Abstract
This paper summarizes recent joint 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 described in steady state by the Wyart-Cates model. 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 [1]. Implementing this idea for time-dependent flows requires the introduction of new concepts including a configuration-dependent ‘jamming coordinate’, alongside a decomposition of the velocity gradient tensor into compressive and extensional components which then enter the evolution equation for particle contacts in distinct ways. The resulting approach [2, 3] is qualitatively successful in addressing (i) the collapse of stress during flow reversal in shear flow, and (ii) the ability of transverse oscillatory flows to unjam the system. However there is much work required to refine this approach towards quantitative accuracy, by incorporating more of the physics of contact evolution under flow as determined by close interrogation of particle-based simulations.
Highlights
Recent years have seen a shift in our understanding of the rheology of dense suspension of hard, non-Brownian particles in a Newtonian solvent
It is possible to recover some aspects of the Stokesian picture by replacing the word ‘contact’ in the above discussion with a more general concept involving intact lubrication films and explicit aspherities [7], we stick with the simpler picture of direct particle contacts
At the level of macroscopic constitutive equations, this idea is encoded by a decomposition of the macroscopic rate of strain tensor E = (L + LT )/2, where Li j = ∂ jvi is the velocity gradient tensor, into its compressive and extensile components, E = Ec + Ee. These have distinct effects on the evolution of the particle contact distribution, which we describe by a microstructure tensor nn created from the vectors n between neighbours
Summary
Recent years have seen a shift in our understanding of the rheology of dense suspension of hard, non-Brownian particles in a Newtonian solvent. Naive application of Stokesian physics would imply that such particles, if spherical and governed by a no-slip boundary condition, never come into direct contact because the force needed to create a finite interparticle normal velocity diverges as the fluid film between them becomes thin [4]. The magnitude drops discontinuously before slowly recovering to steady state, because the direct contact forces that are present carry compressive but not tensile forces (unlike a lubrication film) This was demonstrated long ago in the experiments of Gadala-Maria and Acrivos [5] on flow reversal, and recently confirmed in forensic detail by Lin et al [6]. A fundamental limitation is that it is a steadystate theory only
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