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On the validity of Squire's theorem for viscoelastic fluid flows

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Autor(es):
Furlan, Laison Junio da Silva ; de Mendonca, Marcio Teixeira ; de Araujo, Matheus Tozo ; de Souza, Leandro Franco
Número total de Autores: 4
Tipo de documento: Artigo Científico
Fonte: Journal of Non-Newtonian Fluid Mechanics; v. 307, p. 8-pg., 2022-07-21.
Resumo

This work presents a practical methodology to verify the validity of Squire's theorem for viscoelastic fluid flow stability analysis. Squire's theorem presents a relationship between two-dimensional and three-dimensional disturbances. The theorem shows that the critical Reynolds number for two-dimensional disturbances is smaller than any value for which unstable three-dimensional disturbances exist. This conclusion simplifies the stability analysis for fluid flows which satisfies this theorem by becoming sufficient for the stability analysis to look only for the two-dimensional disturbances to find the most dangerous condition. In the present investigation, the validity of Squire's theorem is accessed for viscoelastic fluid flows considering the Upper-Convected Maxwell, Oldroyd-B, Giesekus, LPTT and FENE-type models. The mass, momentum, and viscoelastic constitutive equations are manipulated to arrive at the equivalent two-dimensional equations required for Squire's Theorem validity. It was verified that Squire's theorem is valid for the Upper-Convected Maxwell and the Oldroyd-B isotropic models as already known in the literature, showing that the proposed methodology is consistent with previous results. However, for the Giesekus, the LPTT and the FENE-type anisotropic models, the analysis shows that Squire's theorem is not valid, indicating the relation between the isotropic behavior of the fluids and the validity of Squire's theorem. (AU)

Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
Beneficiário:Francisco Louzada Neto
Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs