A generalised Phan–Thien—Tanner model

Ferrás, Luís Jorge Lima; Morgado, Maria Luísa; Rebelo, Magda; McKinley, Gareth H.; Afonso, A.M.

doi:10.1016/j.jnnfm.2019.06.001

Cited by 48 publications

(50 citation statements)

References 11 publications

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“…This new model can further improve the accuracy of the description of real data obtained with the original exponential function of the trace of the stress tensor, as shown in [18].…”

Section: Generalized Phan-thien and Tanner Modelmentioning

confidence: 95%

“…(18) allows a good fit to experimental rheological data, in flows with defined kinematics where C À1 can be computed explicitly; but, it would be desirable to obtain also an improved frame-invariant differential model, that is easier to handle both mathematically and numerically, when compared to integral models, for solving complex flow problems with spatially varying kinematics. The model to be presented was recently proposed by our research group [18], and basically takes advantage of the flexible functional form of the Mittag-Leffler function by inserting this function into the already well-known Phan-Thien and Tanner (PTT) model, replacing the classical linear and exponential functions of the trace of the stress tensor.…”

Section: Generalized Phan-thien and Tanner Modelmentioning

confidence: 99%

“…Since we consider a simple plane shear flow aligned with the x-axis, we have that σ yy _ γ ðÞ ¼ σ xx ξ= 2 À ξ ðÞ and σ zz _ γ ðÞ ¼ 0 (see [18] for more details).…”

Section: Steady-state Shear Flowsmentioning

confidence: 99%

“…The steady unidirectional extensional viscosity is defined as η E ¼ σ xx À σ yy ÀÁ = _ ς, where _ ς is the imposed elongation rate [18], and can be obtained by solving the system of equations (for a simpler technique that does not involve an iterative procedure, please consult [18]) Fluid Flow Problems…”

Section: Steady-state Elongational Flowsmentioning

confidence: 99%

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Recent Advances in Complex Fluids Modeling

Ferrás¹,

Morgado²,

Rebelo³

et al. 2019

Fluid Flow Problems

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In this chapter, we present a brief description of existing viscoelastic models, starting with the classical differential and integral models, and then focusing our attention on new models that take advantage of the enhanced properties of the Mittag-Leffler function (a generalization of the exponential function). The generalized models considered in this work are the fractional Kaye-Bernstein, Kearsley, Zapas (K-BKZ) integral model and the differential generalized exponential Phan-Thien and Tanner (PTT) model recently proposed by our research group. The integral model makes use of the relaxation function obtained from a step-strain applied to the fractional Maxwell model, and the differential model generalizes the familiar exponential Phan-Thien and Tanner constitutive equation by substituting the exponential function of the trace of the stress tensor by the Mittag-Leffler function. Since the differential model is based on local operators, it reduces the computational time needed to predict the flow behavior, and, it also allows a simpler description of complex fluids. Therefore, we explore the rheometric properties of this model and its ability (or limitations) in describing complex flows.

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“…This new model can further improve the accuracy of the description of real data obtained with the original exponential function of the trace of the stress tensor, as shown in [18].…”

Section: Generalized Phan-thien and Tanner Modelmentioning

confidence: 95%

Section: Generalized Phan-thien and Tanner Modelmentioning

confidence: 99%

“…Since we consider a simple plane shear flow aligned with the x-axis, we have that σ yy _ γ ðÞ ¼ σ xx ξ= 2 À ξ ðÞ and σ zz _ γ ðÞ ¼ 0 (see [18] for more details).…”

Section: Steady-state Shear Flowsmentioning

confidence: 99%

Section: Steady-state Elongational Flowsmentioning

confidence: 99%

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Recent Advances in Complex Fluids Modeling

Ferrás¹,

Morgado²,

Rebelo³

et al. 2019

Fluid Flow Problems

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“…[2] It is important to improve the fitting capabilities of differential models and reduce the computational effort needed to compute the integral models. In a recent work, Ferrás et al [5] proposed the generalised Phan-Thien-Tanner (gPTT), an improved differential model based on the Nhan Phan-Thien and Roger Tanner constitutive equation (PTT model [3] ), derived from the Lodge-Yamamoto type of network theory for polymeric fluids. This model considers the Mittag-Leffler function as a function of the trace of the stress tensor (instead of the classical linear and exponential functions), and provides one or two new fitting constants in order to obtain additional fitting flexibility.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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This work presents analytical and numerical studies for pure Couette and combined Poiseuille-Couette flows under slip. The fluid behaviour is described by the recently proposed viscoelastic model, known as the generalised simplified Phan-Thien-Tanner constitutive equation, that considers the Mittag-Leffler function instead of the classical linear and exponential functions of the trace of the stress tensor, and provides one or two new fitting constants in order to achieve additional fitting flexibility. The solutions derived in this work allow a better understanding of the model and its influence on the slippery behaviour of some complex fluids, contributing in this way to improve the modeling of complex fluids. K E Y W O R D S Couette flow, generalised simplified PTT, Mittag-Leffler, Poiseuille-Couette flow, PTT model, wall slip

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A generalised distributed‐order Maxwell model

Ferrás

Morgado

Rebelo

2022

Math Methods in App Sciences

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In this work, we present a generalised viscoelastic model using distributed-order derivatives. The model consists of two distributed-order elements (distributed springpots) connected in series, as in the Maxwell model. The new model generalises the fractional viscoelastic model presented by Schiessel and Blumen and allows for a more broad and accurate description of complex fluids when a proper weighting function of the order of the derivatives is chosen. We discuss the connection between classical, fractional and viscoelastic models of distributed order and highlight the fundamental concepts that support these constitutive equations. We also derive the relaxation modulus, the storage and loss modulus and the creep compliance for specific weighting functions.

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A generalised Phan–Thien—Tanner model

Cited by 48 publications

References 11 publications

Recent Advances in Complex Fluids Modeling

Recent Advances in Complex Fluids Modeling

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

A generalised distributed‐order Maxwell model

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