Convoluted models and high-Weissenberg predictions for micellar thixotropic fluids in contraction–expansion flows

Abstract This study is concerned with finite element/volume modelling of contraction–expansion axisymmetric pipe flows for thixotropic and non-thixotropic viscoelastic models. To obtain solutions at high Weissenberg numbers ( Wi ) under a general differential form W i τ p ∇ = 2 ( 1 − β ) D − f τ p , both thixotropic Bautista–Manero micellar and non-thixotropic EPTT f -functionals have been investigated. Here, three key modifications have been implemented: first, that of convoluting EPTT and micellar Bautista–Manero f -functionals, either in a multiplicative ( Conv * ) or additive ( Conv + ) form; second, by adopting f -functionals in absolute form (ABS- f -correction); and third, by imposing pure uniaxial-extension velocity-gradient components at the pure-stretch flow-centreline (VGR-correction). With this combination of strategies, highly non-linear solutions have been obtained to impressively high Wi [=O(5000+)]. This capability permits analysis of industrial applications, typically displaying non-linear features such as thixotropy, yield stress and shear banding. The scope of applications covers enhanced oil-recovery, industrial processing of plastics and foods, as well as in biological and microfluidic flows. The impact of rheological properties across convoluted models (moderate-hardening, shear-thinning) has been observed through steady-state solutions and their excess pressure-drop ( epd ) production, stress, f -functional field structure, and vortex dynamics. Three phases of vortex-behaviour have been observed with rise in elasticity, along with upstream–downstream Moffatt vortices and plateauing epd -behaviour at high- Wi levels. Moreover, enhancement of positive-definiteness in stress has improved high- Wi solution attenuation.