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Register a new userA rheological state diagram for rough colloids in shear flow
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The flow of dense suspensions, glasses, and granular materials is heavily influenced by frictional interactions between constituent particles. However, neither hydrodynamics nor friction has successfully explained the full range of flow phenomena in concentrated suspensions. Particles with asperities represent a case in point. Lubrication hydrodynamics fail to completely capture two key rheological properties - namely, that the viscosity increases drastically and the first normal stress difference can switch signs as volume fraction increases. Yet, simulations that account for interparticle friction are also unable to fully predict these properties. Furthermore, experiments show that rheological behavior can vary depending on particle roughness and deformability. We seek to resolve these apparent contradictions by systematically tuning the roughness of model colloids, investigating their viscosity and first normal stress differences under steady shear, and finally generating a rheological state diagram that demonstrates how surface roughness influences the transition between shear thickening and dilatancy. Our simulations, which are in good agreement with the experiments, suggest that friction between rough particles is significant. In addition, we find that roughness progressively lowers the critical conditions required for the onset of shear thickening and dilatancy. Our results thus provides a major contribution in the field of suspension rheology with broad relevance to granular and particulate materials. For instance, particle geometry can be tuned to increase the efficacy of materials that turn solid-like on the application of stimuli. On the other hand, engineers who work with concentrated slurries can now use images of the constituent particles to estimate optimal flow processing conditions.
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We study the strain response to steady imposed stress in a spatially homogeneous, scalar model for shear thickening, in which the local rate of yielding Gamma(l) of mesoscopic `elastic elements is not monotonic in the local strain l. Despite this, the macroscopic, steady-state flow curve (stress vs. strain rate) is monotonic. However, for a broad class of Gamma(l), the response to steady stress is not in fact steady flow, but spontaneous oscillation. We discuss this finding in relation to other theoretical and experimental flow instabilities. Within the parameter ranges we studied, the model does not exhibit rheo-chaos.
The Boltzmann equation for inelastic Maxwell models is considered to determine the rheological properties in a granular binary mixture in the simple shear flow state. The transport coefficients (shear viscosity and viscometric functions) are {em exactly} evaluated in terms of the coefficients of restitution, the (reduced) shear rate and the parameters of the mixture (particle masses, diameters and concentration). The results show that in general, for a given value of the coefficients of restitution, the above transport properties decrease with increasing shear rate.
We study a simple scalar constitutive equation for a shear-thickening material at zero Reynolds number, in which the shear stress sigma is driven at a constant shear rate dotgamma and relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R(sigma_1) and a linear decay at rate lambdasigma_2. Here sigma_{1,2}(t) = tau_{1,2}^{-1}int_0^tsigma(t)exp[-(t-t)/tau_{1,2}] {rm d}t are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when tau_2>tau_1 and 0>R(sigma)>-lambda so that monotonicity is restored only through the strongly retarded term (which might model a slow evolution of material structure under stress). Within the unstable region we find a period-doubling sequence leading to chaos. Instability, but not chaos, persists even for the case tau_1to 0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows.
We analyse the flow curves of a two-dimensional assembly of granular particles which are interacting via frictional contact forces. For packing fractions slightly below jamming, the fluid undergoes a large scale instability, implying a range of stress and strainrates where no stationary flow can exist. Whereas small systems were shown previously to exhibit hysteretic jumps between the low and high stress branches, large systems exhibit continuous shear thickening arising from averaging unsteady, spatially heterogeneous flows. The observed large scale patterns as well as their dynamics are found to depend on strainrate: At the lower end of the unstable region, force chains merge to form giant bands that span the system in compressional direction and propagate in dilational direction. At the upper end, we observe large scale clusters which extend along the dilational direction and propagate along the compressional direction. Both patterns, bands and clusters, come in with infinite correlation length similar to the sudden onset of system-spanning plugs in impact experiments.
Colloidal shear thickening presents a significant challenge because the macroscopic rheology becomes increasingly controlled by the microscopic details of short ranged particle interactions in the shear thickening regime. Our measurements here of the first normal stress difference over a wide range of particle volume fraction elucidate the relative contributions from hydrodynamic lubrication and frictional contact forces, which have been debated. At moderate volume fractions we find $N_1<0$, consistent with hydrodynamic models, however at higher volume fractions and shear stresses these models break down and we instead observe dilation ($N_1>0$), indicating frictional contact networks. Remarkably, there is no signature of this transition in the viscosity, instead this change in the sign of $N_1$ occurs while the shear thickening remains continuous. These results suggest a scenario where shear thickening is driven primarily by the formation of frictional contacts, with hydrodynamic forces playing a supporting role at lower concentrations. Motivated by this picture, we introduce a simple model which combines these frictional and hydrodynamic contributions and accurately fits the measured viscosity over a wide range of particle volume fraction and shear stress.
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