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

Emmanuelle Abisset-Chavanne (1) , Julien Férec (2) , Gilles Ausias (2) , Elías Cueto (3) , Francisco Chinesta (1) , Roland Keunings (4)

1 GeM - Institut de Recherche en Génie Civil et Mécanique
2 LIMATB - Laboratoire d'Ingénierie des Matériaux de Bretagne
3 I3A - Aragón Institute of Engineering Research [Zaragoza]
4 ICTEAM - Institute of Information and Communication Technologies, Electronics and Applied Mathematics

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.

Mots clés: Rod suspensions; Jeffery's equation; Size effects; Second gradient; Rod bending; hyper-stress; viscoelasticity

Domaines: Sciences de l'ingénieur [physics]

Emmanuelle Abisset-Chavanne, Julien Férec, Gilles Ausias, Elías Cueto, Francisco Chinesta, et al.. A Second-Gradient Theory of Dilute Suspensions of Flexible Rods in a Newtonian Fluid. Archives of Computational Methods in Engineering, 2015, 22 (3), pp.511-527. ⟨10.1007/s11831-014-9128-6⟩. ⟨hal-01515081⟩