The Influence of the Transient Extensional Viscosity on the
Couette Pressure Correction and the Vortex Growth Dynamics in an
Asymmetric Abrupt Contraction/Expansion

Jonathan P. Rothstein & Gareth H. McKinley
Dept. of Mechanical Engineering, M.I.T., 77 Massachusetts Ave., Cambridge, MA 02139.

Recent measurements and Brownian dynamics simulations of the tensile stress growth and birefringence in transient uniaxial elongation of dilute polymer solutions have revealed the existence of a 'stress-conformation' hysteresis [Doyle et al. JNNFM 1998]. In a strong stretching flow, the average configuration and resulting stress in a polymer chain are found to evolve along quite different paths during stretching and relaxation. This hysteresis arises from non-equilibrium coupling between the macroscopic flow field and the fluid microstructure, and provides an additional mechanism for dissipation of mechanical energy. To capture such effects, recent closed-form constitutive models have postulated the existence of an additional, purely-dissipative contribution to the polymeric stress. In a complex, spatially-nonhomogeneous flow such effects may be expected to result in enhanced values of dynamical quantities such as the total pressure drop in the domain. We investigate this hysteresis in a prototypical complex flow: the motion of a viscoelastic fluid through an abrupt axisymmetric contraction-expansion of various contraction ratios. The test fluid is a well-characterized dilute polymer solution of monodisperse polystyrene dissolved in oligomeric styrene. Measurements of the total pressure drop across the orifice plate show a monotonic increase with Deborah number that can be decomposed into three distinct pressure growth regimes independent of the contraction ratio or the local curvature of the re-entrant lip. Flow visualization, LDV and DPIV measurements are employed to further characterize the flow; specifically the upstream vortex growth dynamics. We observe that increasing the contraction ratio beyond a critical value results in a transition from a shear dominated regime characterized by the appearance of an elastic lip vortex near the re-entrant corner at moderate Deborah numbers to an extension dominated regime characterized by a large elastic corner vortex which fingers out towards the re-entrant corner. The critical value of the contraction ratio for transition from the lip to corner vortex varies with the fluid used. We show that these drastic differences in the upstream vortex growth dynamics for different contraction ratios and fluids can be related to the degree of strain hardening experienced by the fluid in transient uniaxial extension.

To be presented at The Society of Rheology's 71st Annual Meeting in Madison, Wisconsin on Monday October 18, 1999.