247i

Modeling flow of dilute polymeric solutions in complex kinematics flows using closed form constitutive equations or single segment elastic dumbbell models has attracted considerable attention in the past decade. However, to date most simulations in complex kinematics flows have not been able to quantitatively describe the experimentally observed flow dynamics, such as vortex growth, free surface, interface motion etc., or the measured frictional drag properties [1-6]. This lack of quantitative prediction of experimental findings can be attributed to the fact that single segment elastic dumbbell models as well as closed form constitutive equations obtained by invoking various closures such as the FENE-P, FENE-LS can at best qualitatively describe the polymer dynamics and rheological properties of dilute polymer solutions as evinced by recent fluorescence microscopy studies of model macromolecules, namely DNA, in a variety of flow fields [7,8]. However, these studies have also demonstrated that multi-segment bead-rod and bead spring descriptions of dilute polymeric solutions can describe both single molecule dynamics such as molecular individualism, and unraveling dynamics, as well as the solution rheological properties such as viscosity and mean molecular extension with good accuracy [7,8]. These findings clearly underscore the fact that a multi-segment description of the macromolecule or reduced order coarse grained models that contain information regarding the internal degrees of freedom of the macromolecule are required for quantitatively accurate modeling of dilute polymer solutions under flow. Motivated by this fact, we have developed a highly accurate and CPU efficient algorithm for multiscale simulation of dilute polymeric solutions in complex kinematics flows using a bead-spring chains [9].

In this study, we have used our recently developed multiscale algorithm to model flow of a dilute polymeric solution through 4:1:4 axisymmetric contraction/expansion geometry utilizing single and multi-segment bead-spring descriptions as well as the FENE-P closed form constitutive equations. It should be noted that this geometry has been selected not only because it contains many important features of typical polymer processing flows, namely, contraction/expansion as well as recirculation but also due to the fact that a wealth of experimental data is available in terms of vortex dynamics and frictional drag properties [10,11]. In this presentation, we will discuss the influence of various model parameters, such as internal degrees of freedom, finite extensibility, closure approximation, and stress-conformation hysterisis on the predicted vortex dynamics and the frictional drag properties of the flow over a wide range of De. In turn, a unified approach for process level simulation of dynamics of dilute polymeric solutions will be suggested.

[1] R. Keunings, Micro-macro methods for the multiscale simulation of viscoelastic flow using molecular models of kinetic theory, Rheology Reviews, D.M. Binding and K. Walters (Eds.), British Society of Rheology, (2004) 67-98.

[2] B. Yang, B. Khomami, Simulation of sedimentation of a sphere in a viscoelastic fluid using molecular based constitutive models, J. Non-Newtonian Fluid Mech. 82 (1999) 429-452.

[3] J. Li, W. R. Burghardt, B. Yang, B. Khomami, Flow birefringence and computational studies of a shear thinning polymer solution in axisymmetric stagnation flow, J. Non-Newtonian Fluid Mech. 74 (1998) 151-193.

[4] J. Li, W. R. Burghardt, B. Yang, B. Khomami, Birefringence and computational studies of a polystyrene Boger fluid in axisymmetric stagnation flow, J. Non-Newtonian Fluid Mech. 91 (2000) 189-220.

[5] A. M. Grillet, B. Yang, B. Khomami, E. G. Sahqfeh, Modeling of viscoelastic lid driven cavity flow using finite element simulations, J. Non-Newtonian Fluid Mech. 88 (1999) 99-131.

[6] P. Szabo, J.M. Rallison, E.J. Hinch, Start up of flow of a FENE-fluid through a 4:1:4 constriction in a tube, J. Non-Newtonian Fluid Mech. 72 (1997) 73-86.

[7] E.S. G. Shaqfeh, The dynamics of single-molecule DNA in flow, J. Non-Newtonian Fluid Mech.,130, (2005) 1-28.

[8] R. G. Larson, The rheology of dilute solutions of flexible polymers: progress and problems, J. Rheol., 49, (2005) 1-70.

[9] A.P. Koppol, R. Sureshkumar, B.Khomami, An efficient algorithm for multiscale flow simulation of dilute polymeric solutions using bead-spring chains, Submitted to J. Non-Newtonian Fluid Mech. (2006).

[10] J. P. Rothstein, G. H. Mckinley, Extensional flow of a polystyrene boger fluid through a 4:1:4 contraction/expansion, J. Non-Newtonian Fluid Mech. 86 (1999) 61-88.

[11] J. P. Rothstein, G. H. Mckinley, The axisymmetric contraction-expansion: the role of extensional rheology on vortex growth dynamics and the enhanced pressure drop, J. Non-Newtonian Fluid Mech. 98 (2001) 33-63.

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