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) that the rheological parameters of periodically forced dilute suspensions of slender bodies vary chaotically. This demonstration, if confirmed experimentally, will have important implications for both suspension rheology and chaos theory. In this paper, we develop expressions for Green's function and the average rotation rate for a semi-dilute suspension of periodically forced slender bodies aligned along a finite set of directions. The present theory can yield physically meaningful results, either as an approximation to the evolution of an initially uniformly distributed suspension of slender rods, 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.