Structures in Extensional Flow of Visco-Elastic Fluids

Exact solutions of partial differential equations describing the evolution of viscoelastic stresses are presented in the extensional flow of fluids whose constitutive response may be described by Oldroyd and Giesekus models. Singular solutions for a range of values of the Weissenberg number are presented and the results of Renardy (J. Non-Newtonian Fluid Mech. 138 (2006) 204-205), and Becherer et al. (J. Non-Newtonian Fluid Mech. 153 (2008) 183-190) are deduced for the case of upper convected Maxwell (UCM) fluid and one independent spatial variable. The effect of variable boundary data at the inflow can be studied as viscoelastic stresses over two spatial variables are considered. As such, our results are applicable to a wider range of flow problems.