A numerical analysis of the evolution of bundle orientation in concentrated fibre-bundle suspensions

The rheology of Newtonian concentrated fibre-bundle suspensions with nearly planar orientation states is investigated within the framework of the homogenization method for periodic discrete structures. These suspensions are seen as forming a connected network of bundles. At their contact points, the flow induces local Newtonian interaction forces and moments. Numerical rheometry experiments are performed on representative elementary volumes of these suspensions to explore the influence of bundle volume fraction and orientation state on the rate of change of bundle orientation. Three bundle orientation distributions are particularly investigated: Gaussian-based, uniform and crenellated orientation distributions. Two types of numerical simulations are performed, i.e., instantaneous and time-evolution ones. The obtained numerical results permit to discuss the role of the shape of the orientation distribution, typically on the rate of change of the second-order orientation tensor. They are also compared to the well-known Jeffery theory and its subsequent modifications like the Folgar-Tucker theory. The accuracy of some well-known closure approximation functions of the fourth-order orientation tensor is examined. It appears that, in the case treated here where the suspending fluid and the fibre-fibre interactions are Newtonian, the Jeffery's equation gives a fairly good fit (the best fit of all examined theories) of the homogenization results, despite the completely different physics of both approaches. Some differences are observed in situations where fibre-bundles are highly aligned along the flow direction. It is also observed that the shape of the orientation distribution strongly affects the rate of the orientation change. At last, the tested closure approximations can lead to good description of some particular cases of orientation distributions. Nonetheless, in general cases, they are not relevant at all so that other strategies would have to be used in order to compute the evolution of fibre orientation. (C) 2009 Elsevier B.V. All rights reserved.