A Second-Gradient Theory of Dilute Suspensions of Flexible Rods in a Newtonian Fluid

Most suspension descriptions used nowadays are based on Jeffery’s model or some phenomenological modifications of it that do not take into account size effects: the kinematics and stresses do not involve a micro-mechanical characteristic length and thus, the predicted rheological properties are necessarily independent of rod length. More sophisticated models able to enrich first-gradient kinematics as well as to activate rod-bending mechanisms are needed, in particular to explain the mild elasticity observed experimentally. In this paper we propose a second-gradient theory for dilute suspensions of flexible rods in a Newtonian fluid that is indeed able to activate rod bending and predict viscoelastic behaviour.