Flow birefringence of dilute polymer solutions in two-dimensional flows

Abstract

Flow birefringence measurements have been obtained on three molecular weight samples (2−8 × 106 M W ,M W /M N = 1.14−1.3) of polystyrene in dilute solution (50–100 ppm) in a viscous polychorinated biphenyl solvent. The flows were generated using a four roll mill which could simulate a wide range of two dimensional flows in which the flow type (i.e. the ratio of the rate of rotation to the rate of strain) could be varied independently of the velocity gradient. The normalized birefringence, corrected for concentration, (Δn/nc), was observed to approach a saturation value at high velocity gradients in purely extensional flow. This saturation value was independent of both the molecular weight and the concentrationc, in agreement with theory. In addition, the magnitude of the saturation value is consistent with nearly fully extended chains and suggests extensions in the range of 20–50 times the rest state size. The data for the birefringence over a wide range of flows was found to be well correlated against the eigenvalue of the velocity gradient tensor in agreement with the results of the “strong/weak” flow theories ofTanner (1976) andOlbricht et al. (1980). The experiments are compared with a simple dumbbell model which incorporates the effects of a nonlinear spring variable hydrodynamic friction, and internal viscosity. It is shown that this simple model can simulate the experimental results surprisingly well if the effects of molecular weight distribution and finite transit times in the flow device are taken into account.