Analytical and numerical studies for slip flows of a generalised Phan‐Thien–Tanner fluid

Ribau, A. M.; Ferrás, Luís Jorge Lima; Morgado, Maria Luísa; Rebelo, Magda; Afonso, A.M.

doi:10.1002/zamm.201900183

Cited by 6 publications

(2 citation statements)

References 6 publications

(10 reference statements)

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“…The stress function, K(σ kk ), is given by a new formulation that imparts more flexibility and accuracy to the model predictions, as discussed in [27,29,30]. It is given by:…”

Section: Governing Equationsmentioning

confidence: 99%

Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation

et al. 2021

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In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach 99% of its fully-developed value) of a pressure-driven viscoelastic fluid flow (between parallel plates) modelled by the generalised Phan–Thien and Tanner (gPTT) constitutive equation. The governing equations are solved using the finite-difference method, and, a thorough analysis on the effect of the model parameters α and β is presented. The numerical results showed that in the creeping flow limit (Re=0), the development length for the velocity exhibits a non-monotonic behaviour. The development length increases with Wi. For low values of Wi, the highest value of the development length is obtained for α=β=0.5; for high values of Wi, the highest value of the development length is obtained for α=β=1.5. This work also considers the influence of the elasticity number.

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“…The stress function, K(σ kk ), is given by a new formulation that imparts more flexibility and accuracy to the model predictions, as discussed in [27,29,30]. It is given by:…”

Section: Governing Equationsmentioning

confidence: 99%

Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation

et al. 2021

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“…This model was previously studied for Couette and pressure driven flows, in the absence EO [28,29], therefore this work aims to assess the influence of the new model parameters for combined electro-osmotic/pressure driven flows.…”

Section: Introductionmentioning

confidence: 99%

A study on mixed electro-osmotic/pressure-driven microchannel flows of a generalised Phan-Thien–Tanner fluid

et al. 2021

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This work presents new semi-analytical solutions for the combined fully-developed electro-osmotic (EO) pressure-driven flow in microchannels of viscoelastic fluids, described by the generalised Phan-Thien-Tanner model (gPTT) recently proposed by Ferrás et al. [Journal of Non-Newtonian Fluid Mechanics, 269: 88-99, 2019]. This generalised version of the PTT model presents a new function for the trace of the stress tensor -the Mittag-Leffler function -where one or two new fitting constants are considered in order to obtain additional fitting flexibility. The semi-analytical solution is obtained under sufficiently weak electric potentials that allows the Debye-Hückel approximation for the electrokinetic fields and for thin electric double layers.Based on the solution, the effects of the various relevant dimensionless numbers are assessed and discussed, such as the influence of εW i 2 , of the parameters α and β of the gPTT model, and also of κ, the dimensionless Debye-Hückel parameter. We conclude that the new model characteristics enhance the effects of both εW i 2 and κ on the velocity distribution across the microchannels. The effects of a high zeta potential are also studied numerically.

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Analytical study of the annular flow of a generalised Phan-Thien–Tanner fluid

Ribau,

Ferrás,

Morgado

et al. 2023

Acta Mech

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The annular flow of complex viscoelastic fluids, described by the generalised Phan-Thien–Tanner model, is studied. This model considers the Mittag-Leffler function instead of the usual linear or exponential functions of the trace of the stress tensor, and includes two new parameters that provide additional fitting flexibility. We derive a semi-analytical solution that provides a better understanding of the behaviour of this type of fluid in annular flows and also helps to improve the modelling of complex materials.

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Analytical and numerical studies for slip flows of a generalised Phan‐Thien–Tanner fluid

Cited by 6 publications

References 6 publications

Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation

Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation

A study on mixed electro-osmotic/pressure-driven microchannel flows of a generalised Phan-Thien–Tanner fluid

Analytical study of the annular flow of a generalised Phan-Thien–Tanner fluid

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