THE HYDRODYNAMIC STRESS IN A SUSPENSION OF RODS

A theory is presented to describe the momentum transport properties of suspensions containing randomly placed, slender fibers. The theory is based on a diagrammatic representation of the multiple scattering expansion for the averaged Green's function as developed in the authors' previous work on the heat and mass transfer properties of fiber dispersions [Phys. Fluids A 1, 3 (1989)]. The "best one-body approximation" is used to calculate the wavenumber-dependent, ensemble-averaged stress for both aligned and isotropically oriented fiber dispersions. Both the dilute and semidilute concentration regimes are considered. The effective viscosity is calculated as a limit of the previously obtained wavenumber-dependent properties. In the semidilute concentration regime the scaling form originally suggested by Batchelor [J. Fluid Mech. 46, 813 (1971)] is recovered for both orientation distributions and its relation to short range "screening" is discussed. Corrections to this result in a "semidilute expansion" for small volume fraction are calculated and the dependence of these corrections on orientation distribution and particle shape is demonstrated. © 1989 American Institute of Physics.