Hi Fidelity Multiscale Flow Simulation of Sedimentation of a Sphere In Dilute Polymeric Solutions
Arash Abedijaberi, Chemical and Biomolecular Engineering, University of Tennessee in Knoxville, Chemical & Biomolecular Engineering, 1512 Middle Drive, Knoxville, TN 37996-2200 and Bamin Khomami, Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996.
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 and/or interface motion, or the measured frictional drag properties. 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. However, multi-segment bead-rod and bead spring descriptions of dilute polymeric solutions have been shown to describe both single molecule dynamics as well as the solution rheological properties. These findings clearly underscore the fact that a multi-segment description of the macromolecule with sufficient information regarding the internal degrees of freedom is required for accurate modeling of dilute polymer solutions under flow. Motivated by this fact, we have recently performed multiscale flow simulation of dilute polymeric solutions in a 4:1:4 axisymmetric contraction/expansion geometry utilizing single and multi-segment bead-spring descriptions. Our success in quantitatively describing both vortex dynamics and the frictional drag properties of this flow over a wide range of De has motivated extension of this approach to other complex kinematics flows, namely, sedimentation of a sphere in a tube. In particular, we have carried out extensive multiscale flow simulations in tubes of various diameters. A detailed comparison of computational and experimental results (sedimentation of a sphere in various tubes filled with a polyisobutylene based Boger fluid) clearly demonstrate that multiscale simulations with micromechanical models that accurately describe the internal degrees of freedom of the macromolecules as well as their polydispersity are capable of providing accurate prediction of the drag coefficient of the sphere over a broad range of De and tube diameters.