Investigation of a microscopic-based model for polymeric fluids using micro-macro simulations

Michigan Technological University, Houghton MI

Investigators

Abstract

The goal of this project is the analysis and further development of a class of microscopic-based, stochastic models for polymeric fluids previously introduced by the PI. In this class of models, the dynamics of the macromolecules is described by two independent Gaussian stochastic processes, one based in network theory and the other in reptation theory for concentrated polymer solutions and polymer melts, while the expression for the stress tensor is given as the expectation of a function of these dynamics. Previous work of the PI has established the good performance of this model in predicting some material functions of several polymer melts in rheometric flows. In this work, the ability of the model to describe quantitatively the behavior of polymeric liquids in engineering flow fields is evaluated. This is achieved by developing a micro-macro simulation program and solving a flow problem in an engineering geometry. In the micro-macro simulation approach, the coarse-grained molecular model is coupled to the conservation equations from continuum mechanics. The system is then solved by iterating the following two steps: (1) The polymer stress field is computed from a known discrete velocity field using stochastic simulation techniques, and (2) Updated velocity and pressure fields are found using the finite element method to solve the conservation equations, where the polymer stress from the first step enters the momentum equation as a known body force. The model is further developed by modifying its dynamics as represented by the stochastic processes. Examples of modifications are the inclusion of terms to account for nonaffine deformation of the configuration vectors and the introduction of noise into the time evolution of the stochastic processes. Polymeric fluids have a complex microstructure formed by their molecules which gives them both viscous and elastic properties. Among the unresolved challenges in viscoelastic fluid mechanics and the related fields of rheology, materials science and polymer physics are the development of accurate rheological, or stress, models for viscoelastic fluids and the development of good numerical simulation techniques for solving flow problems in engineering applications. This research project aims to advance both of these developments. Such developments are needed for understanding the physics of these complex fluids and for establishing the relevant connections between an engineering flow process and the material behavior and microstructure of the fluid being processed. It is known that the quality and efficiency of an engineering processing procedure and the properties of the processed material are affected strongly by the stresses experienced by the fluid during processing. Since the stress experienced by a polymeric fluid during processing is determined by the flow-induced microstructure within the fluid, it is desirable that stress models for such fluids take microstructure into account. The goal of this research is the analysis and further development of a class of microscopic-based models for polymeric fluids previously introduced by the PI. Toward this goal, a micro-macro simulation program is developed which combines the microscopic-based description of the molecules' dynamics and related stress with a macroscopic description of the flow field. This program is then used to analyze the model in an engineering flow process. The model is also further developed through the inclusion of additional physics by modifying its dynamics.