A microscopic theory for discontinuous shear thickening of frictional granular materials

Saitoh, Kuniyasu; Hayakawa, Hisao

doi:10.1051/epjconf/201714003063

Cited by 6 publications

(3 citation statements)

References 11 publications

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“…The difficulty including the mutual friction in terms of statistical mechanics is to have the contributions from the coupled stress and the spin temperature in addition to the shear stress, the normal stress difference and the pressure. A recent paper has already partially reproduced a hysteresis in the flow curve, which is one of the characteristics of the DST by choosing the shear stress, the temperature (the pressure) and the spin temperature [58].…”

Section: Discussionmentioning

confidence: 99%

Kinetic theory of discontinuous shear thickening for a dilute gas-solid suspension

Hayakawa

Takada²

2016

Preprint

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A kinetic theory for a dilute gas-solid suspension under a simple shear is developed. With the aid of the corresponding Boltzmann equation, it is found that the flow curve (stress-strain rate relation) has a S-shape as a crossover from the Newtonian to the Bagnoldian for a granular suspension or from the Newtonian to a fluid having a viscosity proportional to the square of the shear rate for a suspension consisting of elastic particles. The existence of the S-shape in the flow curve directly leads to a discontinuous shear thickening (DST). This DST corresponds to the discontinuous transition of the kinetic temperature between a quenched state and an ignited state. The results of the eventdriven Langevin simulation of hard spheres perfectly agree with the theoretical results without any fitting parameter. The simulation confirms that the DST takes place in the linearly unstable region of the uniformly sheared state.

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Section: Discussionmentioning

confidence: 99%

Kinetic theory of discontinuous shear thickening for a dilute gas-solid suspension

Hayakawa

Takada²

2016

Preprint

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“…Several recent works have sought to explain DST as a transition from a state where hydrodynamic lubrication forces prevent particles from prolonged contact, to a state where such lubrication forces are overcome, particle contacts increase, and elastic Coulomb frictional forces at those contacts become important [49][50][51][52]. Other works [15,17,19,20,51,[53][54][55] have described DST as a precursor of the discontinuous jump in stress associated with the shear-driven jamming of frictional particles [15,16]. While both DST and shear banding have been associated with discontinuous transitions, it remains unclear if there is a direct connection between these two phenomena.…”

Section: Introductionmentioning

confidence: 99%

Shear banding, discontinuous shear thickening, and rheological phase transitions in athermally sheared frictionless disks

2017

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We report on numerical simulations of simple models of athermal, bidisperse, soft-core, massive disks in two dimensions, as a function of packing fraction ϕ, inelasticity of collisions as measured by a parameter Q, and applied uniform shear strain rate γ[over ̇]. Our particles have contact interactions consisting of normally directed elastic repulsion and viscous dissipation, as well as tangentially directed viscous dissipation, but no interparticle Coulombic friction. Mapping the phase diagram in the (ϕ,Q) plane for small γ[over ̇], we find a sharp first-order rheological phase transition from a region with Bagnoldian rheology to a region with Newtonian rheology, and show that the system is always Newtonian at jamming. We consider the rotational motion of particles and demonstrate the crucial importance that the coupling between rotational and translational degrees of freedom has on the phase structure at small Q (strongly inelastic collisions). At small Q, we show that, upon increasing γ[over ̇], the sharp Bagnoldian-to-Newtonian transition becomes a coexistence region of finite width in the (ϕ,γ[over ̇]) plane, with coexisting Bagnoldian and Newtonian shear bands. Crossing this coexistence region by increasing γ[over ̇] at fixed ϕ, we find that discontinuous shear thickening can result if γ[over ̇] is varied too rapidly for the system to relax to the shear-banded steady state corresponding to the instantaneous value of γ[over ̇].

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“…This study will be reported elsewhere [40] (see also Ref. [41]). We should note that contact states between grains are important to describe typical DSTs in dense suspensions.…”

Section: Discussionmentioning

confidence: 83%

Enskog kinetic theory of rheology for a moderately dense inertial suspension

Takada,

Hayakawa,

Santos

et al. 2020

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A microscopic theory for discontinuous shear thickening of frictional granular materials

Cited by 6 publications

References 11 publications

Kinetic theory of discontinuous shear thickening for a dilute gas-solid suspension

Kinetic theory of discontinuous shear thickening for a dilute gas-solid suspension

Shear banding, discontinuous shear thickening, and rheological phase transitions in athermally sheared frictionless disks

Enskog kinetic theory of rheology for a moderately dense inertial suspension

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