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On the effect of nonhomogeneous flow fields on the orientation distribution and rheology of fiber suspensions
Author(s) -
Shanker Ravi,
Gillespie J. W.,
Güçeri S. I.
Publication year - 1991
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760310304
Subject(s) - shear flow , mechanics , rheology , materials science , fiber , stokes flow , simple shear , angular velocity , orientation (vector space) , flow (mathematics) , velocity gradient , classical mechanics , distribution function , shear rate , shear (geology) , shear stress , physics , geometry , mathematics , thermodynamics , composite material
The influence of nonhomogeneous flow fields on the orientation distribution and rheology of fiber suspensions is investigated. The Stokes‐Burger model is used to approximate the forces and moments on the fiber for the subsequent calculation of fiber angular velocities for nonhomogeneous cases where the velocity gradients vary over the fiber length. For simple shear flows, an analytical solution based on the Stokes‐Burgers model is derived. Fiber angular velocities are compared to previously published results. An iterative numerical technique is developed to calculate the otherwise indeterminate fiber angular velocities for other nonhomogeneous flows, such as non‐isothermal Hele‐Shaw flows. The value of shear is derived for which the angular motion of the fiber in a quadratic velocity field is identical to that in a linear shear flow. Subsequently, numerical solutions for orientation distribution functions are presented for cases where analytical solutions for distribution functions are not obtainable. The rheological properties are then studied, using the orientation tensor description, for nonhomogeneous flow fields where the fiber motion can be approximated by that in a shear flow, the equivalent shear rate obtained from the numerical scheme.