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Computations with viscoplastic and viscoelastoplastic fluids

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Abstract

This numerical study focuses on regularised Bingham-type and viscoelastoplastic fluids, performing simulations for 4:1:4 contraction–expansion flow with a hybrid finite element–finite volume subcell scheme. The work explores the viscoplastic regime, via the Bingham–Papanastasiou model, and extends this into the viscoelastoplastic regime through the Papanastasiou–Oldroyd model. Our findings reveal the significant impact that elevation has in yield stress parameters, and in sharpening of the stress singularity from that of the Oldroyd/Newtonian models to the ideal Bingham form. Such aspects are covered in field response via vortex behaviour, pressure-drops, stress field structures and yielded–unyielded zones. With rising yield stress parameters, vortex trends reflect suppression in both upstream and downstream vortices. Viscoelastoplasticity, with its additional elasticity properties, tends to disturb upstream–downstream vortex symmetry balance, with knock-on effects according to solvent-fraction and level of elasticity. Yield fronts are traced with increasing yield stress influences, revealing locations where relatively unyielded material aggregates. Analysis of pressure drop data reveals significant increases in the viscoplastic Bingham–Papanastasiou case, O (12%) above the equivalent Newtonian fluid, that are reduced to 8% total contribution increase in the viscoelastoplastic Papanastasiou–Oldroyd case. This may be argued to be a consequence of strengthening in first normal stress effects.

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Notes

  1. To date, the concept of the yield stress and its definition remains a subject of controversy. Hence, in the literature, doubts are often expressed whether the yield stress exists in reality (as discussed in a plenary lecture by K. Walters at the YPF 2009 conference).

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Authors and Affiliations

  1. Institute of Non-Newtonian Fluid Mechanics, Swansea University, School of Engineering, Swansea, SA28PP, UK

    Fawzi Belblidia, Hamid Reza Tamaddon-Jahromi & Michael Francis Webster

  2. Institute of Mathematics and Physics, University of Aberystwyth, Aberystwyth, SY23 3BZ, UK

    Ken Walters

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  1. Fawzi Belblidia
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  2. Hamid Reza Tamaddon-Jahromi
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  3. Michael Francis Webster
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  4. Ken Walters
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Correspondence to Michael Francis Webster.

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Belblidia, F., Tamaddon-Jahromi, H.R., Webster, M.F. et al. Computations with viscoplastic and viscoelastoplastic fluids. Rheol Acta 50, 343–360 (2011). https://doi.org/10.1007/s00397-010-0481-6

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  • DOI: https://doi.org/10.1007/s00397-010-0481-6

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