Analytical solution of the Poiseuille flow of a De Kee viscoplastic fluid
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914631072612352 |
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| author | Syrakos, Alexandros Charalambous, Aggelos Georgiou, Georgios C. |
| author_facet | Syrakos, Alexandros Charalambous, Aggelos Georgiou, Georgios C. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_02942 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytical solution of the Poiseuille flow of a De Kee viscoplastic fluid Syrakos, Alexandros Charalambous, Aggelos Georgiou, Georgios C. Fluid Dynamics 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. |
| title | Analytical solution of the Poiseuille flow of a De Kee viscoplastic fluid |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2401.02942 |