Publisher’s Note: Nonlocal Constitutive Relation for Steady Granular Flow [Phys. Rev. Lett.<b>108</b>, 178301 (2012)]

Kamrin, Ken; Koval, Georg

doi:10.1103/physrevlett.108.199904

Cited by 105 publications

(228 citation statements)

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“…In this case, one can precisely define topological rearrangements (T1 events) associated with the switching of bubble neighbors, where one of the polygonal edges decreases to zero and then a new edge is created. T1 events can be isolated and localized, or occur as multiple, correlated rearrangements 41,42 . In fact, one event at a given location in the system at a given time can trigger another at a different location later in time.…”

Section: Introductionmentioning

confidence: 99%

Stable small bubble clusters in two-dimensional foams

et al. 2017

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Key features of the mechanical response of amorphous particulate materials, such as foams, emulsions, and granular media, to applied stress are determined by the frequency and size of particle rearrangements that occur as the system transitions from one mechanically stable state to another. This work describes coordinated experimental and computational studies of bubble rafts, which are quasi-two dimensional systems of bubbles confined to the air-water interface. We focus on small mechanically stable clusters of four, five, six, and seven bubbles with two different sizes with diameter ratio σ L /σ S ≃ 1.4. Focusing on small bubble clusters, which can be viewed as subsystems of a larger system, allows us to investigate the full ensemble of clusters that form, measure the respective frequencies with which the clusters occur, and determine the form of the bubble-bubble interactions. We emphasize several important results. First, for clusters with N > 5 bubbles, we find using discrete element simulations that short-range attractive interactions between bubbles give rise to a larger ensemble of distinct mechanically stable clusters compared to that generated by long-range attractive interactions. The additional clusters in systems with short-range attractions possess larger gaps between pairs of neighboring bubbles on the periphery of the clusters. The ensemble of bubble clusters observed in experiments is similar to the ensemble of clusters with long-range attractive interactions. We also compare the frequency with which each cluster occurs in simulations and experiments. We find that the cluster frequencies are extremely sensitive to the protocol used to generate them and only weakly correlated to the energy of the clusters.

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Section: Introductionmentioning

confidence: 99%

Stable small bubble clusters in two-dimensional foams

et al. 2017

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“…33 has provided an analytical derivation of the HL model itself and its closure relation D = αΓ, as well as of the phenomenological 'nonlocal fluidity equation', which has in turn been successfully applied to study experimental systems such as in Refs. [42][43][44] . So, although the diffusive assumption is restricted to an intermediate regime of low but finite shear rates, these previous studies and their connections with experiments support furthermore the relevance of investigating analytically the class of diffusive ALYS models, as we do thereafter.…”

Section: Figmentioning

confidence: 99%

Non-trivial rheological exponents in sheared yield stress fluids

Agoritsas

Martens

2017

Soft Matter

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In this work we discuss possible physical origins for non-trivial exponents in the athermal rheology of soft materials at low but finite driving rates. A key ingredient in our scenario is the presence of a self-consistent mechanical noise that stems from the spatial superposition of long-range elastic responses to localized plastically deforming regions. We study analytically a mean-field model, in which this mechanical noise is accounted for by a stress diffusion term coupled to the plastic activity. Within this description we show how a dependence of the shear modulus and/or the local relaxation time on the shear rate introduces corrections to the usual mean-field prediction, concerning the Herschel-Bulkley-type rheological response of exponent 1/2. This feature of the mean-field picture is then shown to be robust with respect to structural disorder and partial relaxation of the local stress. We test this prediction numerically on a mesoscopic lattice model that implements explicitly the long-range elastic response to localized shear transformations, and we conclude on how our scenario might be tested in rheological experiments.

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“…Various non-local models have been introduced that successfully account for these situations [4,5,[7][8][9][10][11][12]. In spite of the differences in their formulations, these nonlocal models are all based on the key assumption that there exists a meso-scale length which is larger than the grain size d and that it represents the extent of non-locality, i.e., the influence on the flow at one point due to flows at its neighbouring points.…”

Section: Introductionmentioning

confidence: 99%

Partial jamming and non-locality in dense granular flows

Kharel

Rognon

2017

EPJ Web Conf.

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Abstract. Dense granular flows can exhibit non-local flow behaviours that cannot be predicted by local constitutive laws alone. Such behaviour is accompanied by the existence of diverging cooperativity length. Here we show that this length can be attributed to the development of transient clusters of jammed particles within the flow. By performing DEM simulation of dense granular flows, we directly measure the size of such clusters which scales with the inertial number with a power law. We then derive a general non-local relation based on kinematic compatibility for the existence of clusters in an arbitrary non-homogenous flow. The kinematic nature of this derivation suggests that non-locality should be expected in any material regardless of their local constitutive law, as long as transient clusters exist within the flow.

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Publisher’s Note: Nonlocal Constitutive Relation for Steady Granular Flow [Phys. Rev. Lett.108, 178301 (2012)]

Cited by 105 publications

References 0 publications

Stable small bubble clusters in two-dimensional foams

Stable small bubble clusters in two-dimensional foams

Non-trivial rheological exponents in sheared yield stress fluids

Partial jamming and non-locality in dense granular flows

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