A minimal model for the unsteady flow of shear-thickening suspensions
Dense suspensions with particle sizes between the colloidal (<1μm) and granular (>50μm) regimes are ubiquitous industrially, from cement to chocolate. In this intermediate size regime, shear thickening results from the transition between lubricated and frictional particle contacts at a critical stress. The steady shear flow of these suspensions is well described by a phenomenological theory . For high volume fractions, which show discontinuous shear thickening (a sudden increase in viscosity), the relation between shear rate and stress is non-monotonic.
Macroscopically this is unstable and the theory only represents the local steady-state rheology. Experimentally, the bulk flow is unsteady, inhomogeneous and often chaotic above the onset stress.
This time-dependent flow appears unpredictable, but to begin understanding the flow we focus on periodic shear rate oscillations seen close to the shear-thickening onset stress. Here we show that these oscillations can be quantitatively modelled by extending the Wyart & Cates theory to account for the measurement system inertia and strain-dependent micro-structural response of the suspension. In our dynamical model, the shear rate oscillations arise from the interplay between the momentum of the measurement system and the underlying local rheology. The success of this model suggests a more general approach to describe time-dependent phenomena in shear-thickening systems.
 M. Wyart and M. E. Cates, /Phys. Rev. Lett./, *112*, 098302 (2014).
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