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Bagley correction: the effect of contraction angle and its prediction

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Abstract

The excess pressure losses due to end effects (mainly entrance) in the capillary flow of a branched polypropylene melt were studied both experimentally and theoretically. These losses were first determined experimentally as a function of the contraction angle ranging from 10° to 150°. It was found that the excess pressure loss function decreases for the same apparent shear rate with increasing contraction angle from 10° to about 45°, and consequently slightly increases from 45° up to contraction angles of 150°. Numerical simulations using a multimode K-BKZ viscoelastic and a purely viscous (Cross) model were used to predict the end pressures. It was found that the numerical predictions do agree well with the experimental results for small contraction angles up to 30°. However, the numerical simulations under-predict the end pressure for larger contraction angles. The effects of viscoelasticity, shear, and elongation on the numerical predictions are also assessed in detail. Shear is the dominant factor controlling the overall pressure drop in flows through small contraction angles. Elongation becomes important at higher contraction angles (greater than 45°). It is demonstrated in abrupt contractions (angle of 180°) that both the entrance pressure loss and the vortex size are strongly dependent on the extensional viscosity for this branched polymer. It is suggested that such an experiment (visualisation of entrance flow) can be useful in evaluating the validity of constitutive equations and it can also be used to fitting parameters of rheological models that control the elongational viscosity.

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Acknowledgements

Financial assistance from the Natural Sciences and Engineering Research Council (NSERC) of Canada and the General Secretariat for Research and Technology (GGET) of Greece are gratefully acknowledged. The authors are indebted to Prof. Alexander Gotsis of the University of Delft for providing rheological experimental data, especially on the elongational viscosity.

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Authors and Affiliations

  1. School of Mining Engineering and Metallurgy, National Technical University of Athens, Zografou 157 80, Athens, Greece

    Evan Mitsoulis

  2. Department of Chemical Engineering, The University of British Columbia, Main Mall, 2216, Vancouver, BC, V6T 1Z4, Canada

    Savvas G. Hatzikiriakos

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  1. Evan Mitsoulis
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  2. Savvas G. Hatzikiriakos
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Correspondence to Savvas G. Hatzikiriakos.

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Mitsoulis, E., Hatzikiriakos, S.G. Bagley correction: the effect of contraction angle and its prediction. Rheol Acta 42, 309–320 (2003). https://doi.org/10.1007/s00397-003-0294-y

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  • DOI: https://doi.org/10.1007/s00397-003-0294-y

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