An analysis of unsteady one-dimensional stretching of a viscoelastic fluid

The time-dependent response of a viscoelastic liquid to unsteady one-dimensional stretching deformations was examined. Oldroyd's three-constant model for a viscoelastic fluid was used. Two cases representing two different stretching histories were analyzed: a sine stretching pulse and a step stretching pulse. The results show that high elongational viscosity may be easily reached in both cases. As the relaxation time of the liquid becomes comparable to the pulse width, elongational viscosity increases with the increase in maximum stretching rates. Conditions to maintain high levels of elongational viscosity at a subsequently reduced stretching rate were given as functions of the relaxation time and initial stretching rates. In view of recent turbulent boundary layer data, the results were used to discuss possible explanations of turbulent drag reduction in polymer solutions. It was concluded that the basic mechanisms for drag reduction in polymer soluations. It was concluded that the basic mechanisms for drag reducation may be related to the effects of high elongational viscosity and local stabilization of small shear disturbances.