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Register a new userUnsteady flow, clusters and bands in a model shear-thickening fluid
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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.
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How does pore liquid reconfigure within shear bands in wet granular media? Conventional wisdom predicts that liquid is drawn into dilating granular media. We, however, find a depletion of liquid in shear bands despite increased porosity due to dilatancy. This apparent paradox is resolved by a microscale model for liquid transport at low liquid contents induced by rupture and reconfiguration of individual liquid bridges. Measured liquid content profiles show macroscopic depletion bands similar to results of numerical simulations. We derive a modified diffusion description for rupture-induced liquid migration.
We consider the shear rheology of concentrated suspensions of non-Brownian frictional particles. The key result of our study is the emergence of a pronounced shear-thickening regime, where frictionless particles would normally undergo shear-thinning. We clarify that shear thickening in our simulations is due to enhanced energy dissipation via frictional inter-particle forces. Moreover, we evidence the formation of dynamically correlated particle-clusters of size $xi$, which contribute to shear thickening via an increase in emph{viscous} dissipation. A scaling argument gives $etasim xi^2$, which is in very good agreement with the data.
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.
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.
Recent experiments (Le Bouil et al., Phys. Rev. Lett., 2014, 112, 246001) have analyzed the statistics of local deformation in a granular solid undergoing plastic deformation. Experiments report strongly anisotropic correlation between events, with a characteristic angle that was interpreted using elasticity theory and the concept of Eshelby transformations with dilation; interestingly, the shear bands that characterize macroscopic failure occur at an angle that is different from the one observed in microscopic correlations. Here, we interpret this behavior using a mesoscale elastoplastic model of solid flow that incorporates a local Mohr-Coulomb failure criterion. We show that the angle observed in the microscopic correlations can be understood by combining the elastic interactions associated with Eshelby transformation with the local failure criterion. At large strains, we also induce permanent shear bands at an angle that is different from the one observed in the correlation pattern. We interpret this angle as the one that leads to the maximal instability of slip lines.
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