Direct simulation of concentrated fiber suspensions subjected to bending effects

When fiber suspensions become concentrated, standard mesoscale theories do not allow a precise description of the fine physics involved at the microscopic level. Thus one way of studying the kinematics and the rheological effects of such suspensions is to make a direct numerical simulation (or DNS for abbreviation). In previous works authors proposed DNS for these types of suspensions. However when it was carried out the elasticity associated with fibers was not introduced in the suspensions; fibers were considered purely rigid and free of bending when they were subjected to interaction forces. In this work a DNS of fiber suspensions in transient and steady shear flows is presented. The suspensions are considered along with interactions between fibers and the statistical evolutions of a population of fibers (such as orientation components and number of interactions between fibers) have been described. Then in the frame of a beam theory approach, the elasticity of the suspensions is introduced by considering that the forces acting of each fiber lead to the bending of the fibers. Thus this bending results in a physical elastic behavior illustrated quantitatively by an elastic energy stored within the suspensions. These added aspects on the DNS of concentrated fiber suspensions constitute the main originality of this paper.