Mapping the Discontinuous Shear Thickening Transition to an Equilibrium Phase Transition*

Discontinuous Shear Thickening, the abrupt change in viscosity of a dense suspension as the rate of shear is increased, appears to arise, at least for certain systems, because the inter-particle contacts change from lubricated to frictional in nature. This change also manifests at the microscopic level as clustering of vertices in a dual space representation of forces (the force-tiling representation), opening the door for microscopic theories to describe DST. We model this collective reorganization of vertices as an equilibrium phase transition between an isotropic and a clustered phase of particles interacting via an ultra-soft potential of the form of step function [1]. We find signatures of a new phase transition at low densities: a regime that had not been investigated earlier but is relevant to DST. We use a cluster-based analysis scheme to compare the predictions of this model with numerical simulations of dense non-Brownian suspensions. We find that near DST, several properties of the point pattern of vertices bear a remarkable similarity to those arising in this simple model. We discuss generalizations to other potentials and examine the mapping for conditions of shear jamming. [1] W. Klein, et. al., Physica A 205, 738 (1994)