Orientational dispersion of fibers in extensional flows

Abstract

A kinetic theory is presented that predicts the dispersion of particle orientation, solely as a result of hydrodynamic interactions, about the principal axis of extension in uniaxial and planar extensional flows. The mean-squared displacement of the orientation vector is calculated in both the asymptotic dilute and semidilute concentration regimes. In the dilute regime (where nL3≪1, with n the fiber number density and L the fiber length) it is found that the mean-squared displacement is O[nL3/ln2(r)], where r is the fiber aspect ratio. For semidilute suspensions (where nL3≫1) it is predicted that the dispersion is O[ln(nL3)/nL3]. Thus the dispersion increases as the concentration is increased from infinite dilution and then ultimately decreases in the semidilute regime. The physical reasons for this behavior are discussed and, in particular, the semidilute scaling is demonstrated to be a consequence of the short-range particle screening that develops in semidilute suspensions [Phys. Fluids A 1, 3 (1989); 2, 7 (1990)]. The effect of this orientational dispersion on the material properties of fiber composites is also considered.