Applied Mathematics and Mechanics

, Volume 8, Issue 9, pp 829–838 | Cite as

The effect of the hydrodynamic interaction on the rheological properties of Hookean dumbbell suspensions in steady state shear flow

  • Fan Xi-jun


The diffusion equation for the configurational distribution function of Hookean dumbbell suspensions with the hydrodynamic interaction (HI) was solved, in terms of Galerkin's method, in steady state shear flow; and viscosity, first and second normalstress coefficients and molecular stretching were then calculated. The results indicate that the HI included in a microscopic model of molecules gives rise to a significant effect on the macroscopic properties of Hookean dumbbell suspensions. For example, the viscosity and the first normal stress coefficient, decreasing as shear rate increases, are no longer constant; the second normal-stress coefficient, being negative with small absolute value and shear-rale dependent, is no longer zero; and an additional stretching of dumbbells is yielded by the HI. The viscosity junction and the first normal-stress coefficient calculated from this method are in agreement with those predicted from the self-consistent average method qualitatively, while the negative second normal-stress coefficient from the former seems to be more reasonable than the positive one from the latter.


Viscosity Shear Rate Normal Stress Rate Increase Industrial Mathematic 
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Copyright information

© Shanghai University of Technology 1987

Authors and Affiliations

  • Fan Xi-jun
    • 1
  1. 1.Department of Chemial EngineeringZhejiang UniversityHangzhou

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