Physics of the flow of concentrated suspensions
Guy, Ben Michael
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A particulate suspension under shear is a classic example of a system driven out of equilibrium. While it is possible to predict the equilibrium phase behaviour of a quiescent suspension, linking microscopic details to bulk properties under flow remains an open challenge. Our current understanding of sheared suspensions is restricted to two disparate regimes, the colloidal regime, for particle sizes d < 1 μm and the granular regime, for d > 50 μm. The physics of the industrially-relevant intermediate size regime, 1 μm ≲ d ≲ 50 μm, is unclear and has not been explored previously. In this thesis, we use conventional rheometry on a range of model spheres to develop the foundations of a predictive understanding of suspension flow across the entire size spectrum. In the first part of the thesis, we show that in repulsive particulate systems the rheology is characterised by two viscosity "branches" diverging at different volume fractions ϕRCP and ϕm, which represent states of flow with lubricated (frictionless) and frictional interactions between particles. In the intermediate size regime, there is a transition between these two branches above a critical onset stress σ* which manifests as shear thickening. This σ* is related to a barrier (invariably due to the charge or steric stabilisation) keeping particle surfaces apart. Our data are quantitatively fit by the Wyart and Cates theory for frictional thickening  if we assume that probability distribution of forces in the system is similar to in dry granular media. The onset stress for shear thickening is found to decrease with the inverse square of the particle size σ* / d¯ ² for diverse systems. We show that it is the competition between the scaling of σ*(d) and the size dependence of the entropic stress scale (~ d¯ ³) that controls the crossover from colloidal to granular rheology with increasing size. Granular systems are "always shear thickened" under typical experimental conditions, while colloidal systems are always in a frictionless state. In the second part of the thesis, we explore the validity of the frictional framework for shear thickening. Although it quantitatively predicts our steady-state rheology, the frictional framework contradicts traditional fluid-mechanical thinking and has yet to be rigorously tested experimentally. In fact, there is a large body of literature that attributes thickening to purely hydrodynamic effects. Using dimensional analysis and simple physical arguments we examine possible physical origins for thickening and show that previously-proposed mechanisms can be subdivided into three types: two-particle hydrodynamic thickening, many-particle hydrodynamic thickening ("hydroclusters") and frictional-contact driven thickening. Many of these mechanisms can are inconsistent with the experimental two-branch phenomenology and can be disregarded. We further narrow down possible causes of thickening using the technique of flow reversal, which disentangles the relative contributions of contact and hydrodynamic forces to the viscosity. Consistent with recent simulations  and theory , we find that in each case thickening is dominated by the formation of frictional contacts and that hydrodynamic thickening, if present, is subdominant.