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

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 (ε=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 τrz, N1 and N2 (signature of vortex dynamics) stress fields, and Π-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.