Analytical solution of the Poiseuille flow of a De Kee viscoplastic fluid

Alexandros Syrakos; Aggelos Charalambous; Georgios C. Georgiou

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arXiv · 2401.02942

Analytical solution of the Poiseuille flow of a De Kee viscoplastic fluid

Alexandros Syrakos·Aggelos Charalambous·Georgios C. Georgiou

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Abstract

We provide an explicit analytical solution of the planar Poiseuille flow of a viscoplastic fluid governed by the constitutive equation proposed by De Kee and Turcotte (Chem. Eng. Commun. 6 (1980) 273-282). Formulae for the velocity and the flow rate are derived, making use of the Lambert W function. It is shown that a solution does not always exist because the flow curve is bounded from above and hence the rheological model can accommodate stresses only up to a certain limit. In fact, the flow curve reaches a peak at a critical shear rate, beyond which it exhibits a negative slope, giving rise to unstable solutions.

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Alexandros Syrakos, Aggelos Charalambous, Georgios C. Georgiou. 2024-01-05. Analytical solution of the Poiseuille flow of a De Kee viscoplastic fluid. https://arxiv.org/abs/2401.02942

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