Viscous and elastic stresses in extensional rheometry

Abstract

The steady and transient stress data of Orr and Sridhar (Journal of Non-Newtonian Fluid Mechanics, 67 (1996) 77–103) for fluid A and fluid B in uniaxial extension is compared with transient stress growth and stress relaxation predicted using the FENE-CR model. It is shown that a rapid initial stress relaxation following uniaxial extension, which resembles the data of Orr and Sridhar, is predicted by the FENE-CR model due to the increasing stiffness of the nonlinear spring with chain extension. It is further shown that the magnitude of the initial stress decrease predicted by the FENE-CR model depends approximately linearly on the rate of strain and if the analysis procedure of Orr and Sridhar is applied to the predicted results for the FENE-CR model, an apparent viscous stress contribution is obtained from the purely elastic FENE-CR model. Finally, the magnitude of the apparent viscous stress contribution predicted by the FENE-CR model is found to be similar to the apparent viscous stress contribution obtained experimentally. It is therefore concluded that the rapid initial stress decrease in the experiments is most likely due primarily to the nonlinear dependence of the elastic stresses on the end-to-end length of the polymer chain and that viscous contributions to the polymer stress are much smaller than the initial analysis of the experiments suggested. Since the polyisobutylenes in fluids A and B are polydisperse, multi mode models intended to mimic the effects of a molecular weight distribution are also considered. The multi mode model is shown to increase the rate of stress relaxation at short times, but to slow down the rate of stress relaxation at long times. It is conjectured that polydispersity effects may be responsible for the slow retraction of polymers observed experimentally.