Two-Scales Kinetic Theory Model of Short-Fibers Aggregates

This paper proposes a first attempt to define a two scales kinetic theory to describe concentrated suspensions involving short fibers, nano-fibers or nanotubes. In this case, fiber-fiber interactions can not be neglected and rich microstructures issued from these interactions can be observed, involving a diversity of fibers 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 model to describe such microstructure: at the finest scale we study the cluster kinematic based on the behaviour of the rods that constitute it, at a coarser scale, we use clusters distribution to derive the effect of the clusters presence on the suspensions properties.