Abstract: A general expression for the correlation of the simple shear (tan ) to the molecular parameters and the shear rate ( ) was deduced. It shows that the simple shear (tan ) may be resolved into free recoil (recoverable strain) and viscous heating (unrecoverable strain). The magnitudes of the simple shears for recoil (tan E) and (tan V) for viscous heating not only depended on the molecular parameters and the operational variables, but also on the exponential fractions of the recoverable (1- ) and unrecoverable ( ) conformations for recoil and viscous heating. Therefore the magnitudes of the simple shears (tan E) for recoil and (tan V) for viscous heating are, respectively, expressed as the partition function to the (1- )th power and the partition function to the ( )th power. Thus correlations of the total recoil and the ultimately recoverable strains to the molecular parameters [ , a, η0, GN0 and (1- )] and the operational variables ( ), (L=D) and tr) were deduced respectively, which show that at very different shear rates ( ) the polymeric liquids may exhibit a very different viscoelastic behaviors. After introducing the uniform two-dimensional extension, the definition of swelling ratio and the ratio of L to D [De=(L/D)], two expressions for the ultimate die swelling effect and the ultimate extrudate swelling ratio BEVT5 to the molecular parameters [ , a, η0, GN0 and (1- )] and the operational variables ( , (L/D) and tr) were obtained. The two correlation expressions were verified by the experimental data of high-density polyethylene (HDPE) which shows that the two correlation expressions can be used to predict the correlations of the ultimate extrudate swelling behaviors of polymeric liquids to the molecular parameters and the operational variables.

Key words: Die swell, Viscoelastic recoil, Entanglement