EXPERIMENTAL AND NUMERICAL STUDY OF THE SWELLING OF A VISCOELASTIC LIQUID USING THE STREAM TUBE METHOD AND A KINEMATIC SINGULARITY APPROXIMATION

The present paper deals with experimental and numerical aspects of the swelling problem. The rheological characterization of an industrial polystyrene and determination of flow parameters (jet surface, velocities, etc.) are involved. The data are fed into a viscoelastic integral constitutive equation. The swell problem is analysed using the stream tube method and a specific kinematic approximation of the singularity at the junction point between the wall and the free surface. A method is proposed for determining the swelling ratio by considering approximate functions for the streamlines. The numerical results are consistent with those of the literature, for low Weissenberg numbers. Moreover, the present analysis enables us, using approximate expansions for the kinematic functions in the singularity domain, to reach higher Weissenberg numbers than 20. In this case, the numerical predictions of the model are still consistent with the experimental data, particularly for those of the jet surface and velocity profiles.