Modelling particle migration in rod suspensions: frommicro-mechanics to a macroscopic field description

This work proposes a micro-mechanical model describing the interactions of a test particle immersed in a semi- concentrated suspension of rigid rods. For that purpose, after revisiting the main elements related to suspensions exhibiting second-order velocity gradient effects, a micro-mechanical model is proposed that allows us to define a sort of interaction field giving the force acting on a test particle due to the rod kinematics at any point of the flow domain. Finally, a macroscopic description is derived that only involves the second-order orientation tensor and its spatial gradient. The model presented in this work shows that migration in fibre suspensions depends on the fibre concentration and orientation distribution and not only on the flow shear rate as is the case in suspensions of spheres.