Fluid Dynamics

, Volume 8, Issue 6, pp 860–865 | Cite as

Influence of internal viscosity of macromolecules on the viscoelastic behavior of polymer solutions

  • V. N. Pokrovskii
  • V. I. Chuprinka


In the description of the motion of solutions of polymers, macromolecules may be treated schematically either as perfectly rigid or perfectly flexible particles [1]. Study of the flow of a suspension of such particles for rigid ellipsoids of revolution [2] and for perfectly flexible necklaces [3] leads to equations of motion that describe the basic features of the viscoelastic behavior of weak solutions of rigid and flexible macromolecules. It is to be expected that some classes of macromolecules have intermediate properties [1] and that their motion in a flow should be represented by partly rigid particles, i.e., particles with internal viscosity. In order to estimate the influence of internal viscosity on the properties of polymer solutions it is sufficient to consider the behavior of a suspension of partly rigid dumbbells, In the present paper, in which a dilute suspension of partly rigid dumbbells is considered, expressions are calculated for the stress tensor, which is defined in terms of the moments of the distribution function, and the relaxation equations for the moments. Together with the continuity equation and the equation of motion, these relations form a system of equations of motion of the suspension that is in the general case not closed. The results in limiting cases when the internal viscosity is zero or infinite coincide with the well-known results [4]. Some types of flow of a suspension of dumbbells with weak internal viscosity were studied in [5].


Polymer Viscosity Distribution Function Macromolecule Stress Tensor 
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Literature cited

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    V. N. Tsvetkov, V. E. Éskin, and S. Ya. Frenkel', Structure of Macromoiecules in Solutions [in Russian], Nauka, Moscow (1964).Google Scholar
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    V. N. Pokrovskii, “Stresses, viscosity, and optical anisotropy of a moving suspension of rigid ellipsoids,” Usp. Fiz. Nauk,105, No. 4 (1971).Google Scholar
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    V. N. Pokrovskii, “Relaxation processes in deformable polymer systems,” in: Successes of Polymer Rheology [in Russian], Khimiya, Moscow (1970), p. 134.Google Scholar
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    R. B. Bird, H. B. Warner, Jr., and D. C. Evans, “Kinetic theory and rheology of dumbbell suspensions with Brownian motion,” Adv. Polymer Sci.,8, No. 1 (1971).Google Scholar
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    H. C. Booij and P. H. van Wiechen, “Effect of internal viscosity on me deformation of a linear macromolecule in a sheared solution,” J. Chem. Phys.,52, No. 10 (1970).Google Scholar
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    S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys.,15, No. 1 (1943).Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • V. N. Pokrovskii
    • 1
  • V. I. Chuprinka
    • 1
  1. 1.Moscow

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