### Abstract

The bulk rheology of bidisperse mixtures of granular materials is examined under homogeneous shear flow conditions using the event-driven simulation method. The granular material is modelled as a system of smooth inelastic disks, interacting via the hard-core potential. In order to understand the effect of size and mass disparities, two cases were examined separately, namely, a mixture of different sized particles with particles having either the same mass or the same material density. The relevant macroscopic quantities are the pressure, the shear viscosity, the granular energy (fluctuating kinetic energy) and the first normal stress difference. Numerical results for pressure, viscocity and granular energy are compared with a kinetic-theory constitutive model with excellent agreement in the low dissipation limit even at large size disparities. Systematic quantitative deviations occur for stronger dissipations. Mixtures with equal-mass particles show a stronger shear resistance than an equivalent monodisperse system; in contrast, however, mixtures with equal-density particles show a reduced shear resistance. The granular energies of the two species are unequal, implying that the equipartition principle assumed in most of the constitutive models does not hold. Inelasticity is responsible for the onset of energy non-equipartition, but mass disparity significantly enhances its magnitude. This lack of energy equipartition can lead to interesting non-monotonic variations of the pressure, viscosity and granular energy with the mass ratio if the size ratio is held fixed, while the model predictions (with the equipartition assumption) suggest a monotonic behaviour in the same limit. In general, the granular fluid is non-Newtonian with a measurable first normal stress difference (which is positive if the stress is defined in the compressive sense), and the effect of bidispersity is to increase the normal stress difference, thus enhancing the non-Newtonian character of the fluid.

Original language | English |
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Pages (from-to) | 69-103 |

Number of pages | 35 |

Journal | Journal of fluid mechanics |

Issue number | 476 |

DOIs | |

Publication status | Published - 10 Feb 2003 |

Externally published | Yes |

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*Journal of fluid mechanics*, no. 476, pp. 69-103. https://doi.org/10.1017/S002211200200263X

**Rheology of bidisperse granular mixtures via event-driven simulations.** / Alam, Meheboob; Luding, Stefan.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Rheology of bidisperse granular mixtures via event-driven simulations

AU - Alam, Meheboob

AU - Luding, Stefan

PY - 2003/2/10

Y1 - 2003/2/10

N2 - The bulk rheology of bidisperse mixtures of granular materials is examined under homogeneous shear flow conditions using the event-driven simulation method. The granular material is modelled as a system of smooth inelastic disks, interacting via the hard-core potential. In order to understand the effect of size and mass disparities, two cases were examined separately, namely, a mixture of different sized particles with particles having either the same mass or the same material density. The relevant macroscopic quantities are the pressure, the shear viscosity, the granular energy (fluctuating kinetic energy) and the first normal stress difference. Numerical results for pressure, viscocity and granular energy are compared with a kinetic-theory constitutive model with excellent agreement in the low dissipation limit even at large size disparities. Systematic quantitative deviations occur for stronger dissipations. Mixtures with equal-mass particles show a stronger shear resistance than an equivalent monodisperse system; in contrast, however, mixtures with equal-density particles show a reduced shear resistance. The granular energies of the two species are unequal, implying that the equipartition principle assumed in most of the constitutive models does not hold. Inelasticity is responsible for the onset of energy non-equipartition, but mass disparity significantly enhances its magnitude. This lack of energy equipartition can lead to interesting non-monotonic variations of the pressure, viscosity and granular energy with the mass ratio if the size ratio is held fixed, while the model predictions (with the equipartition assumption) suggest a monotonic behaviour in the same limit. In general, the granular fluid is non-Newtonian with a measurable first normal stress difference (which is positive if the stress is defined in the compressive sense), and the effect of bidispersity is to increase the normal stress difference, thus enhancing the non-Newtonian character of the fluid.

AB - The bulk rheology of bidisperse mixtures of granular materials is examined under homogeneous shear flow conditions using the event-driven simulation method. The granular material is modelled as a system of smooth inelastic disks, interacting via the hard-core potential. In order to understand the effect of size and mass disparities, two cases were examined separately, namely, a mixture of different sized particles with particles having either the same mass or the same material density. The relevant macroscopic quantities are the pressure, the shear viscosity, the granular energy (fluctuating kinetic energy) and the first normal stress difference. Numerical results for pressure, viscocity and granular energy are compared with a kinetic-theory constitutive model with excellent agreement in the low dissipation limit even at large size disparities. Systematic quantitative deviations occur for stronger dissipations. Mixtures with equal-mass particles show a stronger shear resistance than an equivalent monodisperse system; in contrast, however, mixtures with equal-density particles show a reduced shear resistance. The granular energies of the two species are unequal, implying that the equipartition principle assumed in most of the constitutive models does not hold. Inelasticity is responsible for the onset of energy non-equipartition, but mass disparity significantly enhances its magnitude. This lack of energy equipartition can lead to interesting non-monotonic variations of the pressure, viscosity and granular energy with the mass ratio if the size ratio is held fixed, while the model predictions (with the equipartition assumption) suggest a monotonic behaviour in the same limit. In general, the granular fluid is non-Newtonian with a measurable first normal stress difference (which is positive if the stress is defined in the compressive sense), and the effect of bidispersity is to increase the normal stress difference, thus enhancing the non-Newtonian character of the fluid.

U2 - 10.1017/S002211200200263X

DO - 10.1017/S002211200200263X

M3 - Article

SP - 69

EP - 103

JO - Journal of fluid mechanics

JF - Journal of fluid mechanics

SN - 0022-1120

IS - 476

ER -