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The molecular constitutive models, like FENE-P for polymer solutions, areknown to have convergence issues at relatively larger flow rates. In thisstudy, we investigate the possibility of a numerically efficient GNF-basedapproximation of FENE-P, which would closely approximate the flow field.Firstly, we compare the flow fields predicted by FENE-P and an equivalent GNFmodel. For these studies, we considered the flow around a sphere and selectedthe Carreau-Yasuda model as the representative GNF. This is made equivalent tothe FENE-P by selecting parameters to equalize the viscosity-shear ratedependence. Our results show severe deficiencies of the GNF model, owing to itsinability to account for chain stretching, particularly near the stagnationpoints. Next, the effect of extensional components on the local viscosity wasadded by formulating an equivalent GNF-X [Journal of Rheology 64, 493 (2020)]model. Even this failed to capture the asymmetry in the stress and flowprofiles and predicted very large stresses at both stagnation points, relativeto FENE-P. Hence, we proposed a novel modified formalism (denoted as GNF-XM)that was able to capture all trends successfully. The drag coefficients fromGNF-XM agreed well with FENE-P predictions for all flow rates considered.Significantly, the computational times required to solve the flow field withGNF-XM is about an order of magnitude lower than that of FENE-P, especially athigher flow rates. Thus, we have successfully formulated a highly efficientGNF-based approximation to the FENE-P, whose formalism can be extended to othersimilarly complicated constitutive models.

Formulation of an equivalent GNF model as an efficient approximation for flow of polymer solutions described by FENE-P