Die Swell and Normal Stresses: An Explanation
Journal Articles
Overview
Research
Identity
Additional Document Info
View All
Overview
abstract
AbstractNewtonian fluids show a small increase (about 10%) in cross-section diameter on emerging from a capillary at low Reynolds numbers (Re≪1). Highly viscous elastic fluids, such as polymer melts, exhibit a far greater increase, sometimes between 200 and 300%. This phenomenon is often referred to as “Barus effect” or “die swell” and is usually described quantitatively in terms of the swelling ratio (d/D), which is the ratio of extrudate diameter to capillary die diameter. The swelling of polymer extrudates is generally attributed to normal stresses which are released when the extrudate emerges from a capillary die. The exact mechanism of this swelling process is far from being fully understood, even for the simpler case of Newtonian fluids. Because so many plastics processes involve extrusion through dies, prediction and control of die swell are of great technological importance. Several expressions have been proposed for the prediction of die swell, centered on the concept of the elastic recovery of the swelling process. These expressions relate the swelling ratio (d/D) to the recoverable shear (σ), which is defined as half the ratio of first normal stress difference to shear stress. The papers of Nakajima, Graessley, and Bagley discuss the solidlike response of the extrudate on emerging from the die. They apply the concepts of rubber elasticity to predict a swelling ratio (d/D) asymptotically proportional, for large values of swelling, to the square root of the recoverable shear. Tanner's expression is based on the elastic recovery of a “BKZ” fluid and predicts a swelling ratio asymptotically proportional to the cube root of the recoverable shear. Experimental evaluations of the above expressions have been carried out by a number of investigators. However, no definite conclusions can be drawn because of the highly questionable determination of normal stresses at the shear rates involved in die swell (10−103s−1). Despite the many investigations on die swell, there is very little known of how the polymer structure influences the swelling ratio. The existing expressions for predicting die swell can incorporate the polymer structure effects through the definition of shear modulus, which is related by Hooke's law to the recoverable shear. The shear modulus, however, is unambiguously defined only at small deformations. Consequently, for the large deformations involved in die swell, a new theory is definitely needed. In this paper a new expression for die swell is developed based on non-Gaussian chain statistics as applied to a molecular network.
