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High-Weissenberg predictions for micellar fluids in contraction–expansion flows

J.E. López-Aguilar, M.F. Webster, H.R. Tamaddon-Jahromi, O. Manero, Michael Webster Orcid Logo, Hamid Tamaddon-Jahromi

Journal of Non-Newtonian Fluid Mechanics, Volume: 222, Pages: 190 - 208

Swansea University Authors: Michael Webster Orcid Logo, Hamid Tamaddon-Jahromi

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Abstract

This study is concerned with the numerical modelling of thixotropic and non-thixotropic materials in contraction-expansion flows at high Weissenberg number (We). Thixotropy is represented via a new micellar time-dependent constitutive model for worm-like micellar systems and contrasted against netwo...

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Published in: Journal of Non-Newtonian Fluid Mechanics
ISSN: 03770257
Published: 2015
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa24184
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Abstract: This study is concerned with the numerical modelling of thixotropic and non-thixotropic materials in contraction-expansion flows at high Weissenberg number (We). Thixotropy is represented via a new micellar time-dependent constitutive model for worm-like micellar systems and contrasted against network-based time-independent PTT forms. The work focuses on steady-state solutions in axisymmetric rounded-corner 4:1:4 contraction-expansion flows for the benchmark solvent-fraction of β=1/9 and moderate hardening characteristics (=0.25). In practice, this work has relevance to industrial and healthcare applications, such as enhanced oil-reservoir recovery and microfluidics. Simulations have been performed via a hybrid finite element/finite volume algorithm, based around an incremental pressure-correction time-stepping structure. To obtain high-We solutions, both micellar and PTT constitutive equation f-functionals have been amended by (i) adopting their absolute values appealing to physical arguments (ABS-correction); (ii) through a change of stress variable, Π=τp+(ηp0/λ1)I, that aims to prevent the loss of evolution in the underlying initial value problem; and finally, (iii) through an improved realisation of velocity gradient boundary conditions imposed at the centreline (VGR-correction). On the centreline, the eigenvalues of Π are identified with its Π–stress-components, and discontinuities in Π–components are located and associated with the f-functional-poles in simple uniaxial extension. Quality of solution is described through rz, N1 and N2 (signature of vortex dynamics) stress fields, and -eigenvalues. With {micellar, EPTT} fluids, the critical Weissenberg number is shifted from critical states of Wecrit={4.9, 220} without correction, to Wecrit={O(102), O(103)} with ABS-VGR-correction. Furthermore, such constitutive equation correction has been found to have general applicability.
Keywords: high-elasticity solutions, positive definiteness, wormlike micelles, Bautista-Manero models, numerical simulation, hybrid finite element/volume method, enhanced oil-recovery
College: Faculty of Science and Engineering
Start Page: 190
End Page: 208