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

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Brito, Ricardo and Soto, Rodrigo and Garzó, Vicente (2020) Energy nonequipartition in a collisional model of a confined quasi-two-dimensional granular mixture. Physical review E, 102 (5). ISSN 2470-0045

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Official URL: https://doi.org/10.1103/PhysRevE.102.052904




Abstract

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/Tj 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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©2020 American Physical Society. The work of R.B. has been supported by the Spanish Ministerio de Economía y Competitividad through Grant No. FIS2017-83709-R. The research of R.S. has been supported by the Fondecyt Grant No.1180791 of ANID (Chile). The work of V.G. has been supported by the Spanish Ministerio de Economía y Competitividad through Grant No. FIS2016-76359-P and by the Junta de Extremadura (Spain) Grants No. IB16013 and No. GR18079, partially financed by "Fondo Europeo de Desarrollo Regional" funds.

Uncontrolled Keywords:Physics, Fluids & Plasmas; Physics, Mathematical
Subjects:Sciences > Physics > Thermodynamics
ID Code:63430
Deposited On:22 Jan 2021 13:01
Last Modified:25 Jan 2021 09:33

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