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

• Critical Wi extended to Wicrit = 5000+ via convoluted approach.
• Three phases in upstream–downstream vortex-dynamics; high-Wi Moffatt vortices.
• f-functional, Wicrit and positive definiteness correlation.
• Plateauing epd predictions at high-Wi.
• Periodic boundary-condition implementation for consistent Wi = 5000+ solutions.

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 Wiτp∇=2(1−β)D−fτp, 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.

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