From Single-Scale to Two-Scales Kinetic Theory Descriptions of Rods Suspensions

This paper proposes a first attempt to define a two-scales kinetic theory description of suspensions involving short fibers, nano-fibers or nanotubes. We start revisiting the description of dilute enough suspensions for which microscopic, mesoscopic and macroscopic descriptions are available and all them have been successfully applied for describing the rheology of such suspensions. When the suspensions become too concentrated fiber-fiber interactions cannot be neglected and then classical dilute theories fail for describing the rich microstructure evolution. In the semi-concentrated regime some interaction mechanisms that mimetic the randomizing effect of fiber-fiber interactions were successfully introduced. Finally, when the concentration becomes high enough, richer microstructures can be observed. They involve a diversity of fiber clusters or aggregates with complex kinematics, and different sizes and shapes. These clusters can interact to create larger clusters and also break because the flow induced hydrodynamic forces. In this paper we propose a double-scale kinetic theory model that at the first scale consider the kinematics of the clusters, whose structure itself is described at the finest scale, the one related to the rods constituting the clusters.