Influence of Fiber Length on the Viscous Flow of an Oriented Fiber Assembly

Abstract

The effective elongational viscosity for an oriented fiber assembly of discontinuous fibers suspended in a viscous matrix fluid is developed for a fiber array with variable overalp length of both symmetric and antisymmetric geometries. The results for symmetric and antisymmetric geometries are shown to be equivalent. For variation in fiber length within the assembly, an integral representation is developed and normalized frequency functions of zeroth and first order are exercised. Effective elongational viscosity is calculated for actual fiber length data. Results are compared to predictions for the constant fiber length equal to the mean length and the relative contributions of each fiber length interval to the effective viscosity are determined. Results show that small percentages of long fibers can have a disproportional large influence upon effective assembly viscosity. Finally, for independent fiber length and overlap length distributions of zeroth order, the average effective viscosity is shown to be a polynomial relation of second order in fiber length and third order in overlap length.