We present a phenomenological model for granular suspension rheology in which particle interactions enter as constraints to relative particle motion. By considering constraints that are formed and released by stress respectively, we derive a range of experimental flow curves in a single treatment and predict singularities in viscosity and yield stress consistent with literature data. Fundamentally, we offer a generic description of suspension flow that is independent of bespoke microphysics.Concentrated particulate dispersions are ubiquitous in industry. When the particle size is in the granular (i.e., non-Brownian) regime (radius R ≳ 1 µm), their flow is notoriously difficult to predict and control [1, 2]. Paradoxically, a suspension of non-Brownian hard particles has no intrinsic time or stress scale and so should have a viscosity η that is independent of shear stress σ and ratė γ [2, 3]. In reality, three classes of flow curve η(σ) are observed, none of which is Newtonian. Some granular suspensions shear thin (dη dσ < 0, class 1) [4,5], others shear thicken (dη dσ > 0, class 2) [6-8] while others show a varied combination of thinning and thickening (class 3): thinning then thickening (class 3a) [9, 10], thickening then thinning (class 3b) [11][12][13] or more complex behavior [10,14,15] (class 3c). In each class, the suspensions can become solid-like [16] or flow unstably [17,18].Such behavior likely stems from details of the particle interactions [2] set by, e.g., surface chemistry [19] or roughness [20]. Most models incorporate such interactions in a bespoke manner. Notably, a phenomenological model by Wyart and Cates (WC) [21] predicts thickening (class 2) due to a transition from frictionless (static friction coefficient µ ≈ 0) to frictional (µ > 0) particle contacts above a critical "onset stress". Atomic force microscopy confirms this picture for several systems [15,22] and the WC model fits a number of experimental flow curves [7,8,18]; although, quantitative discrepancies with microscopic simulations remain [23].To recast the WC model within a more general framework, recall that frictional contacts constrain interparticle sliding. Crucially, the WC model is agnostic to the exact mechanism by which sliding is constrained, so that disparate microphysics, e.g., stress-induced interlocking of asperities [20,24], hydrogen bonding [25] or 'traditional' Coulomb friction can all give rise to the same macroscopic, shear-thickening phenomenology.In this broader framework, the WC model deals with a single type of constraint: sliding. Rolling (rotations about axes perpendicular to the line of centres) and twisting (rotations about the line of centres) degrees of freedom remain unconstrained. By assuming that sliding constraints are formed at increasing stress, the WC model accounts for class 2 behavior, which, however, is rare in practice. Real systems are typically class 1 or 3, for which current explanations involve the ad hoc "bolting together" of different kinds of bespoke physics [10].Here, we generalize the ...

Competing time scales generate novelty. Here, we show that a coupling between the time scales imposed by instrument inertia and the formation of inter-particle frictional contacts in shear-thickening suspensions leads to highly asymmetric shear-rate oscillations. Experiments tuning the presence of oscillations by varying the two time-scales support our model. The observed oscillations give access to a shear-jamming portion of the flow curve that is forbidden in conventional rheometry. Moreover, the oscillation frequency allows us to quantify an intrinsic relaxation time for particle contacts. The coupling of fast contact network dynamics to a slower system variable should be generic to many other areas of dense suspension flow, with instrument inertia providing a paradigmatic example.

Yielding behavior is well known in attractive colloidal suspensions. Adhesive non-Brownian suspensions, in which the interparticle bonds are due to finite-size contacts, also show yielding behavior. We use a combination of steady-state, oscillatory and shear-reversal rheology to probe the physical origins of yielding in the latter class of materials, and find that yielding is not simply a matter of breaking adhesive bonds, but involves unjamming from a shear-jammed state in which the micro-structure has adapted to the direction of the applied load. Comparison with a recent constraint-based rheology model shows the importance of friction in determining the yield stress, suggesting novel ways to tune the flow of such suspensions.

We show that a suspension of non-Brownian calcite particles in glycerol-water mixtures can be tuned continuously from being a yield-stress suspension to a shear-thickening suspension—without a measurable yield stress—by the addition of various surfactants. We interpret our results within a recent theoretical framework that models the rheological effects of stress-dependent constraints on inter-particle motion. Bare calcite particle suspensions are found to have finite yield stresses. In these suspensions, frictional contacts that constrain inter-particle sliding form at an infinitesimal applied stress and remain thereafter, while adhesive bonds that constrain inter-particle rotation are broken as the applied stress increases. Adding surfactants reduces the yield stress of such suspensions. We show that, contrary to the case of surfactant added to colloidal suspensions, this effect in non-Brownian suspensions is attributable to the emergence of a finite onset stress for the formation of frictional contacts. Our data suggest that the magnitude of this onset stress is set by the strength of surfactant adsorption to the particle surfaces, which therefore constitutes a new design principle for using surfactants to tune the rheology of formulations consisting of suspensions of adhesive non-Brownian particles.

Particle size is a key variable in understanding the behaviour of the particulate products that underpin much of our modern lives. Typically obtained from suspensions at rest, measuring the particle...

Microscopic dynamics reveal the origin of the bulk rheological response in complex fluids. In model systems particle motion can be tracked, but for industrially relevant samples this is often impossible....

Interfacial rheology is important for understanding properties such as Pickering emulsion or foam stability. Currently, the response is measured using a probe directly attached to the interface. This can both disturb the interface and is coupled to flow in the bulk phase, limiting its sensitivity. We have developed a contactless interfacial method to perform interfacial shear rheology on liquid/liquid interfaces with no tool attached directly to the interface. This is achieved by shearing one of the liquid phases and measuring the interfacial response via confocal microscopy. Using this method, we have measured steady shear material parameters such as interfacial elastic moduli for interfaces with solidlike behavior and interfacial viscosities for fluidlike interfaces. The accuracy of this method has been verified relative to a double-wall ring geometry. Moreover, using our contactless method, we are able to measure lower interfacial viscosities than those that have previously been reported using a double-wall ring geometry. A further advantage is the simultaneous combination of macroscopic rheological analysis with microscopic structural analysis. Our analysis directly visualizes how the interfacial response is strongly correlated to the particle surface coverage and their interfacial assembly. Furthermore, we capture the evolution and irreversible changes in the particle assembly that correspond with the rheological response to steady shear.

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