First-Order Approximations for the Effective Shearing Viscosities of Continuous-Fiber Suspensions

Abstract

The effective shearing viscosities required to model aligned-continuous-fiber suspensions as a transversely isotropic fluid are investigated. Relations for the longitudinal shearing viscosity and the transverse shearing viscosity are developed by considering the kinematics of adjacent rigid fibers interacting with the viscous fluid matrix in states of shear deformation. This simple micromechanical analysis revealed that the longitudinal and transverse shearing viscosities of the medium may be considered to be equal. The present prediction for the in-plane shearing viscosity accounts for the constraint of fiber inextensibility and differs from previous relations [4-6]. In addition, the relationships presented herein were used in Reference [11], but development and discussion of these relationships, as given in the following, are lacking in the literature. Predictions for both Newtonian and shear thinning Carreau matrix fluids are presented and compared to results of a finite-element analysis as well as the earlier work of Christensen [10]. Finally, these simple relations are compared to experimental observations in order to evaluate their validity.