The sands of time run faster near the end

Koivisto, Juha; Durian, Douglas J.

doi:10.1038/ncomms15551

Cited by 36 publications

(43 citation statements)

References 29 publications

(59 reference statements)

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“…3, and it is similar to that in Ref. [4]. The hopper consists of a flat-bottomed cylinder with inner diameter D h = 195 ± 0.5 mm and height h = 250 ± 1 mm.…”

Section: Methodsmentioning

confidence: 70%

“…The Stokes number is St = (1/9)ρ g v t d/η, which here is about Re/3. It refers specifically to grain inertia [31], the importance of which is overestimated by using v t since the discharge speed is smaller in water than in air [3,4] and also since the relative speed of neighboring grains in the coarse-grained flow field is smaller still. Even so, Ref.…”

Section: Methodsmentioning

confidence: 99%

“…And the growing mass of grains collected underneath is not level but forms a conical pile down which the added grains avalanche. Another striking difference is that the discharge rate of grains is constant, as long-described by the empirical Beverloo equation [1,2], and sometimes it can even increase with time [3,4]; by contrast, the fluid discharge rate always decreases with time as the bucket empties and the gravitational pressure head goes down. But an even bigger difference is that grains can clog [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

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Effect of interstitial fluid on the fraction of flow microstates that precede clogging in granular hoppers

Koivisto

Durian

2017

Phys. Rev. E

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We report on the nature of flow events for the gravity-driven discharge of glass beads through a hole that is small enough that the hopper is susceptible to clogging. In particular, we measure the average and standard deviation of the distribution of discharged masses as a function of both hole and grain sizes. We do so in air, which is usual, but also with the system entirely submerged under water. This damps the grain dynamics and could be expected to dramatically affect the distribution of the flow events, which are described in prior work as avalanche-like. Though the flow is slower and the events last longer, we find that the average discharge mass is only slightly reduced for submerged grains. Furthermore, we find that the shape of the distribution remains exponential, implying that clogging is still a Poisson process even for immersed grains. Per Thomas and Durian [Phys. Rev. Lett. 114, 178001 (2015)], this allows for an interpretation of the average discharge mass in terms of the fraction of flow microstates that precede, i.e., that effectively cause, a stable clog to form. Since this fraction is barely altered by water, we conclude that the crucial microscopic variables are the grain positions; grain momenta play only a secondary role in destabilizing weak incipient arches. These insights should aid ongoing efforts to understand the susceptibility of granular hoppers to clogging. We report on the nature of flow events for the gravity-driven discharge of glass beads through a hole that is small enough that the hopper is susceptible to clogging. In particular, we measure the average and standard deviation of the distribution of discharged masses as a function of both hole and grain sizes. We do so in air, which is usual, but also with the system entirely submerged under water. This damps the grain dynamics and could be expected to dramatically affect the distribution of the flow events, which are described in prior work as avalanche-like. Though the flow is slower and the events last longer, we find that the average discharge mass is only slightly reduced for submerged grains. Furthermore, we find that the shape of the distribution remains exponential, implying that clogging is still a Poisson process even for immersed grains. Per Thomas and Durian [Phys. Rev. Lett. 114, 178001 (2015)], this allows for an interpretation of the average discharge mass in terms of the fraction of flow microstates that precede, i.e., that effectively cause, a stable clog to form. Since this fraction is barely altered by water, we conclude that the crucial microscopic variables are the grain positions; grain momenta play only a secondary role in destabilizing weak incipient arches. These insights should aid ongoing efforts to understand the susceptibility of granular hoppers to clogging.

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“…3, and it is similar to that in Ref. [4]. The hopper consists of a flat-bottomed cylinder with inner diameter D h = 195 ± 0.5 mm and height h = 250 ± 1 mm.…”

Section: Methodsmentioning

confidence: 70%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effect of interstitial fluid on the fraction of flow microstates that precede clogging in granular hoppers

Koivisto

Durian

2017

Phys. Rev. E

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“…Over the years, this equation has been used in diverse situations. Some examples are vibrated silos [9], a system where the material is driven by a conveyor belt [10], mixtures of granular media [11,12], water submerged grains [13], or even the flow of air bubbles through a two-dimensional (2D) slit [14]. However, despite the popularity of the expression of Beverloo et al [8], it involves some features of uncertain physical sense, such as the inclusion of the bulk density ρ B instead of the flowing density or the reduced aperture size D − kd p , which accounts for a hypothetical forbidden area of the orifice through which the beads are not allowed to pass.…”

Section: Introductionmentioning

confidence: 99%

Role of particle size in the kinematic properties of silo flow

2017

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We experimentally analyze the effect that particle size has on the mass flow rate of a quasi two-dimensional silo discharged by gravity. In a previous work, Janda et al. [Phys. Rev. Lett. 108, 248001 (2012)] introduced a new expression for the mass flow rate based on a detailed experimental analysis of the flow for 1-mm diameter beads. Here, we aim to extend these results by using particles of larger sizes and a variable that was not explicitly included in the proposed expression. We show that the velocity and density profiles at the outlet are self-similar and scale with the outlet size with the same functionalities as in the case of 1-mm particles. Nevertheless, some discrepancies are evidenced in the values of the fitting parameters. In particular, we observe that larger particles lead to higher velocities and lower packing fractions at the orifice. Intriguingly, both magnitudes seem to compensate giving rise to very similar flow rates. In order to shed light on the origin of this behavior we have computed fields of a solid fraction, velocity, and a kinetic-stress like variable in the region above the orifice.

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“…An unexpected surge in the flow rate appears near the end of the discharge, which is attributed to a pumping effect produced by the interstitial fluid moving faster than the grains. In flow-controlled experiments the surge disappears and the flow rate becomes constant [17].In this article, we study the simultaneous discharge of glass beads and water from a cylindrical silo. An important difference with previous works is that our system is not underwater but it hangs freely in air from a force sensor that allows us to determine the flow rate throughout the emptying process.…”

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confidence: 99%

The simultaneous discharge of liquid and grains from a silo

2018

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The flow rate of water through an orifice at the bottom of a container depends on the hydrostatic pressure whereas for a dry granular material is nearly constant. But what happens during the simultaneous discharge of grains and liquid from a silo? By measuring the flow rate as a function of time, we found that: (i) different regimes appear, going from constant flow rate dominated by the effective fluid viscosity to a hydrostatic-like discharge depending on the aperture and grain size, (ii) the mixed material is always discharged faster than dry grains but slower than liquid, (iii) for the mixture, the liquid level drops faster than the grains level but they are always linearly proportional to one another, and (iv) a sudden growth in the flow rate happens during the transition from a biphasic to a single phase discharge. These results are associated to the competition between the decrease of hydrostatic pressure above the granular bed and the hydrodynamic resistance. A model combining the Kozeny-Carman, Bernoulli and mass conservation equations is proposed and the numerical results are in good agreement with experiments.The clepsydra was an ancient device used to measure the passage of time based on the slow discharge of water through an orifice at the bottom of a graduated vessel. Its origin is unknown but presumably appeared in China about six thousands years ago [1]. The markings in this antiquity are non-uniformly separated since the flow rate depends on the hydrostatic pressure due to the water column above the orifice. On the other hand, the clepsammia, or sandglass, appeared millennia later probably in Alexandria [2] although evidence of its origin only dates from the middle ages [3]. In this device, the flow rate of grains through the bottleneck is independent of the granular column height because the stress acting on the material is redirected towards the container walls through contact force chains. This fact attracted scientists during the last 60 years, being the discharge of dry granular materials from hoppers widely investigated [4][5][6][7][8][9][10][11].The flow rate Q of dry grains through an orifice can be estimated using the Beverloo equation [4]:where D and d are the aperture and particle diameters, C and k are dimensionless fitting parameters related to friction and particle shape, ρ is the material density and g is the acceleration of gravity. The above equation must be modified by introducing an exponential factor when the ratio D/d is considerably increased [8]. More recently, experiments performed at different g's proved that the square root scaling proposed by Beverloo is relevant [10]. It has also been found that the initial packing fraction of the granular column does not affect considerably the flow rate [11][12][13] because the material under discharge is fluidized before reaching the silo aperture [11]. Even in unconventional systems of repelling particles, Q remains constant during the discharge [14,15]. In all the above studies, the interstitial medium is air and its presence was n...

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The sands of time run faster near the end

Cited by 36 publications

References 29 publications

Effect of interstitial fluid on the fraction of flow microstates that precede clogging in granular hoppers

Effect of interstitial fluid on the fraction of flow microstates that precede clogging in granular hoppers

Role of particle size in the kinematic properties of silo flow

The simultaneous discharge of liquid and grains from a silo

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