Minimally Rigid Clusters in Dense Suspension Flow

Abstract

Dense suspensions are a prototype of fluid that can dynamically enhance its 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 from the frictional contact network the subset of mechanically rigid clusters at each strain step. We find that rigid clusters emerge at large shear stress well before the onset of jamming and that the continual break-up 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 new insight beyond mean-field models and uncover a new contribution to dissipation in dense suspensions

Scaling relationships between viscosity and diffusivity in shear-thickening suspensions

“…90 Note that this “rigid cluster” is different from the rigid clusters extracted using various algorithms like the pebble game on the contact network. 91–93…”

“…90 Note that this ''rigid cluster'' is different from the rigid clusters extracted using various algorithms like the pebble game on the contact network. [91][92][93] In the following, we use scaled quantities defined as scaled stress s = s/s 0 , scaled shear rate _ g ¼ _ g=_ g 0 , scaled diffusivity D ˜= D/(a 2 _ g), and scaled size of rigid clusters x = x/a.…”