Hydrodynamics of binary mixtures of granular gases with stochastic coefficient of restitution

Serero, D.; Gunkelmann, Nina; Pöschel, Thorsten

doi:10.1017/jfm.2015.501

Cited by 11 publications

(7 citation statements)

References 49 publications

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“…But a significant part can go into transverse components of translational energy and rotational energy. Thus, this is a simple demonstration of the idea that β z (and β x ) must be treated as a random variable rather than a fixed quantity as in the case of the normal coefficient of restitution associated with spherical particles in a granular gas, although recent efforts have treated this quantity as a random variable (Gunkelmann et al, 2014;Serero et al, 2015).…”

Section: Resultsmentioning

confidence: 99%

Rarefied particle motions on hillslopes – Part 2: Analysis

et al. 2021

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Abstract. We examine a theoretical formulation of the probabilistic physics of rarefied particle motions and deposition on rough hillslope surfaces using measurements of particle travel distances obtained from laboratory and field-based experiments, supplemented with high-speed imaging and audio recordings that highlight effects of particle–surface collisions. The formulation, presented in a companion paper (Furbish et al., 2021a), is based on a description of the kinetic energy balance of a cohort of particles treated as a rarefied granular gas, as well as a description of particle deposition that depends on the energy state of the particles. Both laboratory and field-based measurements are consistent with a generalized Pareto distribution of travel distances and predicted variations in behavior associated with the balance between gravitational heating due to conversion of potential to kinetic energy and frictional cooling due to particle–surface collisions. For a given particle size and shape these behaviors vary from a bounded distribution representing rapid thermal collapse with small slopes or large surface roughness, to an exponential distribution representing approximately isothermal conditions, to a heavy-tailed distribution representing net heating of particles with large slopes. The transition to a heavy-tailed distribution likely involves an increasing conversion of translational to rotational kinetic energy leading to larger travel distances with decreasing effectiveness of collisional friction. This energy conversion is strongly influenced by particle shape, although the analysis points to the need for further clarity concerning how particle size and shape in concert with surface roughness influence the extraction of particle energy and the likelihood of deposition.

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Section: Resultsmentioning

confidence: 99%

Rarefied particle motions on hillslopes – Part 2: Analysis

et al. 2021

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“…However, this method goes beyond the Maxwellian approximation since it determines the exact velocity distribution functions f i . In this context, the comparison of DSMC results versus analytical results for very dilute systems (φ → 0) can be used to asses the accuracy of the Maxwellian approximation (32) for determining the cooling rates (34). The second method is MD simulations.…”

Section: A Temperaturesmentioning

confidence: 99%

“…One approach, when momentum is not conserved, is the stochastic thermostat, which adds a random force acting on every particle with zero correlation time, and amplitude related to the intensity of the kicks [28][29][30][31]. Other models, which are appropriate when momentum is conserved, consider random restitution coefficients (larger or smaller than 1) that lead to a homogeneous steady state [32][33][34]. In the present article we will consider the so-called model also valid for smooth plates, where the thermostat is a collisional one, so that energy is injected in every collision [35].…”

Section: Introductionmentioning

confidence: 99%

Energy nonequipartition in a collisional model of a confined quasi-two-dimensional granular mixture

2020

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A collisional model of a confined quasi-two-dimensional granular mixture is considered to analyze homogeneous steady states. The model includes an effective mechanism to transfer the kinetic energy injected by vibration in the vertical direction to the horizontal degrees of freedom of grains. The set of Enskog kinetic equations for the velocity distribution functions of each component is derived first to analyze the homogeneous state. As in the one-component case, an exact scaling solution is found where the time dependence of the distribution functions occurs entirely through the granular temperature T . As expected, the kinetic partial temperatures T i of each component are different and, hence, energy equipartition is broken down. In the steady state, explicit expressions for the temperature T and the ratio of partial kinetic temperatures T i /T j are obtained by considering Maxwellian distributions defined at the partial temperatures T i . The (scaled) granular temperature and the temperature ratios are given in terms of the coefficients of restitution, the solid volume fraction, the (scaled) parameters of the collisional model, and the ratios of mass, concentration, and diameters. In the case of a binary mixture, the theoretical predictions are exhaustively compared with both direct simulation Monte Carlo and molecular dynamics simulations with a good agreement. The deviations are identified to be originated in the non-Gaussianity of the velocity distributions and on microsegregation patterns, which induce spatial correlations not captured in the Enskog theory.

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“…One approach is the stochastic thermostat, which adds a random force acting on every particle with zero correlation time, and amplitude related with the intensity of the kicks [28][29][30]. Other models consider random restitution coefficients (larger or smaller than one) that lead to a homogeneous steady state [31][32][33]. In the present article we will consider the so-called ∆-model, where the thermostat is a collisional one, so that energy is injected in every collision [34].…”

Section: Introductionmentioning

confidence: 99%

Energy nonequipartition in a collisional model of a confined quasi-two-dimensional granular mixture

Brito,

Soto,

Garzó

2020

Preprint

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A collisional model of a confined quasi-two-dimensional granular mixture is considered to analyze homogeneous steady states. The model includes an effective mechanism to transfer the kinetic energy injected by vibration in the vertical direction to the horizontal degrees of freedom of grains. The set of Enskog kinetic equations for the velocity distribution functions of each component is derived first to analyze the homogeneous state. As in the one-component case, an exact scaling solution is found where the time dependence of the distribution functions occurs entirely through the granular temperature T . As expected, the kinetic partial temperatures Ti of each component are different and hence, energy equipartition is broken down. In the steady state, explicit expressions for the temperature T and the ratio of partial kinetic temperatures Ti/Tj are obtained by considering Maxwellian distributions defined at the partial temperatures Ti. The (scaled) granular temperature and the temperature ratios are given in terms of the coefficients of restitution, the solid volume fraction, the (scaled) parameters of the collisional model, and the ratios of mass, concentration, and diameters. In the case of a binary mixture, the theoretical predictions are exhaustively compared with both direct simulation Monte Carlo and molecular dynamics simulations with a good agreement. The deviations are identified to be originated in the non-Gaussianity of the velocity distributions and on microsegregation patterns, which induce spatial correlations not captured in the Enskog theory.

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Hydrodynamics of binary mixtures of granular gases with stochastic coefficient of restitution

Cited by 11 publications

References 49 publications

Rarefied particle motions on hillslopes – Part 2: Analysis

Rarefied particle motions on hillslopes – Part 2: Analysis

Energy nonequipartition in a collisional model of a confined quasi-two-dimensional granular mixture

Energy nonequipartition in a collisional model of a confined quasi-two-dimensional granular mixture

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