Retrieving Equivalent Shear Viscosity for Molten Polymers from 3-D Nonisothermal Capillary Flow Simulation

For highly viscous polymer melts, considerable fluid temperature rises produced by viscous heating can be a disturbing factor in viscosity measurements. By scrutinizing the experimental and simulated capillary pressure losses for polymeric liquids, we demonstrate the importance of applying a viscous heating correction to the shear viscosity, so as to correct for large errors introduced by the undesirable temperature rises. Specifically, on the basis of a theoretical derivation and 3-D nonisothermal flow simulation, an approach is developed for retrieving the equivalent shear viscosity in capillary rheometry, and we show that the shear viscosity can be evaluated by using the average fluid temperature at the wall, instead of the bulk temperature, as previously assumed. With the help of a viscous Cross model in analyzing the shear-dominated capillary flow, it is possible to extract the viscous heating contribution to capillary pressure loss, and the general validity of the methodology is assessed using the experiments on a series of thermoplastic melts, including polymers of amorphous, crystalline, and filler-reinforced types. The predictions of the viscous model based on the equivalent viscosity are found to be in good to excellent agreement with experimental pressure drops. For all the materials studied, a near material-independent scaling relation between the dimensionless temperature rise (Θ) and the Nahme number (Na) is found, Θ ~ Na^0.72, from which the fluid temperature rise due to viscous heating as well as the resultant viscosity change can be predicted.