Unsteady flow of viscoelastic fluid with the fractional K-BKZ model between two parallel plates

Sin, Chung‐Sik; Zheng, Liancun; Sin, Jun-Sik; Liu, Fawang; Lin, Li

doi:10.1016/j.apm.2017.03.029

Cited by 25 publications

(15 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, it is important to note that neither model can capture the shear thinning observed at large strains and high Weissenberg numbers [26]. To describe these nonlinear effects it will be important in future work to also incorporate nonlinear effects in the integral expressions for the stress, for example through a factorizable equation of K-KBKZ form [26,85,42]. where, since it was assumed that the flow is axisymmetric, ∂ ∂θ = 0.…”

Section: Discussionmentioning

confidence: 99%

Theoretical and numerical analysis of unsteady fractional viscoelastic flows in simple geometries

et al. 2018

View full text Add to dashboard Cite

In this work we discuss the connection between classical and fractional viscoelastic Maxwell models, presenting the basic theory supporting these constitutive equations, and establishing some background on the admissibility of the fractional Maxwell model. We then develop a numerical method for the solution of two coupled fractional differential equations (one for the velocity and the other for the stress), that appear in the pure tangential annular flow of fractional viscoelastic fluids. The numerical method is based on finite differences, with the approximation of fractional derivatives of the velocity and stress being inspired by the method proposed by Sun and Wu for the fractional diffusion-wave equation [ Z.Z. Sun, X. Wu, A fully discrete difference scheme for a diffusion-wave system, Applied Numerical Mathematics 56 (2006) 193-209]. We prove solvability, study numerical convergence of the method, and also discuss the applicability of this method for simulating the rheological response of complex fluids in a real concentric cylinder rheometer. By imposing a torsional step-strain, we observe the different rates of stress relaxation obtained with different values of α and β (the fractional order exponents that regulate the viscoelastic response of the complex fluids).

show abstract

Section: Discussionmentioning

confidence: 99%

Theoretical and numerical analysis of unsteady fractional viscoelastic flows in simple geometries

et al. 2018

View full text Add to dashboard Cite

show abstract

“…Flows of viscoelastic fluids with the fractional constitutive model have also been attracted by many authors . In Tan et al, analytical solutions of unsteady flows of viscoelastic fluid with the fractional Maxwell model between two parallel plates were established by employing integral transform techniques.…”

Section: Introductionmentioning

confidence: 99%

“…Flows of viscoelastic fluids with the fractional constitutive model have also been attracted by many authors. [18][19][20][21][22][23][24][25] In Tan et al, 18 analytical solutions of unsteady flows of viscoelastic fluid with the fractional Maxwell model between two parallel plates were established by employing integral transform techniques. Qi and Xu 19 used Fourier sine transform and discrete Laplace transform to obtain the analytical solutions of Poiseuille flow and Couette flow of generalized Oldroyd-B fluid with fractional derivative.…”

mentioning

confidence: 99%

Couette flow of viscoelastic fluid with constitutive relation involving general Caputo‐type fractional derivative

Sin¹,

In²

2020

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In this paper, the general Caputo‐type fractional differential operator introduced by Pr. Anatoly N. Kochubei is applied to the linear theory of viscoelasticity. Firstly, using the general Caputo‐type derivative, a generalized linear viscoelastic constitutive equation is proposed for the first time. Secondly, the momentum equation for the plane Couette flow of viscoelastic fluid with the constitutive relation is given as an integrodifferential equation and the analytical solution of the equation is established by employing the separation of variables method. Lastly, for special cases of the general constitutive relation, the analytical solutions are obtained in terms of the Mittag‐Leffler functions.

show abstract

“…e two categories are different since the former is more intuitive for the comprehension of the motion of a viscoelastic fluid, while the latter can better explain the rheological characteristics of a viscoelastic fluid through the perspective of its mechanical properties. However, when the fluid's velocity is higher, the fractional Maxwell model will gradually develop into a Newtonian fluid and lose viscoelasticity [13]. Similarly, when a viscoelastic fluid has a large deformation, the fractional Maxwell model is less nonlinear, which can lead to incorrect results [14].…”

Section: Introductionmentioning

confidence: 99%

Fractional K-BKZ Numerical Model of the Start-Up Flow for a Viscoelastic Shock Absorber

Mao¹,

Wang²,

Yang³

et al. 2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This paper has proposed a fractional K-BKZ numerical model by adopting the framework of the classical K-BKZ model and the relaxation modulus of the fractional Maxwell model with quasiproperties to study the start-up flow of a viscoelastic shock absorber. The start-up flows in both the orifice and the gap of a shock absorber were simplified to unidirectional accelerated flows in a pipe and between two parallel plates where one plate is accelerating and the other is at rest. The fractional K-BKZ numerical model was then developed using the finite difference method with real-world initial and boundary conditions. Numerical simulation was then performed, and the results were validated through laboratory testing, based on a comparison of the maximum fluid level and the contact angle. The proposed fractional K-BKZ numerical model successfully simulated the characteristics of the viscoelastic material passing through the orifice or the gap of a shock absorber, as demonstrated by accurately capturing the change of the shape of the flow. This fractional K-BKZ numerical model provided better accuracy for the fluid’s viscoelasticity and can be used for shock absorber design.

show abstract

Unsteady flow of viscoelastic fluid with the fractional K-BKZ model between two parallel plates

Cited by 25 publications

References 41 publications

Theoretical and numerical analysis of unsteady fractional viscoelastic flows in simple geometries

Theoretical and numerical analysis of unsteady fractional viscoelastic flows in simple geometries

Couette flow of viscoelastic fluid with constitutive relation involving general Caputo‐type fractional derivative

Fractional K-BKZ Numerical Model of the Start-Up Flow for a Viscoelastic Shock Absorber

Contact Info

Product

Resources

About