Kinetic theory of a confined quasi-one-dimensional gas of hard disks

Mayo, Manuel García; Brey, J. Javier; Soria, M. I. García de; Maynar, P.

doi:10.1016/j.physa.2022.127237

Cited by 5 publications

(2 citation statements)

References 20 publications

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“…The equation is a Boltzmann-like equation in which the collisional contribution takes into account that the only possible collisions are those with an orientation such that the two particles are inside the container. Let us stress that this equation was previously introduced for elastic hard spheres (in this case the walls are at rest and the collisions of particles with the wall do not inject energy), finding also an excellent agreement between the theoretical results and molecular dynamics (MD) simulations [17][18][19]. The formalism can be generalized to arbitrary confinement and for moderate densities at the Enskog level [20].…”

Section: Introductionsupporting

confidence: 55%

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Confined granular gases under the influence of vibrating walls

Mayo,

Petit,

García de Soria

et al. 2023

J. Stat. Mech.

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In this paper we study the dynamics of a system composed of inelastic hard spheres or disks that are confined between two parallel vertically vibrating walls (the vertical direction is defined as the direction perpendicular to the walls). The distance between the two walls is supposed to be larger than twice the diameter of the particles so that the particles can pass over each other, but is still much smaller than the dimensions of the walls. Hence, the system can be considered to be quasi-two-dimensional (quasi-one-dimensional) in the hard spheres (disks) case. For dilute systems, a closed evolution equation for the one-particle distribution function is formulated that takes into account the effects of the confinement. Assuming the system is spatially homogeneous, the kinetic equation is solved approximating the distribution function by a two-temperature (horizontal and vertical) Gaussian distribution. The obtained evolution equations for the partial temperatures are solved, finding a very good agreement with molecular dynamics simulation results for a wide range of parameters (inelasticity, height and density) for states whose projection over a plane parallel to the walls is homogeneous. In the stationary state, where the energy lost in collisions is compensated by the energy injected by the walls, the pressure tensor in the horizontal direction is analyzed and its relation with an instability of the homogeneous state observed in the simulations is discussed.

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Section: Introductionsupporting

confidence: 55%

“…This happens for α ∼ 0.7, independently of the other parameters. The origin and the possible implications for the hydrodynamic description of the system of this transition will be studied in detail elsewhere [29].…”

Section: Evolution Equations For the Horizontal And Vertical Temperat...mentioning

confidence: 99%

Confined granular gases under the influence of vibrating walls

Mayo,

Petit,

García de Soria

et al. 2023

J. Stat. Mech.

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Equation of state of hard-disk fluids under single-file confinement

Montero

Santos

2023

The Journal of Chemical Physics

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The exact transfer-matrix solution for the longitudinal equilibrium properties of the single-file hard-disk fluid is used to study the limiting low- and high-pressure behaviors analytically as functions of the pore width. In the low-pressure regime, the exact third and fourth virial coefficients are obtained, which involve single and double integrals, respectively. Moreover, we show that the standard irreducible diagrams do not provide a complete account of the virial coefficients in confined geometries. The asymptotic equation of state in the high-pressure limit is seen to present a simple pole at the close-packing linear density, as in the hard-rod fluid, but, in contrast to the latter case, the residue is 2. Since, for an arbitrary pressure, the exact transfer-matrix treatment requires the numerical solution of an eigenvalue integral equation, we propose here two simple approximations to the equation of state, with different complexity levels, and carry out an extensive assessment of their validity and practical convenience vs the exact solution and available computer simulations.

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Applications of the kinetic theory for a model of a confined quasi-two dimensional granular mixture: Stability analysis and thermal diffusion segregation

Garzó,

Brito,

Soto

2024

Physics of Fluids

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The Boltzmann kinetic theory for a model of a confined quasi-two dimensional granular mixture derived previously [Garzó et al., “Navier–Stokes transport coefficients for a model of a confined quasi-two dimensional granular binary mixture,” Phys. Fluids 33, 023310 (2021)] is considered further to analyze two different problems. First, a linear stability analysis of the hydrodynamic equations with respect to the homogeneous steady state (HSS) is carried out to identify the conditions for stability as functions of the wave vector, the coefficients of restitution, and the parameters of the mixture. The analysis, which is based on the results obtained by solving the Boltzmann equation by means of the Chapman–Enskog method to first order in spatial gradients, takes into account the (nonlinear) dependence of the transport coefficients and the cooling rate on the coefficients of restitution and applies in principle to arbitrary values of the concentration, and the mass and diameter ratios. In contrast to the results obtained in the conventional inelastic hard sphere (IHS) model, the results show that all the hydrodynamic modes are stable so that the HSS is linearly stable with respect to long enough wavelength excitations. On the other hand, this conclusion agrees with previous stability analysis performed in earlier studies for monocomponent granular gases. As a second application, segregation induced by both a thermal gradient and gravity is studied. A segregation criterion based on the dependence of the thermal diffusion factor Λ on the parameter space of the mixture is derived. In the absence of gravity, the results indicate that Λ is always positive, and hence, the larger particles tend to accumulate near the cold plate. However, when gravity is present, our results show the transition between Λ>0 (larger particles tend to move toward the cold plate) to Λ<0 (larger particles tend to move toward the hot plate) by varying the parameters of the system (masses, sizes, composition, and coefficients of restitution). Comparison with previous results derived from the IHS model is carried out.

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Kinetic theory of a confined quasi-one-dimensional gas of hard disks

Cited by 5 publications

References 20 publications

Confined granular gases under the influence of vibrating walls

Confined granular gases under the influence of vibrating walls

Equation of state of hard-disk fluids under single-file confinement

Applications of the kinetic theory for a model of a confined quasi-two dimensional granular mixture: Stability analysis and thermal diffusion segregation

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