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

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.