Energy nonequipartition, rheology, and microstructure in sheared bidisperse granular mixtures

Meheboob Alam, Stefan Luding

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

Event-driven simulations of smooth inelastic hard disks are used to probe the transport properties and the microstructure of bidisperse granular mixtures. A generic feature of such mixtures is that the two species have different levels of fluctuation kinetic energy (Tl≠ Ts) in contrast with their elastic counterpart. The microscopic mechanism for this energy nonequipartition is shown to be directly tied to the asymmetric nature of collisional probabilities between the heavier and lighter species, compared to their purely elastic counterpart. The degree of collisional asymmetry increases with both increasing inelasticity and mass disparity, thereby increasing the energy ratio Tl/Ts in the same limit. A phenomenological constitutive model, that incorporates energy nonequipartition, captures the nonmonotonic behavior of the transport coefficients, in agreement with the simulation results, whereas the standard constitutive model with equipartition assumption predicts monotonic variations. The sheared granular mixture readily forms clusters, having striped patterns along the extensional axis of the flow. The microstructural flow features are extracted by measuring the cluster-size distributions, the pair-correlation function and the collision-angle distribution. While the inelastic dissipation is responsible for the onset of clustering, we have found that the mass disparity between the two species enhances the degree of clustering significantly in the sense that the size of the largest cluster increases with increasing mass disparity. At the microscopic level, the particle motion becomes more and more streamlined (i.e., ordered along the streamwise direction which is also a signature of enhanced short-range correlations) with increasing dissipation and mass disparity, which is responsible for the enhanced first normal stress difference in the same limit.

Original languageEnglish
Article number063303
Pages (from-to)1-18
Number of pages18
JournalPhysics of fluids
Volume17
Issue number6
DOIs
Publication statusE-pub ahead of print/First online - 8 Jun 2005
Externally publishedYes

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Rheology
rheology
Constitutive models
microstructure
Microstructure
dissipation
transport properties
Hard disk storage
Kinetic energy
Transport properties
energy
particle motion
simulation
kinetic energy
signatures
asymmetry
collisions
probes

Cite this

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title = "Energy nonequipartition, rheology, and microstructure in sheared bidisperse granular mixtures",
abstract = "Event-driven simulations of smooth inelastic hard disks are used to probe the transport properties and the microstructure of bidisperse granular mixtures. A generic feature of such mixtures is that the two species have different levels of fluctuation kinetic energy (Tl≠ Ts) in contrast with their elastic counterpart. The microscopic mechanism for this energy nonequipartition is shown to be directly tied to the asymmetric nature of collisional probabilities between the heavier and lighter species, compared to their purely elastic counterpart. The degree of collisional asymmetry increases with both increasing inelasticity and mass disparity, thereby increasing the energy ratio Tl/Ts in the same limit. A phenomenological constitutive model, that incorporates energy nonequipartition, captures the nonmonotonic behavior of the transport coefficients, in agreement with the simulation results, whereas the standard constitutive model with equipartition assumption predicts monotonic variations. The sheared granular mixture readily forms clusters, having striped patterns along the extensional axis of the flow. The microstructural flow features are extracted by measuring the cluster-size distributions, the pair-correlation function and the collision-angle distribution. While the inelastic dissipation is responsible for the onset of clustering, we have found that the mass disparity between the two species enhances the degree of clustering significantly in the sense that the size of the largest cluster increases with increasing mass disparity. At the microscopic level, the particle motion becomes more and more streamlined (i.e., ordered along the streamwise direction which is also a signature of enhanced short-range correlations) with increasing dissipation and mass disparity, which is responsible for the enhanced first normal stress difference in the same limit.",
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Energy nonequipartition, rheology, and microstructure in sheared bidisperse granular mixtures. / Alam, Meheboob; Luding, Stefan.

In: Physics of fluids, Vol. 17, No. 6, 063303, 08.06.2005, p. 1-18.

Research output: Contribution to journalArticleAcademicpeer-review

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N2 - Event-driven simulations of smooth inelastic hard disks are used to probe the transport properties and the microstructure of bidisperse granular mixtures. A generic feature of such mixtures is that the two species have different levels of fluctuation kinetic energy (Tl≠ Ts) in contrast with their elastic counterpart. The microscopic mechanism for this energy nonequipartition is shown to be directly tied to the asymmetric nature of collisional probabilities between the heavier and lighter species, compared to their purely elastic counterpart. The degree of collisional asymmetry increases with both increasing inelasticity and mass disparity, thereby increasing the energy ratio Tl/Ts in the same limit. A phenomenological constitutive model, that incorporates energy nonequipartition, captures the nonmonotonic behavior of the transport coefficients, in agreement with the simulation results, whereas the standard constitutive model with equipartition assumption predicts monotonic variations. The sheared granular mixture readily forms clusters, having striped patterns along the extensional axis of the flow. The microstructural flow features are extracted by measuring the cluster-size distributions, the pair-correlation function and the collision-angle distribution. While the inelastic dissipation is responsible for the onset of clustering, we have found that the mass disparity between the two species enhances the degree of clustering significantly in the sense that the size of the largest cluster increases with increasing mass disparity. At the microscopic level, the particle motion becomes more and more streamlined (i.e., ordered along the streamwise direction which is also a signature of enhanced short-range correlations) with increasing dissipation and mass disparity, which is responsible for the enhanced first normal stress difference in the same limit.

AB - Event-driven simulations of smooth inelastic hard disks are used to probe the transport properties and the microstructure of bidisperse granular mixtures. A generic feature of such mixtures is that the two species have different levels of fluctuation kinetic energy (Tl≠ Ts) in contrast with their elastic counterpart. The microscopic mechanism for this energy nonequipartition is shown to be directly tied to the asymmetric nature of collisional probabilities between the heavier and lighter species, compared to their purely elastic counterpart. The degree of collisional asymmetry increases with both increasing inelasticity and mass disparity, thereby increasing the energy ratio Tl/Ts in the same limit. A phenomenological constitutive model, that incorporates energy nonequipartition, captures the nonmonotonic behavior of the transport coefficients, in agreement with the simulation results, whereas the standard constitutive model with equipartition assumption predicts monotonic variations. The sheared granular mixture readily forms clusters, having striped patterns along the extensional axis of the flow. The microstructural flow features are extracted by measuring the cluster-size distributions, the pair-correlation function and the collision-angle distribution. While the inelastic dissipation is responsible for the onset of clustering, we have found that the mass disparity between the two species enhances the degree of clustering significantly in the sense that the size of the largest cluster increases with increasing mass disparity. At the microscopic level, the particle motion becomes more and more streamlined (i.e., ordered along the streamwise direction which is also a signature of enhanced short-range correlations) with increasing dissipation and mass disparity, which is responsible for the enhanced first normal stress difference in the same limit.

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