Numerical Simulations of the Flow of Dilute Polymer Solutions in a Four-Roll Mill
J. Feng and L. G. Leal
J. Non-Newtonian Fluid Mech. 72, 187-218 (1997)
Abstract - We study the startup flow of dilute polymer solutions in a four-roll mill by using FENE dumbbell models. Because this flow is inhomogeneous and contains an extension-dominated region at the stagnation point, strong coupling between the flow field and the polymer configuration can be expected. Our effort at simulating such flows and making meaningful comparisons with experiments is a major step toward assessing and improving molecularly-based constitutive models for dilute solutions. The first objective of the paper is to examine the behavior of the Chilcott-Rallison version of the FENE model (FENE-CR) with varying parameters c, De and L. At moderately high values of De and L, the polymer stretching mainly happens within a "birefringent strand" along the exiting flow axis emanating from the stagnation point. The coupling between flow and polymer stretching is exhibited by concerted flow suppression and reduction of polymer extension. In particular, the model predicts double-humped velocity and strain rate profiles across the outflow axis, in qualitative agreement with experiments. The second objective of the paper is to examine the effects of two additional features that can be added to the basic FENE-CR model: shear-thinning and an extra viscous stress. For shear-thinning we use the FENE-P model and for the viscous stress we adopt the expression recently proposed by Rallison [J. Non-Newtonian Fluid Mech., 68 (1997) 61-83]. For the Deborah numbers studied here, shear-thinning causes a small increase in the steady-state polymer stretching at the stagnation point. The strain rate there is also somewhat higher than the corresponding FENE-CR value. The extra viscous stress tends to reduce polymer stretching and the strain rate at the stagnation point. In previous studies, the FENE-CR model has been shown to over-predict polymer stretching. Thus, the extra viscous stress will bring predictions of the model closer to experiments.