Shear state of freely evolving granular gases

Brey, J. Javier; Ruiz‐Montero, M. J.; Domínguez, A.

doi:10.1103/physreve.78.041301

Cited by 8 publications

(16 citation statements)

References 29 publications

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“…The kinetic theory for disks with considerable dissipation [36,77,97,102,184,185] leads to transport coefficients with r-dependent factors, see e.g. Ref.…”

Section: Stronger Dissipationmentioning

confidence: 99%

“…Various types of instabilities in complex fluids are reviewed, e.g., in Refs. [35,36,154,163] and references therein.…”

Section: Overview Of Recent Researchmentioning

confidence: 99%

“…Here, only the results of Ref. [102] are revisited, which do contain r-dependent terms, but neglect higher order gradients/moments and corrections to the distribution functions [36,101]. Anisotropy and other effects [77,96] should not be expected in this level of approximation.…”

Section: Stronger Dissipationmentioning

confidence: 99%

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Towards dense, realistic granular media in 2D

Luding¹

2009

Nonlinearity

133

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The development of an applicable theory for granular matter -with both qualitative and quantitative value -is a challenging prospect, given the multitude of states, phases and (industrial) situations it has to cover. Given the general balance equations for mass, momentum, and energy, the limiting case of dilute and almost elastic granular gases, where kinetic theory works perfectly well, is the starting point.In most systems, low density coexists with very high density, where the latter is an open problem for kinetic theory. Furthermore, many additional non-linear phenomena and material properties are important in realistic granular media, involving, e.g.: (i) multi-particle interactions and elasticity (ii) strong dissipation, (iii) friction, (iv) long-range forces and wet contacts (v) wide particle size-distributions, and (vi) various particle shapes. Note that, while some of these issues are more relevant for high density, others are important for both low and high densities; some of them can be dealt with by means of kinetic theory, some can not. This paper is a review of recent progress towards more realistic models for dense granular media in 2D, even though most of the observations, conclusions, and corrections given are qualitatively true also in 3D. Starting from an elastic, frictionless and monodisperse hard sphere gas, the (continuum) balance equations of mass, momentum and energy are given. The equation of state, the (Navier-Stokes level) transport coefficients and the energy-density dissipation rate are considered. Several corrections are applied to those constitutive material laws -one by one -in order to account for the realistic physical effects and properties listed above.

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“…The kinetic theory for disks with considerable dissipation [36,77,97,102,184,185] leads to transport coefficients with r-dependent factors, see e.g. Ref.…”

Section: Stronger Dissipationmentioning

confidence: 99%

“…Various types of instabilities in complex fluids are reviewed, e.g., in Refs. [35,36,154,163] and references therein.…”

Section: Overview Of Recent Researchmentioning

confidence: 99%

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Towards dense, realistic granular media in 2D

Luding¹

2009

Nonlinearity

133

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“…This is in contrast with rectangular geometry, where the shear mode bifurcates at a smaller system size than the clustering mode [10,35,38,39]. This fact enabled us to investigate a strongly nonlinear dynamics of a linearly unstable clustering mode in a 2D setting, without worrying about the shear mode.…”

Section: Discussionmentioning

confidence: 96%

“…where l ν = 2ν 0 /(Λρ 2 0 ) is the critical length for the shear instability in a rectangular geometry [10,35,38,39]. By virtue of Eq.…”

Section: B Small-amplitude Modes Are Decoupledmentioning

confidence: 99%

Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas

2010

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We employ Navier-Stokes granular hydrodynamics to investigate the long-time behavior of clustering instability in a freely cooling dilute granular gas in two dimensions. We find that, in circular containers, the homogeneous cooling state (HCS) of the gas loses its stability via a sub-critical pitchfork bifurcation. There are no time-independent solutions for the gas density in the supercritical region, and we present analytical and numerical evidence that the gas develops thermal collapse unarrested by heat diffusion. To get more insight, we switch to a simpler geometry of a narrowsector-shaped container. Here the HCS loses its stability via a transcritical bifurcation. For some initial conditions a time-independent inhomogeneous density profile sets in, qualitatively similar to that previously found in a narrow-channel geometry. For other initial conditions, however, the dilute gas develops thermal collapse unarrested by heat diffusion. We determine the dynamic scalings of the flow close to collapse analytically and verify them in hydrodynamic simulations. The results of this work imply that, in dimension higher than one, Navier-Stokes hydrodynamics of a dilute granular gas is prone to finite-time density blowups. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.

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Fluctuations, correlations, and Casimir-like forces in the homogeneous cooling state of a granular gas

Jiménez Oliva,

Rodriguez-Lopez,

Khalil

2024

Physics of Fluids

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The fluctuating hydrodynamics by Brey et al. [Phys. Rev. E 83, 041303 (2011)] is analytically solved to get the long-time limit of the fluctuations of the number density, velocity field, and energy density around the homogeneous cooling state of a granular gas, under physical conditions where it keeps stable. Explicit expressions are given for the nonwhite contributions in the elastic limit. For small dissipation, the latter is shown to be much smaller than the inelastic contributions, in general. The fluctuation-induced Casimir-like forces on the walls of the system are calculated assuming a fluctuating pressure tensor resulting from perturbing its Navier–Stokes expression. This way, the Casimir-like forces emerge as the correlation between the longitudinal velocity and the energy density. Interestingly, the fluctuation-induced forces push/pull the system toward the square or rectangular geometry where they vanish, in good agreement with the event-driven numerical simulations.

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Shear state of freely evolving granular gases

Cited by 8 publications

References 29 publications

Towards dense, realistic granular media in 2D

Towards dense, realistic granular media in 2D

Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas

Fluctuations, correlations, and Casimir-like forces in the homogeneous cooling state of a granular gas

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