Extensional Flow of a Polystyrene Boger Fluid 
Through a 4:1:4 Axisymmetric Contraction/Expansion*

Jonathan P. Rothstein and Gareth H. McKinley
 Dept. of Mechanical Engineering, Massachusetts Institute of Technology
Cambridge, MA 02139; USA


The creeping flow of a dilute (0.025wt%) monodisperse Polystyrene/Polystyrene Boger fluid through a 4:1:4 axisymmetric contraction/expansion is experimentally observed for a wide range of Deborah numbers.  Pressure drop measurements across the orifice plate show a large extra pressure drop that increases monotonically with Deborah number above the value observed for a similar Newtonian fluid at the same flow rate.  This enhancement in the dimensionless pressure drop is not associated with the onset of a flow instability, yet it is not predicted by existing steady-state or transient numerical computations with simple dumbbell models.  It is conjectured that this extra pressure drop is the result of an additional dissipative contribution to the polymeric stress arising from a stress-conformation hysteresis in the strong non-homogeneous extensional flow near the contraction plane. Such a hysteresis has been independently measured and computed in recent studies of homogeneous transient uniaxial stretching of PS/PS Boger fluids [Doyle et al. JNNFM, 76, 1997].  Flow visualizations and velocity field measurements using digital particle image velocimetry (DPIV) show large upstream growth of the corner vortex with increasing Deborah number.  At large Deborah numbers, the onset of an elastic instability is observed, first locally as small amplitude fluctuations in the pressure  measurements, and then globally as an azimuthal precessing of the upstream corner vortex accompanied by periodic oscillations in the pressure drop across the orifice. 

Keywords: axisymmetric contraction, Couette correction, entrance pressure drop, dissipative stress, 
       polystyrene Boger fluid

* Paper presented at "Mechanics of Nonlinear Materials"  Banff, May 1998.

Published: J. Non-Newtonian Fluid Mech., 86, 1999, p. 61-88.