locally turbulent near the center of the cross-slot, above a certain flow rate threshold.