Direct Calculation of the motion of rigid fibres in a viscous fluid
Résumé
Fibre-like particles into a polymer matrix enables to enhance the mechanical properties of a composite material. The degree of enhancement depends strongly on the fibre orientation which depends itself on the required flow during the forming process in moulding for instance. The numerical modelling of a fluid with fibres deals with an evolution equation involving the second orientation tensor. However, it results from homogenisation procedures from Jeffery equation for the orientation of a single particle and from Folker-Plank equation for the probability distribution of orientation. Therefore, this approach has a limited domain of validity, depending on the shape, the aspect ratio and the volume fraction of fibres. We propose here to simulate directly the motion of a dense population of fibers in a polymeric fluid, taking into account the exact particle interaction, by using a multidomain approach in a global Finite Element calculation. The first interest of this direct approach is to avoid the need of an explicit form of drag and lubrication forces acting between fibres. This presentation will focus on the influence of the particle shape on the motion of a single particle (Jeffery's equation works well provided that an equivalent aspect ratio is used), the fibre motion near a wall is still described if an increased effective shear rate is used, the numerical calculation with a great number of fibres and the averaging to produce macroscopic properties of fibre suspensions. In this way, we can determine the evolution of Folgar-Tucker diffusion constant and the validity of closure approximation with respect to the volume fraction of fibres.