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Granular shear flows of flat disks and elongated rods without and with friction
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10.1063/1.4812386
/content/aip/journal/pof2/25/6/10.1063/1.4812386
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/6/10.1063/1.4812386

Figures

Image of FIG. 1.
FIG. 1.

Numerical models of granular shear flows with (a) flat disks and (b) elongated rods at the solid volume fraction of 0.1. The dimensions of cylindrical particles are illustrated in (c).

Image of FIG. 2.
FIG. 2.

Normalized shear stress as a function of solid volume fraction for various particle aspect ratios ( = 0, = 0.95, = 8.7 × 10 Pa, = 100 s). The kinetic theory curve is for frictionless spheres.

Image of FIG. 3.
FIG. 3.

Normalized shear stresses as a function of the maximum value of / and / at different solid volume fractions ( = 0, = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 4.
FIG. 4.

Apparent friction coefficient as a function of solid volume fraction for various aspect ratios ( = 0, = 0.95, = 8.7 × 10 Pa, = 100 s). The kinetic theory curve is for frictionless spheres.

Image of FIG. 5.
FIG. 5.

Particle alignment during shear flows with (a) disks and (b) elongated rods at a solid volume fraction of 0.5 ( = 0, = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 6.
FIG. 6.

(a) Description of particle orientation using the angles α and β, (b) probability density distributions of the particle inclination angle α, and (c) probability density distributions of the particle azimuthal angle β for the particles of various aspect ratios at the solid volume fraction of 0.5 ( = 0, = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 7.
FIG. 7.

Variation of order parameter with the maximum dimensional ratio of / and / for dense flows at the solid volume fraction of ν = 0.5 ( = 0, = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 8.
FIG. 8.

Six types of cylinder-cylinder contacts.

Image of FIG. 9.
FIG. 9.

Number percentage of contacts of a specific type as a function of solid volume fraction for (a) = 0.1, (b) = 1, and (c) = 6 ( = 0, = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 10.
FIG. 10.

Number percentage of contacts of a specific type as a function of particle aspect ratio (). The solid volume fraction is fixed at 0.6 for various aspect ratio particles ( = 0, = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 11.
FIG. 11.

Normalized shear stress as a function of solid volume fraction for the cylindrical particles with various coefficients of restitution ( = 4, = 0.0, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 12.
FIG. 12.

Apparent friction coefficient as a function of solid volume fraction for cylindrical particles with various coefficients of restitution ( = 4, = 0.0, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 13.
FIG. 13.

Variation of normalized shear stress with solid volume fraction for particles with and without friction. The surrounding images show snapshots of force chains at the specified solid volume fractions. The force chains are plotted by connecting the centers of two particles in contact. The thicknesses of the lines, scaled by the current maximum contact force, indicate the magnitudes of the contact forces. The inserted diagram shows the variation of time-averaged coordination number with solid volume fraction for particles with and without friction ( = 4, = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 14.
FIG. 14.

Snapshot of particle velocity vectors for a dense shear flow of frictionless particles at the solid volume fraction of = 0.5 ( = 0.0, = 4, = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 15.
FIG. 15.

Three snapshots of above-average-force chains at different dimensionless time instants (γ · ) are shown in the top row (a)-(c) and the corresponding snapshots of particle velocity vectors are shown in the bottom row (d)-(f) for the dense shear flow with frictional particles at the solid volume fraction of = 0.5 ( = 0.5, = 4, = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 16.
FIG. 16.

Normalized shear stress as a function of solid volume fraction for (a) flat disks ( < 1) and (b) rods ( ≥ 1) with different interparticle friction coefficients ( = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 17.
FIG. 17.

Apparent friction coefficient as a function of solid volume fraction for (a) flat disks ( < 1) and (b) rods ( ≥ 1) with different interparticle friction coefficients ( = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 18.
FIG. 18.

Order parameter as a function of solid volume fraction for the flows with and without interparticle friction ( = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 19.
FIG. 19.

Normalized shear stress as a function of solid volume fraction for rods with various normalized Young's moduli ( = 0.95, = 100 s).

Image of FIG. 20.
FIG. 20.

Variation of apparent friction coefficient with the solid volume fraction for rods with various normalized Young's moduli ( = 0.95, = 100 s).

Image of FIG. 21.
FIG. 21.

Comparison of the average scaled overlaps and average dimensionless normal forces for particles with two different Young's moduli ( = 0.95, = 100 s).

Image of FIG. 22.
FIG. 22.

Normalized shear stress as a function of normalized Young's modulus for dense, frictional flows with various particle aspect ratios ( = 0.5, = 0.95). Quasi-static flows at a low shear rate of = 1 s are also considered for the rods of = 4 at the solid volume fraction of = 0.6.

Image of FIG. 23.
FIG. 23.

Variation of the apparent friction coefficient with the normalized Young's modulus for dense frictional flows ( = 0.5, = 0.95, = 100 s).

Image of FIG. 24.
FIG. 24.

Three normal stress components as a function of solid volume fraction for shear flows of flat disks ( = 0.1) and elongated rods ( = 6) (a) without and (b) with friction of = 0.5 ( = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 25.
FIG. 25.

Comparison of three temperature components, normalized by their average value, for shear flows of flat disks ( = 0.1) and elongated rods ( = 6) (a) without and (b) with friction of = 0.5 ( = 0.95, = 8.7 × 10 Pa, = 100 s).

Image of FIG. 26.
FIG. 26.

Normalized rotational and translational temperatures as a function of solid volume fraction for shear flows of flat disks ( = 0.1) and elongated rods ( = 6) with = 0.5 ( = 0.95, = 8.7 × 10 Pa, = 100 s).

Tables

Generic image for table
Table I.

Particle properties and simulation parameters.

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/content/aip/journal/pof2/25/6/10.1063/1.4812386
2013-06-28
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Granular shear flows of flat disks and elongated rods without and with friction
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/6/10.1063/1.4812386
10.1063/1.4812386
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