Abstract

This talk will summarize recent work towards a constitutive modelling framework for dense granular suspensions. The aim is to create a time-dependent, tensorial theory that can implement the physics captured in steady state by the Wyart-Cates model of 2014. This model of shear thickening suspensions supposes that lubrication films break above a characteristic normal force so that frictional contact forces come into play: the resulting non-sliding constraints can be enough to rigidify a system that would flow freely at lower stresses. Implementing this idea for time-dependent flows requires the introduction of several new concepts including a configuration-dependent ‘jamming coordinate’, and the decomposition of the velocity gradient tensor into compressive and extensional components which then enter the evolution equation for particle contacts in distinct ways (a key idea due to Helen Wilson and Jurriaan Gillissen). The resulting approach is qualitatively successful in addressing both the collapse of stress during flow reversal in shear flow, and the ability of transverse oscillatory flows to unjam the system. However there is much work required to refine this approach towards quantitative accuracy, incorporating more of the physics of contact evolution under flow as determined by close interrogation of particle-based simulations.