The effect of hydrodynamic interactions on the orientation distribution in a fiber suspension subject to simple shear flow

Abstract

A single, non-Brownian fiber suspended in a viscous, Newtonian fluid undergoing simple shear flow rotates in one of a set of closed orbits known as Jeffery orbits. In a fiber suspension, the hydrodynamic interactions among the fibers determine the distribution of fibers among these orbits. The hydrodynamic interactions in dilute and semidilute suspensions have been studied using slender-body theory. Hydrodynamic, orientational diffusivities were obtained from an ensemble average of the fiber–fiber interactions. The steady-state fiber orientation distribution is controlled by the anisotropy and orientation dependence of the diffusivities. The steady-state and transient fiber orientation distributions are derived using a perturbation analysis for weak hydrodynamic orientational diffusion that is an extension of the work of Leal and Hinch [J. Fluid Mech. 46, 685 (1972)] for weak, isotropic, rotary Brownian motion. In the dilute regime, the steady-state experimental distributions of Anczurowski and Mason [J. Colloid Interface Science 23, 522 (1967)] do not agree with the theoretical predictions. An explanation for these discrepancies accompanied with new experimental results is presented in this work. The theoretical predictions for the steady-state orientation distribution, and the temporal orbit constant correlation function in the semidilute regime are in good agreement with the experimental results of Stover et al. [J. Fluid Mech. 238, 277 (1992)]. The correlation time for the fiber orientation is approximately inversely proportional to fiber concentration in both the dilute and semidilute regimes.