Viscous-like forces control the impact response of shear-thickening dense suspensions

Brassard, Marc Andre; Causley, Neil; Krizou, Nasser; Dijksman, Joshua A.; Clark, Abram H.

doi:10.1017/jfm.2021.611

Cited by 8 publications

(19 citation statements)

References 37 publications

(94 reference statements)

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“…4(b), where one can use β = −0.523 ± 0.064 for all u 0 . Our observed exponents agree with the experimental observations 5,11 . Even though the authors of Ref.…”

Section: A Impactor Motionsupporting

confidence: 92%

“…The absolute values of exponents observed in our simulation is smaller than the solution of the added mass model 8 . The exponents also are close to those obtained in the phenomenology based on the viscous force acting on the dynamically jammed region 11 . This is understandable since the peak of F exists in the early stage where the viscous force still dominates the impactor dynamics.…”

Section: A Impactor Motionsupporting

confidence: 82%

“…Recently, Ref. 11 proposed a model with a drag that depends linearly on the impactor position due to the existence of the viscous force acting on the boundary of the dynamically jammed region, though their model also ignores the role of gravity m I g. Although their model cannot explain the crossover and the elastic motion of the impactor, it can be solved analytically and yields α = 1.5 and β = −0.5. Our proposed model is essentially the same as that Ref.…”

Section: A Impactor Motionmentioning

confidence: 99%

“…Our proposed model is essentially the same as that Ref. 11 proposed with keeping the gravity term (Sec. III C 2) in the early stage.…”

Section: A Impactor Motionmentioning

confidence: 99%

“…If we assume that F I D is proportional to |z| żI , F I D in Eq. ( 2) is identical to the viscous force model 11 .…”

Section: Floating Modelmentioning

confidence: 99%

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Viscoelastic response of impact process on dense suspensions

Hayakawa

2021

Preprint

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We numerically study the impact on dense suspensions using the lattice Boltzmann method simulation. We find that the maximum force acting on the impactor F max takes place at the early stage of the impact and is not related to the rebound process which takes place in the late stage. For F max , we found a crossover from the u 0 independent regime to a power-law regime satisfying F max ∝ u 1.43 0 . On the other hand, the elapsed time t max to reach F max satisfies t max ∝ u −0.52 0 for all u 0 . We propose a viscous floating model, which is similar to the model used in the previous studies to recover crossover behavior and the power-law exponents by taking into account that the drag acting on the impactor is proportional to the depth of the impactor if the impactor depth is smaller than its diameter. Finally, the rebound process can be recovered by adding an elastic term to the model in which the elastic force acting on the impactor is proportional to the number of the connected force chains from the impactor to the bottom plate.

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“…4(b), where one can use β = −0.523 ± 0.064 for all u 0 . Our observed exponents agree with the experimental observations 5,11 . Even though the authors of Ref.…”

Section: A Impactor Motionsupporting

confidence: 92%

Section: A Impactor Motionsupporting

confidence: 82%

Section: A Impactor Motionmentioning

confidence: 99%

“…Our proposed model is essentially the same as that Ref. 11 proposed with keeping the gravity term (Sec. III C 2) in the early stage.…”

Section: A Impactor Motionmentioning

confidence: 99%

“…If we assume that F I D is proportional to |z| żI , F I D in Eq. ( 2) is identical to the viscous force model 11 .…”

Section: Floating Modelmentioning

confidence: 99%

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Viscoelastic response of impact process on dense suspensions

Hayakawa

2021

Preprint

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Transient flows and migration in granular suspensions: key role of Reynolds-like dilatancy

et al. 2022

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We investigate the transient dynamics of a sheared suspension of neutrally buoyant particles in pressure-imposed rheology configuration, subject to a sudden change in shear rate or external pressure. Discrete element method simulations show that, depending on the flow parameters (particle and system size, initial volume fraction), the early stress response of the suspension may differ strongly from the prediction of the suspension balance model based on the steady-state rheology. We show that a two-phase model incorporating the Reynolds-like dilatancy law of Pailha & Pouliquen (J. Fluid Mech., vol. 633, 2009, pp. 115–135), which prescribes the dilation rate of the suspension over a strain scale $\gamma _0$ , captures quantitatively the suspension dilation/compaction over the whole range of parameters investigated. Together with the Darcy flow induced by the pore pressure gradient during dilation or compaction, this Reynolds-like dilatancy implies that the early stress response of the suspension is non-local, with a non-local length scale $\ell$ that scales with the particle size and diverges algebraically at jamming. In regions affected by $\ell$ , the stress level is fixed, not by the steady-state rheology, but by the Darcy fluid pressure gradient resulting from the dilation/compaction rate. Our results extend the validity of the Reynolds-like dilatancy flow rule, initially proposed for jammed suspensions, to flowing suspension below the critical volume fraction at which the suspension jams, thereby providing a unified framework to describe dilation and shear-induced migration. They pave the way for understanding more complex unsteady flows of dense suspensions, such as impacts, transient avalanches or the impulsive response of shear-thickening suspensions.

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