Analytical solution of the Poiseuille flow of a De Kee viscoplastic fluid
Fluid Dynamics
2024-01-08 v1
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.
Keywords
Cite
@article{arxiv.2401.02942,
title = {Analytical solution of the Poiseuille flow of a De Kee viscoplastic fluid},
author = {Alexandros Syrakos and Aggelos Charalambous and Georgios C. Georgiou},
journal= {arXiv preprint arXiv:2401.02942},
year = {2024}
}