Percolation clusters in non-colloidal sheared suspensions
Résumé
This numerical work intends to study percolation clusters in non-colloidal non-Brownian sheared suspensions. Early simulations have indeed revealed the existence of large gap-spanning clusters. However a detailed study on percolation clusters and their role on suspension seems to lack so far. In this work, we consider some numerical simulations based on a fictitious domain method supplemented with a detailed modeling of lubrication and contact forces (including roughness and friction). Simulations show that the average cluster size grows with volume fraction φ and clusters eventually percolate at a critical volume fraction between 0.25 and 0.4 depending on friction, roughness or system size. In any case, for φ > 0.4, there is always at least one spanning cluster in the suspension. Clusters are linear, globally oriented along the compression axis and involve a limited number of particles. They are extremely transient with links forming and breaking continuously and a typical percolation time scale is about 0.1 inverse shear rate. We have also considered scaling laws close to the critical fraction and found a correct agreement with standard percolation theory. The effect of percolation on suspension rheology is however found to be weak because of the small fraction of particles involved. Finally, we have also checked some of the De Gennes conjectures on percolation in suspensions.