Key points are not available for this paper at this time.
Shaqfeh and Fredrickson Phys. Fluids A 2, 7 (1990) renormalized the multiple reflection expansion for hydrodynamic fiber interactions in a semidilute suspension, nl3≫1 and φ≪1, where φ is the fiber volume fraction, n is the number of fibers per unit volume, and l is the fiber half-length. We use the results of Shaqfeh and Fredrickson to obtain the average rotation rate of a fiber in linear shear flows of a semidilute suspension. Specific results are obtained for the case where most of the fibers are oriented in a preferred direction, as occurs in simple shear and extensional flows. The correction to the O(γ̊) Jeffrey rotation rate Proc. R. Soc. London Ser. A 102, 161 (1922); J. Fluid Mech. 14, 284 (1962) due to hydrodynamic interactions is shown to be Oγ̊/ln(1/φ), where γ̊ is the shear rate.
Koch et al. (1990) studied this question.