Numerical Modelling of the Flow of Fibre Suspensions through a Planar Contraction

This study presents results of numerical simulations of the flow of fibre suspensions in a Newtonian fluid through a 4:1 planar contraction. Two approaches are adopted to determine the fibre orientation. The first one uses orientation tensors defined as dyadic products of the orientation vector, while the second one is based on the fibre aligned assumption. An implicit time discretization scheme and a mixed finite element method based on the introduction of the rate of deformation tensor as an additional unknown are used to obtain the steady‐state flow. The numerical technique we use allows us to examine the flow of fibre suspensions in both dilute and semi‐dilute regimes at high values of the parameters controlling inertial and fibre effects. The predicted flow patterns and fibre orientation are discussed, and a systematic comparison between the predictions of the two approaches is presented.