Theory for semi-dilute suspensions of periodically forced slender bodies aligned along finite set of directions

In earlier work we demonstrated numerically (Kumar and Ramamohan, 1995) tha t the rheological parameters of periodically forced dilute suspensions of s lender bodies vary chaotically. This demonstration, if confirmed experiment ally, will have important implications for both suspension rheology and cha os theory. In this paper, we develop expressions for Green's function and t he average rotation rate for a semi-dilute suspension of periodically force d slender bodies aligned along a finite set of directions. The present theo ry can yield physically meaningful results, either as an approximation to t he evolution of an initially uniformly distributed suspension of slender ro ds, or as an approximation to the evolution of an initially nearly aligned suspension of slender rods when the evolution of the orientation vectors is chaotic in some parametric regimes.