Topological insights into dense frictional suspension rheology: Third order loops drive discontinuous shear thickening

Dense suspensions exhibit significant viscosity changes under external deformation, a phenomenon known as shear thickening. Recent studies have identified a stress-induced transition from lubricated, unconstrained interactions to frictional contacts, which play a crucial role in shear thickening. This work investigates the rheological behavior and contact network evolution during continuous and discontinuous shear thickening (CST and DST) in two-dimensional simulations. We find that at low stress, during weak thickening, the frictional contact network is composed of quasilinear chains along the compression axis. With increasing stress, the contact network becomes more isotropic, and forms loop-like structures. We show that third-order loops within the frictional contact network are key to this behavior. Our findings revealed a strong correlation between the number of edges in the third-order loops and the viscosity of the suspension. Notably, this relationship remains independent of the packing fraction, applied stress, and interparticle friction, highlighting the fundamental role of the mesoscale network topology in governing macroscopic rheology.