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

Furlan, Laison Junio da Silva; Mendonça, Márcio; Araujo, Matheus Tozo de; Souza, Leandro Franco de

doi:10.1016/j.jnnfm.2022.104880

Cited by 4 publications

(7 citation statements)

References 29 publications

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“…As presented in Furlan et al, 27 it is impossible to predict the behavior of three-dimensional disturbances by considering Squire's theorem for the Giesekus model. Therefore, it is necessary to perform a separate analysis for three-dimensional disturbances.…”

Section: B Three-dimensional Disturbance Analysismentioning

confidence: 99%

“…[21][22][23][24][25][26] Even today, studies in parallel flows have not been widely developed, and some questions still need to be answered, especially in viscoelastic fluid stability. Furlan et al 27 presented theoretical results regarding the influence of the molecular composition of viscoelastic fluids and its relation to the stability of these fluids. Viscoelastic models with anisotropic terms, such as Giesekus, LPTT, and FENE-type models, do not satisfy Squire's theorem.…”

Section: Introductionmentioning

confidence: 99%

“…Viscoelastic models with anisotropic terms, such as Giesekus, LPTT, and FENE-type models, do not satisfy Squire's theorem. 27 Therefore, three-dimensional disturbances may have a stronger destabilizing effect than two-dimensional ones.…”

Section: Introductionmentioning

confidence: 99%

“…28 Previous investigations on the stability of non-Newtonian flows based on the Giesekus model indicate the need to investigate flow instability to three-dimensional disturbances due to anisotropy. 22,27,29,30 In the present work, the effects of the mobility parameter a G on the stability of the planar Poiseuille flow are investigated and how these effects change when the other parameters (Wi; b, and spanwise wavelength c) change. The results will show that threedimensional disturbances can be more unstable than two-dimensional, as previously suspected but not quantified.…”

Section: Introductionmentioning

confidence: 99%

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Effects of anisotropy on the stability of Giesekus fluid flow

et al. 2022

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In the present work, the stability of a viscoelastic fluid flow is studied by Linear Stability Theory (LST), and some results are verified by Direct Numerical Simulation (DNS). The investigation considers the fluid flow between two parallel plates, modelled by the Giesekus constitutive equation. The results show the influence of the anisotropic tensorial correction parameter $\alpha_G$ on this model, showing a stabilizing influence for two-dimensional disturbances for small values of $\alpha_G$. However, as $\alpha_G$ increases, a reduction in the critical Reynolds number values is observed, possibly hastening the transition to turbulence. Low values for $\alpha_G$ for three-dimensional disturbances cause more significant variations for the critical Reynolds number. This variation decreases as the value of this parameter increases. The results also show that low values of $\alpha_G$ increase the instability of three-dimensional disturbances and confirm that Squire's theorem is not valid for this model. As for the two-dimensional disturbances, the anisotropic term on the Giesekus model lowers the critical Reynolds number for higher quantities of polymer viscosity in the mixture and high values for the Weissenberg number.

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Section: B Three-dimensional Disturbance Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effects of anisotropy on the stability of Giesekus fluid flow

et al. 2022

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“…Hence, the need arises to perform stability analysis for three-dimensional flows for these viscoelastic models, as the two-dimensional analysis does not guarantee that three-dimensional disturbances are more stable, as stated in Squire's theorem. This chapter was published in Furlan et al (2022).…”

Section: Lptt Modelmentioning

confidence: 99%

Linear Stability Theory Applied to Three-Dimensional Viscoelastic Fluid Flows

Furlan¹

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Ao meu orientador, professor Leandro Franco de Souza, pelo apoio e ensinamentos, e também pelo companheirismo e amizade, contribuindo não apenas para a elaboração deste trabalho mas também para a minha formação pessoal.Ao professor Márcio T. Mendonça, pelo apoio e auxílio no desenvolvimento dessa pesquisa. Sem a sua ajuda, certamente este trabalho não seria plenamente desenvolvido. Ao professor André Cavalieri, pelas considerações feitas durante o meu exame de qualificação, considerações essas que foram fundamentais para o avanço e conclusão deste trabalho.Aos professores do departamento de Matemática e Computação da FCT-UNESP, em especial a professora Analice Costacurta Brandi, pela orientação acadêmica, pela amizade e o compartilhamento dos conhecimentos e experiências.Aos meus amigos do LMACC, em especial Matheus Tozo, amigos esses que fiz no dia a dia, dividindo não só o laboratório como também experiências de vida e momentos felizes. Ao funcionário do laboratório LMACC, Leonardo José Martinussi, pelo companheirismo, eficiência e prontidão para sempre ajudar os alunos no que fosse preciso, bem como no uso do cluster Euler. Sem o seu apoio, certamente esta pesquisa enfrentaria maiores dificuldades além das que foram enfrentadas.Aos amigos que fiz na minha vinda para São Carlos, aos amigos que ficaram em Presidente Prudente, e aos amigos que a vida levou para outros caminhos.

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