Minimally rigid clusters in dense suspension flow

Dense suspensions are a prototype of fluid that can dynamically enhance their viscosity to resist strong forcing. Recent work established that the key to a large viscosity increase—often in excess of an order of magnitude—is the ability to switch from lubricated, frictionless particle interactions at low stress to a network of frictional contacts at higher stress. However, to isolate network features responsible for the large viscosity has been difficult, given the lack of an appropriate physics-inspired network measure. Here we apply rigidity theory to simulations of dense suspensions in two dimensions and identify a subset of mechanically rigid clusters at each strain step from the frictional contact network. We find that rigid clusters emerge at large shear stress well before the onset of jamming and that the continual breakup and reconfiguration of system-spanning rigid clusters is responsible for the flow states of the highest viscosity. By showing how viscosity is correlated with the rigidity of the underlying network of contact forces, our results provide insights beyond mean-field models and uncover a new contribution to dissipation in dense suspensions.