Numerical simulation of viscoelastic fluids in cross-slot devices

Abstract

Cross-slot flow for viscoelastic fluids is investigated through various numerical algorithms, demonstrating the effectiveness of such devices to study constitutive models and their resulting rheological properties. Here, the steady problem manifests the long-time exposure to significant extension. Solutions are compared and contrasted for a range of rheological models of varying shear and extensional response, including phenomenologically based models from network-theory of Oldroyd/Phan-Thien–Tanner class, and also kinetic-theory based forms of FENE-CR and pom-pom. Matching rheological fluid characteristics are sought across various models through peak extensional viscosity and Trouton ratio. Using the Oldroyd-B model and for the more solvent-dominated fluid, deformation rate peak-levels are practically unaffected by rise in elasticity. Alternatively, for the more polymeric-based fluid, such peak-levels are reduced with increasing elasticity. Successful attempts have been made to match rheological response and complex flow fields between strain hardening polymeric-based Oldroyd-B and constant shear viscosity FENE-CR models, so that the two fluids display the closest cross-slot flow field features. Here, similar stress field contours are observed for both models over a range of elasticity levels, with comparable pressure-drops. Similarly, strain hardening and strain softening e-PTT models are rheologically matched to SXPP models, which also provide insight into the distribution of molecular backbone-stretch. From the combination of viscometric data and numerical solutions for cross-slot flow, local peaks may be derived in strain-rate and maximum levels of normal stress may be accurately predicted with these models. This demonstrates a significant shift towards qualitative agreement with corresponding experimental findings.