Viscoelastic flow past a confined cylinder of a low-density polyethylene melt

The capabilities of the exponential version of the Phan-Thien-Tanner (PTT) model and the Giesekus model to predict stress fields for the viscoelastic flow of a low density polyethylene melt around a confined cylinder are investigated. Computations are based on a newly developed version of the discontinuous Galerkin method. This method gives convergent results up to a Deborah number of 2.5 for the falling sphere in a tube benchmark problem. Moreover, the specific implicit-explicit implementation allows the efficient resolution of problems with multiple relaxation times which are mandatory for polymer melts. Experimentally, stress fields are related to birefringence distributions by means of the stress optical rule. Three different fits, of equal quality, to available viscometric shear data are used: two for the PTT model and one for the Giesekus model. Comparison of computed and measured fringes reveals that neither of the models is capable of describing the full birefringence pattern sufficiently well. In particular it appears difficult to predict both the birefringent tail at the wake of the cylinder that is dominated by elongational effects and the fringe pattern between cylinder and the walls where a combined shear-elongational flow is present