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Polymer Fluid Dynamics: Continuum and Molecular Approaches.

R B Bird1, A J Giacomin2

  • 1Rheology Research Center, Chemical and Biological Engineering Department, University of Wisconsin-Madison, Madison, Wisconsin 53706.

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|June 9, 2016
PubMed
Summary

This study explores polymer fluid dynamics by comparing continuum and molecular models for stress tensor formulation. Analyzing simple models reveals insights into polymer structure-rheology relationships for industrial applications.

Keywords:
constitutive equationscontinuum mechanicselongational flowsmolecular theoryoscillatory flowspolymersshear flows

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Area of Science:

  • Polymer fluid dynamics
  • Rheology
  • Continuum mechanics
  • Molecular modeling

Background:

  • Polymer fluid dynamics requires continuity, motion, and energy equations, with stress tensor and heat-flux vector being crucial components.
  • Two primary methods exist for stress tensor formulation: continuum expressions and molecular models derived from kinetic theory.

Purpose of the Study:

  • To investigate the relationship between polymer molecular structure and rheological properties using kinetic theory.
  • To analyze simple constitutive equations (2-4 parameters) and their recovery from more general models like the Oldroyd 8-constant model.
  • To explore equivalences between continuum and molecular approaches for describing polymer flow behavior.

Main Methods:

  • Focus on simple constitutive equations with 2-4 adjustable parameters.
  • Examine the recovery of these simple models as special cases of the Oldroyd 8-constant model.
  • Analyze simple flows, including shearing and extensional flows, relevant to industrial operations.

Main Results:

  • The kinetic theory approach provides insights into structure-property relationships in polymers.
  • Simple models with few parameters can be derived from more complex frameworks.
  • Equivalences between continuum and molecular descriptions are explored.

Conclusions:

  • Studying simplified models aids in identifying promising avenues for further research in polymer rheology.
  • Effective description of simple flows is a prerequisite for applying models to complex industrial problems.