Microscopic modelling of orientation kinematics of non-spherical particles suspended in confined flows using unilateral mechanics

The properties of reinforced polymers strongly depend on the microstructural state, that is, the orientation state of the fibres suspended in the polymeric matrix, induced by the forming process. Understanding flow-induced anisotropy is thus a key element to optimize both materials and process. Despite the important progresses accomplished in the modelling and simulation of suspensions, few works addressed the fact that usual processing flows evolve in confined configurations, where particles characteristic lengths may be greater than the thickness of the narrow gaps in which the flow takes place. In those circumstances, orientation kinematics models proposed for unconfined flows must be extended to the confined case. In this short communication, we propose an alternative modelling framework based on the use of unilateral mechanics, consequently exhibiting a clear analogy with plasticity and contact mechanics. This framework allows us to revisit the motion of confined particles in Newtonian and non-Newtonian matrices. We also prove that the confined kinematics provided by this model are identical to those derived from microstructural approaches (Perez et al. (2016) [1])