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Register a new userDynamic and rate-dependent yielding in model cohesive suspensions
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An experimental system has been found recently, a coagulated CaCO3 suspension system, which shows very variable yield behaviour depending upon how it is tested and, specifically, at what rate it is sheared. At Peclet numbers Pe > 1 it behaves as a simple Herschel Bulkley liquid, whereas at Pe < 1 highly non-monotonic flow curves are seen. In controlled stress testing it shows hysteresis and shear banding and in the usual type of stress scan, used to measure flow curves in controlled stress mode routinely, it can show very erratic and irreproducible behaviour. All of these features will be attributed here to a dependence of the solid phase, or, yield stress, on the prevailing rate of shear at the yield point. Stress growth curves obtained from step strain-rate testing showed that this rate-dependence was a consequence of Peclet number dependent strain softening. At very low Pe, yield was cooperative and the yield strain was order-one, whereas as Pe approached unity, the yield strain reduced to that needed to break interparticle bonds, causing the yield stress to be greatly reduced. It is suspected that rate-dependent yield could well be the rule rather than the exception for cohesive suspensions more generally. If so, then the Herschel-Bulkley equation can usefully be generalized to read (in simple shear). The proposition that rate-dependent yield might be general for cohesive suspensions is amenable to critical experimental testing by a range of means and along lines suggested.
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The yielding of concentrated cohesive suspensions can be deformation-rate dependent. One consquence of this is that a single suspension can present in one several different ways, depending upon how it is tested, or more generally, how it is caused to flow. We have seen variously Herschel-Bulkley flow, highly non-monotonic flow curves and highly erratic or chaotic yield, all in one suspension. In controlled-rate testing one sees a systematic effect of deformation rate. In controlled stress testing, matters are more subtle. Whereas step-stress creep testing will elicit reproducible behaviour, any attempt to determine a flow curve by, e.g. stepping up or sweeping stress at an inappropriate rate can lead to highly irreproducible behaviour.
We simulate a dense athermal suspension of soft particles sheared between hard walls of a prescribed roughness profile, using a method that fully accounts for the fluid mechanics of the solvent between the particles, and between the particles and the walls, as well as for the solid mechanics of changes in the particle shapes. We thus capture the widely observed phenomenon of elastohydrodynamic wall slip, in which the soft particles become deformed in shear and lift away from the wall slightly, leaving behind a thin lubricating solvent layer of high shear. For imposed stresses below the materials bulk yield stress, we show the observed wall slip to be dominated by this thin solvent layer. At higher stresses, it is augmented by an additional contribution arising from a fluidisation of the first few layers of particles near the wall. By systematically varying the roughness of the walls, we quantify a suppression of slip with increasing wall roughness. For smooth walls, slip radically changes the steady state bulk flow curve of shear stress as a function of shear rate, by conferring a branch of apparent (slip-induced) flow even for $sigma<sigma_y$, as seen experimentally. We also elucidate the effects of slip on the dynamics of yielding following the imposition of a constant shear stress, characterising the timescales at which bulk yielding arises, and at which slip first sets in.
Simulations are used to study the steady shear rheology of dense suspensions of frictional particles exhibiting discontinuous shear thickening and shear jamming, in which finite-range cohesive interactions result in a yield stress. We develop a constitutive model that combines yielding behavior and shear thinning at low stress with the frictional shear thickening at high stresses, in good agreement with the simulation results. This work shows that there is a distinct difference between solids below the yield stress and in the shear-jammed state, as the two occur at widely separated stress levels, separated by a region of stress in which the material is flowable.
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 performed two-dimensional Molecular Dynamics simulations of cohesive disks under shear. The cohesion between the disks is added by the action of springs between very next neighbouring disks, modelling capillary forces. The geometry of the cell allows disk-disk shearing and not disk-cell wall shearing as it is commonly found in literature. Does a stick-slip phenomenon happen though the upper cover moves at a constant velocity, i.e. with an infinite shearing force? We measured the forces acted by the disks on the upper cover for different shearing rates, as well as the disk velocities as a function of the distance to the bottom of the cell. It appears that the forces measured versus time present a periodic behavior,very close to a stick slip phenomenon, for shearing rates larger than a given threshold. The disks collective displacements in the shearing cell (back and ahead) is the counterpart of the constant velocity of the upper cover leading to a periodic behavior of the shear stress.
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