Numerical simulation of non-isothermal flow of viscoelastic liquids (proceedings of an IUTAM symposium: J.F. Dijksmann and G.D.C. Kuiken (Eds.), Kluwer, Dordrecht, 1995, pp. ix + 195. £61.50.

Abstract

Numerical computations using an adaptive finite element technique have been performed to simulate the experimental studies of sedimentation of a sphere in a polyisobutylene based Boger fluid performed by Arigo et al. [M.T. Agrio, D.R. Rajagopalan, N.T. Shapely and G.H. McKinley, J. Non-Newtonian Fluid Mech., 60, (1995) 225–257]. The Chillcott–Rallison, FENE-P, multimode Giesekus and the single and multimode versions of the model recently proposed by Verhoef et al. [M.R.J. Verhoef, B.H.A.A. vanden Brule and M.A. Hulsen, On the Modeling of a PIB/PB Boger Fluid in Extensional Flow, J. Non-Newtonian Fluid Mech., in press] were used to describe the rheological data of the Boger fluid. Overall, the multimode Giesekus and the multimode version of the Verhoef et al. [M.R.J. Verhoef, B.H.A.A. vanden Brule and M.A. Hulsen, On the Modeling of a PIB/PB Boger Fluid in Extensional Flow, J. Non-Newtonian Fluid Mech., in press] model provide the best representation of the steady shear and transient uniaxial extensional viscosity of the Boger fluid. A comparison of experimentally measured and computed drag coefficients demonstrate that all the models are capable of qualitatively describing the experimental measured drag as a fraction of We. However, none of these dumbbell based models is capable of describing the experimental data quantitatively over a wide range of We and in different tube to sphere radius ratio geometries. In fact, the agreement between the computed and experimental results in this study is much more limited than prior studies of semi-concentrated polymeric solutions in flows with a single acceleration or deceleration of the fluid elements [J-M. Li, W.R. Burghardt, B. Yang and B. Khomami, J. Non-Newtonian Fluid Mech., 74, (1998) 151–193]. In addition, it has been shown that inclusion of dissipative stresses in dumbbell based constitutive equations does give rise to an increase in the predicted drag in comparison to dumbbell models which do not include this contribution. However, inclusion of these dissipative stresses is not sufficient to describe the experimental data quantitatively. Overall, the results of this study indicate that elastic dumbbell based constitutive equations do not contain all of the underlying physics required to describe the fluid dynamics of dilute polymeric solutions in complex flows.