We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the presence of both steady-state and transient shear and uniaxial elongational flows, supplemented by a variable link tension coefficient. Here, we provide the transient and stationary solutions of the tumbling-snake model under biaxial elongation both analytically, for small and large elongation rates, and via Brownian dynamics simulations, for the case of planar elongational flow over a wide range of rates, times, and the model parameters. We show that both the steady-state and transient first planar viscosity predictions are similar to their uniaxial counterparts, in accord with recent experimental data. The second planar viscosity seems to behave in all aspects similarly to the shear viscosity, if shear rate is replaced by elongation rate.

Based on the Generalized bracket, or Beris-Edwards, formalism of non-equilibrium thermodynamics, we have recently proposed [Stephanou et al. Materials, 13, 2867 (2020)] a new differential constitutive model for the rheology of entangled polymer melts and solutions. It has amended the shortcomings of a previous model that was too strict in the values of the convective constraint release parameter for the model not to violate the second law of thermodynamics and has been shown capable of predicting a transient stress undershoot (following the overshoot) at high shear rates. In this work, we wish to further examine this model’s capability of predicting the rheological response of industrial polymer systems by extending it to its multiple-mode version. The comparison against industrial rheological data (High-Density Polyethylene resins), as compared against available experimental data in (a) Small Amplitude Oscillatory shear, (b) start-up shear, and (c) start-up uniaxial elongation, is noted to be good.

Since its introduction, back in the late 1970s, the non-affine or slip parameter, ξ, has been routinely employed by numerous constitutive models as a constant parameter. However, the evidence seems to imply that it should be a function of polymer deformation. In the present work, we phenomenologically modify a constitutive model for the rheology of unentangled polymer melts [P. S. Stephanou et al. J. Rheol. 53, 309 (2009)] to account for a non-constant slip parameter. The revised model predictions are compared against newly accumulated rheological data for a C48 polyethylene melt obtained via direct non-equilibrium molecular dynamics simulations in shear. We find that the conformation tensor data are very well predicted; however, the predictions of the material functions are noted to deviate from the NEMD data, especially at large shear rates.