Fabric evolution of rigid inclusions during mixed coaxial and simple shear flows

Abstract In a slowly moving viscous fluid, a population of non-interacting, rigid inclusions evolves in an oscillatory fashion or creates a stable fabric, depending on the flow geometry and the shape of the inclusions. Using Jeffery's equations for the motion of a rigid ellipsoidal inclusion, a mixed coaxial and simple shear flow was investigated, both analytically and by numerical modeling. Exact results were obtained for spheroidal inclusions. Depending on the axial ratio of the inclusion and the amount of the coaxial component of flow, individual inclusions can move cyclically or rotate to a stable orientation in one of two mutually orthogonal directions. Equations were found which allow us to distinguish between these types of motion and to determine the stable inclusion orientation. The relative motions of individual inclusions determine the preferred orientation in a population of inclusions. In a heterogeneous population with diverse axial ratios, the fabric evolves as the superposition of subfabrics corresponding to subsets with different axial ratios. The orientations of stable subfabrics depend on axial ratios, and could thus be used as kinematic indicators. In cases of a sufficiently large coaxial component of flow, the fabric created by a heterogeneous population may comprise two stable, mutually orthogonal subfabrics. No exact results are available for general (i.e., non-spheroidal) ellipsoidal inclusions, and numerical modeling must be used. If the coaxial component of flow is sufficiently strong, the non-spheroidal inclusions move much like the spheroidal ones. Orthogonal subfabrics may appear as transient features in the evolution of a homogeneous population of non-spheroidal ellipsoidal inclusions.