Time-dependent non-linear dynamics of polymer solutions in microfluidic contraction flow—a numerical study on the role of elongational viscosity

A generalised form of the finitely extensible non-linear elastic (FENE) model for modelling non-linear flow of semi-dilute polymer solutions is proposed. It accounts for conformation-dependent polymer elasticity and predicts shear-thinning shear viscosity, non-linear elongational viscosity and first and second normal stress differences. The rheometric material functions predicted by the model are critically compared with the results of the linear Phan–Thien–Tanner model. The predictabilities of these constitutive models under benchmark flow problems are evaluated by time-dependent simulations, using finite volume method based on a CFD simulation toolbox. The effects of the model parameters, the inertia and the contraction ratio are numerically studied. The modified FENE model qualitatively captures the non-linear flow phenomena of polymer solution in the high elasticity number (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm {El}$\end{document}) flow regime observed in experiments. The results show that an accurate growth function of the elongational viscosity is the key to the prediction of the time-dependent highly asymmetric flow patterns.