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Theoretical and numerical analysis of unsteady fractional viscoelastic flows in simple geometries.
Ferras, Luis L. Ford, Neville J. Morgado, Maria L. Rebelo, Magda S. McKinley, Gareth H. Nobrega, Joao M.
Ferras, Luis L.
Ford, Neville J.
Morgado, Maria L.
Rebelo, Magda S.
McKinley, Gareth H.
Nobrega, Joao M.
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Publication Date
2018-07-12
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Abstract
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
ow 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 \alpha and \beta (the fractional order exponents that regulate the viscoelastic response
of the complex fluids).
Citation
Ferrás, L. L., Ford, N. J., Morgado, M. L., Rebelo, M., McKinley, G. H. & Nóbrega, J. M. (2018). Theoretical and numerical analysis of unsteady fractional viscoelastic flows in simple geometries. Computers and Fluids, 174, 14-33
Publisher
Elsevier
Journal
Computers and Fluids
Research Unit
DOI
10.1016/j.compfluid.2018.07.004
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Type
Article
Language
en
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ISSN
0045-7930