J. Rheol. 46(6), 1419-1443 November/December (2002) INHOMOGENEOUS TRANSIENT UNIAXIAL EXTENSIONAL RHEOMETRY Jonathan P. Rothstein and Gareth H. McKinley Dept. of Mechanical Engineering, Massachusetts Institute of Technology Cambridge, MA 02139; USA Abstract A filament stretching rheometer is used to probe the development of coil-stretch hysteresis in transient non-homogeneous uniaxial elongation of a dilute polymer solution. Laser-Doppler velocimetry measurements are used to measure the steady centerline velocity profile in an elastic test fluid as it flows towards the throat of a 4:1:4 axisymmetric contraction-expansion over a range of Deborah numbers. The corresponding time-varying extension rate experienced by a fluid element as it flows into the contraction is then downloaded to a filament stretching rheometer in order to impose an identical non-homogeneous stretch history. Simultaneous optoelectronic measurements of the flow induced birefringence and mechanical measurements of the total tensile force in the filament allow independent determination of the evolution in the conformational anisotropy and stress. A pronounced stress-conformation hysteresis is observed with the relationship between the polymeric tensile stress and the average anisotropy in the polymer coil conformation evolving differently during the imposed extension and subsequent relaxation. An energy dissipation per unit volume can be calculated from the area enclosed by the stress-conformation hysteresis loop. The critical Deborah number for the onset of hysteresis and the scaling with increasing deformation rate are found to correlate closely with the development of the additional pressure drop that is measured macroscopically during viscoelastic flow through the contraction-expansion. These macroscopic and microscopic measurements both support the existence of an additional dissipative contribution to the polymer stress which must be resolved by constitutive models in order to accurately simulate complex flows of elastic polymer solutions.