Rheology pp 327-332 | Cite as

An Analysis of Rheological Behaviors of Polymer Solution with Beads-Spring Model

  • Yuan-Tse Hsu
  • P. Schümmer


The beads-spring model of Rouse and Zimm has successfully predicted certain viscoelastic properties for a number of polymer solutions both dilute and concentrated. One of the basic refinements to Rouse model was added by Zimm for hydrodynamic interaction (HI) origninating from the perturbation of solvent hydrodynamics within the coil. The constitutive equation of Rouse-Zimm model was constructed, also the necessity of exactly solving the Zimm’s HI problem was recognized and the exact eigenvalues were produced through number of submolecules N=300 by Lodge and Wu. /1/ Nevertherless, because of the complexity of the expression of HI, the analytical expressions of rheological properties of polymer solution in general cases have not yet appeared. In present paper we establish these expressions. from the exact numerical solution of Zimm’s eigenvalue problem partially by comparison with experimental results. It should be mentioned that this investigation is limited to the range of low shear rates.


Polymer Solution Hydrodynamic Interaction Relaxation Time Spectrum Exact Numerical Solution Exact Eigenvalue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. /1/.
    A.S. Lodge and Y.J. Wu, Constitutive equations for polymer solutions derived from the bead-spring model of Rouse and Zimm, Rheol. Acta, 10 (1971) 539–553MATHGoogle Scholar
  2. /2/.
    J. Brandrup and E.H. Immergut (Eds.), Polymer Handbook, Intersci. Pub., New York, (1965) iv–1–iv–72Google Scholar

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Yuan-Tse Hsu
    • 1
  • P. Schümmer
    • 2
  1. 1.Inst. of ChemistryAcademia SinicaBeijingChina
  2. 2.Inst. f. VerfahrenstechnikRWTH AachenAachenGermany

Personalised recommendations