On the modelling of a PIB/PB Boger fluid in extensional flow

Abstract

In this paper we study the transient elongational viscosity of a PIB/PB Boger fluid (fluid B) by performing both experiments and model calculations. The experimental results have been obtained by using a filament stretching device was described by van Nieuwkoop and Muller von Czernicki (J. Non-Newtonian Fluid Mech. 67 (1996) 105–123). We have been able to obtain large strains, up to a Hencky strain of 8. A plateau for the Trouton ratio of close to 10 4 is found while approaching a strain of 8. The plateau value appears to be independent of the strain rate history. The predictions using various multi-mode constitutive models (Giesekus, FENE-P, Hinch, FENE) show that the FENE model is the only model which predicts values for the Trouton ratio that are very close to the experiments for the whole range from strain 1 up to 8. The predictions of the models are computed with the actual strain rate ε ̇ t as determined during the experiments in the middle of the filament. During relaxation, both the FENE-P and the FENE model perform well. In order to be able to make predictions without carrying out the relatively expensive FENE calculations, we have developed a new closed form constitutive equation. The model is based on the dumbbell theory in which the connector force used leads to a viscous stress term. The predictions of the model in transient extensional flows are very good and comparable to the FENE model.