Global topology of contact force networks: Insight into shear thickening suspensions.

Highly concentrated particle suspensions (also called slurries) can undergo a sharp increase in viscosity, or shear thickening, under applied stress. Understanding the fundamental features leading to such rheological change is crucial to optimize flow conditions or to design flow modifiers for slurry processing. While local changes to the particle environment under applied shear can be related to changes in viscosity, there is a broader need to connect the shear thickening transition to the fundamental organization of particle-interaction forces which lead to long-range organization. In particular, at a high volume fraction of particles, recent evidence indicates frictional forces between contacting particles is of importance. Herein, the network of frictional contact forces is analyzed within simulated two-dimensional shear thickening suspensions. Two topological metrics are studied to characterize the response of the contact force network (CFN) under varying applied shear stress. The metrics, geodesic index and the void parameter, reflect complementary aspects of the CFN: One is the connectedness of the contact network and the second is the distribution of spatial areas devoid of particle-particle contacts. Considered in relation to the variation of the viscosity, the topological metrics show that the network grows homogeneously at large scales but with many local regions devoid of contacts, indicating clearly the role of CFN growth in causing the large change in the rheological response at the shear thickening transition.