Effect of pressure on segregation in granular shear flows

Fry, Alexander M.; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.

doi:10.1103/physreve.97.062906

Cited by 38 publications

(88 citation statements)

References 42 publications

(58 reference statements)

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“…We further note that pressure‐induced changes to the packing fraction are relatively small. The packing fraction, ϕ , increases only slightly, from 0.59 to 0.63 for size bidisperse simulations and from 0.58 to 0.63 for density bidisperse simulations over the pressures that are considered . Kinetic theory predicts a relatively small change in the diffusion coefficient for the pressure‐induced changes in ϕ .…”

Section: Influence Of Overburden On Diffusionmentioning

confidence: 96%

“…The domain is periodic in the spanwise and streamwise directions, that is, particles leaving from one side of the domain re‐enter on the opposite side. In order to avoid changes in the velocity profile with changing overburden pressure, a velocity stabilizing force that is linear with depth is applied in the streamwise direction to each particle at every time step, according to

F_{stabilize} = A ((), \overset{γ}{true} y - u_{x}),

where u x is the particle's streamwise velocity, y is the particle's vertical position,

\overset{γ}{true}

is the imposed global shear rate, and A is a control parameter . A similar stabilizing force scheme has been used to control the velocity profile in simulations of frictionless particles .…”

Section: Variable Overburden Shear Flowmentioning

confidence: 99%

“…In this way, the shear rate is nearly constant throughout the depth and under all confinement conditions. This permits the measurement of segregation properties across the entire system (all at the same shear rate) and allows the effects of overburden pressure on diffusion to be studied directly as in previous work on segregation …”

Section: Variable Overburden Shear Flowmentioning

confidence: 99%

“…Having determined the pressure dependence of segregation previously and diffusion in size and density bidisperse flows here, we test whether the continuum model developed previously for free surface flows can accurately predict the mixing behavior of these confined flows. This transport equation for granular flows adds a species‐specific segregation flux to the advection–diffusion equation:

\frac{\partial c_{i}}{\partial t} + \nabla \cdot ((), boldu c_{i}) + \frac{\partial}{\partial y} ((), w_{p, i} c_{i}) = \nabla \cdot ((), D \nabla c_{i}),

where c i is the concentration of a given species, u is the mean velocity field, D is the diffusion coefficient, which is assumed to be isotropic, and

w_{p, i} = S \overset{γ}{true} ((), 1 - c_{i})

is the species‐specific segregation velocity, S being a coefficient dependent on particle size ratio or density ratio .…”

Section: Continuum Modeling Of Confined Flowsmentioning

confidence: 99%

“…Furthermore, we found that the segregation rate in size or density bidisperse flows is nearly linearly dependent over a wide range of flow conditions on the inertial number,

I = \overset{γ}{true} d / \sqrt{P / ρ}

, which includes the effects of shear rate,

\overset{γ}{true}

, particle diameter, d , overburden pressure, P , and particle density, ρ . Each simulation was accurately characterized by a single inertial number (rather than a local inertial number) calculated using the mean particle diameter,

\overset{d}{true}

, and mean particle density,

\overset{ρ}{true}

; consideration of the spatial variation of inertial number may be necessary in more complex flows. A similar inertial number dependence was found for the rate of density segregation of a single intruder particle in shear flows of less dense particles …”

Section: Introductionmentioning

confidence: 99%

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Diffusion, mixing, and segregation in confined granular flows

et al. 2018

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Discrete element method simulations of confined bidisperse granular shear flows elucidate the balance between diffusion and segregation that can lead to either mixed or segregated states, depending on confining pressure. Results indicate that the collisional diffusion is essentially independent of overburden pressure. Because the rate of segregation diminishes with overburden pressure, the tendency for particles to segregate weakens relative to the remixing of particles due to collisional diffusion as the overburden pressure increases. Using a continuum approach that includes a pressure-dependent segregation velocity and a pressure-independent diffusion coefficient, the interplay between diffusion and segregation is accurately predicted for both size and density bidisperse mixtures over a wide range of flow conditions when compared to simulation results. Additional simulations with initially segregated conditions demonstrate that applying a high enough overburden pressure can suppress segregation to the point that collisional diffusion mixes the segregated particles.

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Section: Influence Of Overburden On Diffusionmentioning

confidence: 96%

F_{stabilize} = A ((), \overset{γ}{true} y - u_{x}),

where u x is the particle's streamwise velocity, y is the particle's vertical position,

\overset{γ}{true}

is the imposed global shear rate, and A is a control parameter . A similar stabilizing force scheme has been used to control the velocity profile in simulations of frictionless particles .…”

Section: Variable Overburden Shear Flowmentioning

confidence: 99%

Section: Variable Overburden Shear Flowmentioning

confidence: 99%

\frac{\partial c_{i}}{\partial t} + \nabla \cdot ((), boldu c_{i}) + \frac{\partial}{\partial y} ((), w_{p, i} c_{i}) = \nabla \cdot ((), D \nabla c_{i}),

where c i is the concentration of a given species, u is the mean velocity field, D is the diffusion coefficient, which is assumed to be isotropic, and

w_{p, i} = S \overset{γ}{true} ((), 1 - c_{i})

is the species‐specific segregation velocity, S being a coefficient dependent on particle size ratio or density ratio .…”

Section: Continuum Modeling Of Confined Flowsmentioning

confidence: 99%

“…Furthermore, we found that the segregation rate in size or density bidisperse flows is nearly linearly dependent over a wide range of flow conditions on the inertial number,

I = \overset{γ}{true} d / \sqrt{P / ρ}

, which includes the effects of shear rate,

\overset{γ}{true}

\overset{d}{true}

, and mean particle density,

\overset{ρ}{true}

Section: Introductionmentioning

confidence: 99%

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Diffusion, mixing, and segregation in confined granular flows

et al. 2018

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Modeling segregation of polydisperse granular materials in developing and transient free‐surface flows

et al. 2019

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Predicting segregation and mixing of polydisperse granular materials in industrial processes remains a challenging problem. Here, we extend the application of a general predictive continuum model that captures the effects of segregation, diffusion, and advection in two ways. First, we consider polydisperse segregating flow in developing steady segregation and in developing unsteady segregation. In both cases, several terms in the model that were zero in the previously examined case of fully developed streamwise‐periodic steady segregation in a chute are now non‐zero, which makes application of the model substantially more challenging. Second, we apply the polydisperse approach to density polydisperse materials with the same particle size. Predictions of the model agree quantitatively with experimentally validated discrete element method (DEM) simulations of both size polydisperse and density polydisperse mixtures having uniform, triangular, and log‐normal distributions. © 2018 American Institute of Chemical Engineers AIChE J, 65: 882–893, 2019

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Designing minimally segregating granular mixtures for gravity‐driven surface flows

et al. 2023

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In dense flowing bidisperse particle mixtures varying in size or density alone, smaller particles sink (percolation-driven) and lighter particles rise (buoyancy-driven). But when particle species differ from each other in both size and density, percolation and buoyancy can either enhance (large/light and small/heavy) or oppose (large/heavy and small/light) each other. In the latter case, a local equilibrium can exist in which the two mechanisms balance and particles remain mixed: this allows the design of minimally segregating mixtures by specifying particle size ratio, density ratio, and mixture concentration. Using DEM simulations, we show that mixtures specified by the design methodology remain relatively well-mixed in heap and tumbler flows. Furthermore, minimally segregating mixtures prepared in a fully segregated state in a tumbler mix over time and eventually reach a nearly uniform concentration. Tumbler experiments with large steel and small glass particles validate the DEM simulations and the potential for designing minimally segregating mixtures.

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Effect of pressure on segregation in granular shear flows

Cited by 38 publications

References 42 publications

Diffusion, mixing, and segregation in confined granular flows

Diffusion, mixing, and segregation in confined granular flows

Modeling segregation of polydisperse granular materials in developing and transient free‐surface flows

Designing minimally segregating granular mixtures for gravity‐driven surface flows

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