Numerical Study of Shear Banding in Flows of Fluids Governed by the Rolie-Poly Two-Fluid Model via Stabilized Finite Volume Methods

Abstract

<jats:p>The flow of viscoelastic fluids may, under certain conditions, exhibit shear-banding characteristics that result from their susceptibility to unusual flow instabilities. In this work, 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 Volume Method (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.</jats:p>

Computational Analysis of Shear Banding in Simple Shear Flow of Viscoelastic Fluid-Based Nanofluids Subject to Exothermic Reactions

“…Specifically, the current investigation explores the novel contributions of shear banding phenomena to HTR and Therm-C enhancement. Alternatively (and additionally), the current investigation extends the studies in [25][26][27] (all of which focused on the flow behavior and thermodynamics of particle-free viscoelastic fluids) to nanofluids, specifically VFBN modeled by the Giesekus constitutive model. The study in [25] investigates shear banding phenomena using the two-fluid Rolie-Poly viscoelastic constitutive model and the investigations in [26,27] employ the Johnson-Segalman viscoelastic constitutive model.…”

“…Such widespread use of the viscoelastic (polymeric) fluids, for the improvement and enhancement of, say, HTR and Therm-C, emulsion-polymerization, drag-reduction, etc. can be found for example in [1,4,6,[23][24][25][26][27][28][29][30][31][32][33][34].…”

“…Shear-banding phenomena in shear-flow of viscoelastic fluids represents observable and physical discontinuities in the shear-rate profiles of the flow-velocity and finds wide industrial and domestic application, say in emulsion-polymerization and drop break-up [34]. The main mechanism for shear-banding in [25] falls under the category of what are termed flow-induced inhomogeneities. On the other hand, the mechanism for shear-banding in [26] and [27] falls under the category of constitutive instabilities.…”

“…Fluid viscoelasticity has indeed received wide attention in this regard, specifically for the improvement of certain industrial, domestic, and medical applications. Such widespread use of the viscoelastic (polymeric) fluids, for the improvement and enhancement of, say, HTR and Therm-C, emulsion polymerization, drag reduction, etc., can be found, for example, in [1,4,6,[23][24][25][26][27][28][29][30][31][32][33][34].…”

Computational-Analysis of the Non-Isothermal Dynamics of the Gravity-Driven Flow of Viscoelastic-Fluid-Based Nanofluids Down an Inclined Plane

“…Noting the fundamental importance of the rheology of the base fluid to the modern applications of nanofluids, the studies, say in [1][2][3] focus attention on non-Newtonian (specifically polymeric) base-fluids under various flow conditions. The widespread importance of non-Newtonian fluids, both the Generalized Newtonian Fluids (GNF) as well as the polymeric (viscoelastic) fluids, in contemporary application is quite straightforward for example [1][2][3]6,8,[25][26][27][28][29][30][31][32][33][34].…”