Hydrodynamic, translational diffusion in fiber suspensions subject to simple shear flow

Translational, hydrodynamic diffusivities for fibers and fluid particles in a suspension of fibers undergoing simple shear flow have been calculated. The hydrodynamic interactions between the fibers were treated using slender-body theory. The diffusivities were obtained by averaging over all possible interactions. Both dilute (nl3≪1) and semidilute (nl3≫1 but nl2d≤1) suspensions were studied. Here, n is the number of fibers per unit volume, l is the fiber length, and d is the fiber diameter. In a complementary experimental study, the positions of tracer particles were observed in an index of refraction and density matched semidilute fiber suspension in a cylindrical Couette cell. The effective diffusivity of small tracer spheres that approximated ideal fluid particles exhibited an approximate linear growth with fiber concentration in qualitative agreement with the theoretical predictions. The experimentally measured diffusivities were smaller than the theoretical predictions by about 20%–45%.