Rigidity development in shear-thickening suspensions*

Suspensions in shear flow may undergo a sharp shear-thickening transition, which is closely related to the jamming transition.  Recent work has converged on the view that this transition results from stress-induced frictional contacts.  These contacts reduce the degrees of freedom for the motion of the suspended particles, eventually resulting in a jammed state in which only global rigid body motions of bulk translation and rotation are allowed.  We study the development of the rigid structures in sheared suspensions in two dimensions (2D). using an established simulation tool that captures lubrication hydrodynamics, repulsive conservative interparticle forces. The 2D suspensions exhibit the same phenomenology in terms of shear thickening rheology as do three-dimensional suspensions.  The crucial advantage of two dimensions. for this study is that in. 2D, a pebble game algorithm can be applied to rigorously identify rigid clusters; an added benefit is that larger length scales are accessible at a given computational cost, which allows more effective exploration of scaling relationships involving the system size. The rigid clusters found as a function of stress and solid fraction will be presented, and the finding of a critical concentration at which rigidity occurs will be demonstrated.  The finite-size scaling of the results at large stress will be presented, along with evidence allowing the transition to be associated with. a known universality class.