Dynamics
of Dilute Polymeric Solutions: Coarse Graining Strategies and Multi-Scale Flow
Simulations
Materials Research Laboratory, Department of Chemical
Engineering
Washington University, Saint Louis, MO 63130, USA
Traditionally, coarse-grained kinetic theory based models of dilute polymeric solutions have relied on reduction of the internal degrees of freedom in the micro-mechanical description of the macromolecule. However, in recent years fluorescence microscopy of model macromolecules, namely DNA, in a variety of flow fields has shown that multi-segment bead-rod and bead spring descriptions are required to describe both single molecule dynamics such as molecular individuality, unraveling/tumbling dynamics as well as the rheological properties of the solution, namely, viscosity and the mean molecular extension. 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 chain are required for accurate modeling of polymer dynamics under flow. Motivated by this fact, we have been involved in developing novel coarse graining strategies as well as highly efficient multiscale simulation techniques for dynamics of polymeric solutions under flow. In this presentation our progress in both areas will be discussed. Specifically, I will address the following issues,
1. Development of a reduced-order configuration-based
model for dilute macromolecular solutions that relies on partitioning the phase
space accessible to macromolecules into a few configuration classes, namely,
folds, half dumbbells, kinks, dumbbells, coils and extended states. In turn,
the evolution of the probability distribution of these classes is determined
via a population balance model and the configurational details of molecules
within each class are coarse-grained into a single micro-mechanical variable.
Macroscopic properties such as the stress are calculated as a sum over the
contributions from the configuration classes weighted by their respective
probability of occurrence by using a unique force law that is consistently
derived from Brownian dynamics simulations. The accuracy and efficiency of the
configuration-based model is demonstrated by studying the startup
of steady uniaxial extensional flow followed by relaxation and the startup of steady shear. Furthermore, the applicability of
the configuration-based model to multi-scale flow calculations is demonstrated.
2. Development of a highly efficient algorithm for multiscale
large-scale flow simulation of dilute polymeric solutions described by
multi-segment bead-spring micro-mechanical models. The accuracy and efficiency
of the algorithm is demonstrated via flow simulations in simple and complex
kinematics flows (i.e., plane-Couette, Poiseuille,
and 4-1-4 contraction/expansion).