Rigid Cluster Decomposition of Dense Suspension Flows*

Dense suspensions near their frictional jamming point can show dramatic flow behavior such as discontinuous shear thickening (DST) which culminates in solidification through shear jamming.  Simulations of dense suspensions have shown that shear thickening can be understood as a transition from a state with no frictional contacts to a state with saturated frictional contacts.However, none of these studies have moved beyond this mean-field description to analyze the rigidity of the underlying, dynamically evolving network of frictional particle-particle contacts.Here, we use the pebble-game algorithm to decompose the simulated frictional contact networks into so-called “rigid clusters” which are the minimally rigid portions of the contact network.We find that the DST volume fraction coincides with the system spanning rigid clusters for intermediate friction coefficient. However, we observe deviations from this behavior at high and low friction coefficients where the onset of spanning rigid clusters occurs after DST and before DST, respectively.These results move beyond the current mean-field description and provide an important connection between dense suspensions and dry granular media and provide a potentially new way to understand the onset of rigidity in shear thickening suspensions.