Navier-Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture

Impacto

Downloads

Downloads per month over past year

Garzo, Vicente and Brito, Ricardo and Soto, Rodrigo (2021) Navier-Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture. Physics of fluids, 33 (2). ISSN 1070-6631

[thumbnail of Brito60preprint.pdf]
Preview
PDF
536kB

Official URL: https://doi.org/10.1063/5.0032919




Abstract

The Navier-Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture of inelastic hard spheres are determined from the Boltzmann kinetic equation. A normal or hydrodynamic solution to the Boltzmann equation is obtained via the Chapman-Enskog method for states near the local version of the homogeneous time-dependent state. The mass, momentum, and heat fluxes are determined to first order in the spatial gradients of the hydrodynamic fields, and the associated transport coefficients are identified. They are given in terms of the solutions of a set of coupled linear integral equations. In addition, in contrast to the previous results obtained for low-density granular mixtures, there are also nonzero contributions to the first-order approximations to the partial temperatures T-i((1)) and the cooling rate zeta((1)). Explicit forms for the diffusion transport coefficients, the shear viscosity coefficient, and the quantities T-i((1)) and zeta((1)) are obtained by assuming steady state conditions and by considering the leading terms in a Sonine polynomial expansion. The above transport coefficients are given in terms of the coefficients of restitution, concentration, and the masses and diameters of the components of the mixture. The results apply, in principle, for arbitrary degree of inelasticity and are not limited to specific values of concentration, mass, and/or size ratios. As a simple application of these results, the violation of the Onsager reciprocal relations for a confined granular mixture is quantified in terms of the parameter space of the problem.


Item Type:Article
Additional Information:

© 2021 Author(s). Published under license by AIP Publishing. The research of V.G. was supported by the Spanish Ministerio de Economía y Competitividad through Grant No. FIS2016-76359-P and by the Junta de Extremadura (Spain) (Grant Nos. IB16013 and GR18079), partially financed by "Fondo Europeo de Desarrollo Regional" funds. The work of R.B. was supported by the Spanish Ministerio de Economía y Competitividad through Grant No. FIS2017-83709-R. The research of R.S. was supported by the FONDECYT (Grant No. 1180791) of ANID (Chile).

Uncontrolled Keywords:Mechanics; Physics, Fluids & Plasmas
Subjects:Sciences > Physics > Thermodynamics
ID Code:66881
Deposited On:26 Jul 2021 10:02
Last Modified:18 Aug 2021 10:32

Origin of downloads

Repository Staff Only: item control page