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

Dense suspensions exhibit a significant change in viscosity 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 frictional contact network evolution during continuous and discontinuous shear thickening (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 unweighted contact network becomes more isotropic and forms loop-like structures. We show that third-order loops within the frictional contact network are key to the DST. Our findings revealed a strong correlation between the number of 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 and connecting to the microscopic physics.