Numerical simulations of the planar contraction flow for a polyethylene melt using the XPP model

The Discrete Elastic Viscous Stress Splitting technique in combination with the Discontinuous Galerkin (DEVSS/DG) method is used to simulate a low density polyethylene melt flowing in a transientcontraction flow problem.Numerical results using the original and a modified form of the eXtended Pom-Pom (XPP) model are compared to numerical results obtained with the exponential form of the Phan-Thien Tanner (PTT-a) and the Giesekus model and to experimental data of velocities and stresses. These models are known to be well capable of predicting all characteristic features encountered experimentally.Curiously, the eXtended Pom-Pom mode, formulated with the same non-affine or irreversible stretch dynamics as the original Pom-Pom model, encounters convergence problems using the DEVSS/DG method. A slight modification of the stretch dynamics such that it becomes consistent with other viscoelastic models and in agreement with a modification of the stretch dynamics based on non-equilibrium thermodynamics by van Meerveld [J. Non-Newtonian Fluid Mech.,108: 291-299, 2002] gives a more numerical stable behavior and steady state could be reached. From this it is clear that physical and numerical issues still play a mixed role in numerical viscoelastic flow problem

Differential constitutive equations for polymer melts : the extended Pom-Pom model

The Pom-Pom model, recently introduced by Mcleish andLarson [J.Rheol., 42(1), 1998], is a breakthrough in the fieldof visco-elastic constitutive equations. With this model, a correctnon-linear behaviour in both elongation and shear isaccomplished. The original differential equations,improved with local branch-point displacement, are modified to overcome three drawbacks: solutions in steady state elongation show discontinuities, the equation for orientation is unbounded for high strain rates, the model does not have a second normal stress difference in shear. The modified Extended Pom-Pom model does not show the three problems and is easy for implementation in Finite Element packages, because it is written as a single equation. Quantitative agreement is shown with experimental data in uniaxia! l, planar, equibiaxial elongation as well as shear, reversed flow and step-strain for two commercial LDPE melts and one HDPE melt. Such a good agreement over a full range of well defined rheometric experiments, i.e. shear, including reversed flow for one LDPE melt, and different elongational flows, is exceptional

Differential constitutive equations for polymer melts : the enhanced Pompon models

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Differential constitutive equations for polymer melts : the extended Pom-Pom model

The Pom-Pom model, recently introduced by Mcleish andLarson [J.Rheol., 42(1), 1998], is a breakthrough in the fieldof visco-elastic constitutive equations. With this model, a correctnon-linear behaviour in both elongation and shear isaccomplished. The original differential equations,improved with local branch-point displacement, are modified to overcome three drawbacks: solutions in steady state elongation show discontinuities, the equation for orientation is unbounded for high strain rates, the model does not have a second normal stress difference in shear. The modified Extended Pom-Pom model does not show the three problems and is easy for implementation in Finite Element packages, because it is written as a single equation. Quantitative agreement is shown with experimental data in uniaxia! l, planar, equibiaxial elongation as well as shear, reversed flow and step-strain for two commercial LDPE melts and one HDPE melt. Such a good agreement over a full range of well defined rheometric experiments, i.e. shear, including reversed flow for one LDPE melt, and different elongational flows, is exceptional