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Flow‐alignment and rheology of polymer melts: Computation of the single‐link orientational distribution function
Author(s) -
Kröger Martin
Publication year - 1994
Publication title -
macromolecular symposia
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.257
H-Index - 76
eISSN - 1521-3900
pISSN - 1022-1360
DOI - 10.1002/masy.19940810110
Subject(s) - distribution function , rheology , shear rate , shear flow , computation , flow (mathematics) , boundary value problem , diffusion , galerkin method , spherical harmonics , materials science , physics , mechanics , statistical physics , classical mechanics , thermodynamics , mathematical analysis , mathematics , finite element method , algorithm
The single‐link orientational distribution function and the space‐averaged stresses in the fluid are computed for the case of steady shear flow of polymer melts. The computation is achieved with Galerkin's method with spherical harmonics and Euler polynomials as trial functions. The stress components become power functions of shear rate when the latter is large. The single‐link orientational distribution function f solves the Fokker‐Planck equation subject to a boundary condition for f at the chain ends. A solution is obtained for every shear rate and ratio of the orientational and one‐dimensional diffusion coefficient. It is demonstrated that the Fokker‐Planck equation with appropriate boundary condition is useful in order to predict the flow‐alignment and stresses in good agreement with experimental data as well as with recent results of a nonequilibrium molecular dynamics computer simulation on polymer melts.