Numerical Study of Shear Banding in Flows of Fluids Governed by the Rolie-Poly Two-Fluid Model via Stabilized Finite Volume Methods
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Date
2020-07-09
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Processes | An Open Access Journal from MDPI
Abstract
The flow of viscoelastic fluids may, under certain conditions, exhibit shear-banding
characteristics that result fromtheir susceptibility to unusual flowinstabilities. In thiswork, we explore
both the existing shear banding mechanisms in the literature, namely; constitutive instabilities and
flow-induced inhomogeneities. Shear banding due to constitutive instabilities is modelled via either
the Johnson–Segalman or the Giesekus constitutive models. Shear banding due to flow-induced
inhomogeneities is modelled via the Rolie–Poly constitutive model. The Rolie–Poly constitutive
equation is especially chosen because it expresses, precisely, the shear rheometry of polymer solutions
for a large number of strain rates. For the Rolie–Poly approach, we use the two-fluid model wherein
the stress dynamics are coupled with concentration equations. We follow a computational analysis
approach via an efficient and versatile numerical algorithm. The numerical algorithm is based on the
Finite VolumeMethod (FVM) and it is implemented in the open-source software package, OpenFOAM.
The efficiency of our numerical algorithms is enhanced via two possible stabilization techniques,
namely; the Log-Conformation Reformulation (LCR) and the Discrete Elastic Viscous Stress Splitting
(DEVSS) methodologies. We demonstrate that our stabilized numerical algorithms accurately simulate
these complex (shear banded) flows of complex (viscoelastic) fluids. Verification of the shear-banding
results via both the Giesekus and Johnson-Segalman models show good agreement with existing
literature using the DEVSS technique. A comparison of the Rolie–Poly two-fluid model results with
existing literature for the concentration and velocity profiles is also in good agreement.
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doi:10.3390/pr8070810