RT null
T1 Dynamic properties in a collisional model for confined granular fluids: a Review
A1 Brito López, Ricardo
A1 Soto, Rodrigo
A1 Garzó, Vicente
AB Granular systems confined in a shallow box and subjected to vertical vibration provide an attractive geometry for studying fluidized granular media. In this configuration, grains acquire kinetic energy in the vertical direction through collisions with the confining walls, and this energy is subsequently transferred to the horizontal degrees of freedom via interparticle collisions. In recent years, the so-called (Formula presented.) -model has been introduced as a simplified yet effective description of the dynamics of granular systems in such geometries. This review presents the results obtained from kinetic theory for the granular (Formula presented.) -model. To model the energy transfer mechanism, a fixed velocity increment (Formula presented.) is added to the normal component of the relative velocity during collisions. In this way, the vertical motion is effectively integrated out while retaining the collisional energy injection characteristic of the confined setup. This mechanism compensates for the energy loss due to inelastic collisions and leads to stable homogeneous steady states that can be analyzed within the framework of kinetic theory. The Enskog kinetic equation is formulated for this model and first analyzed in homogeneous steady states, yielding the stationary temperature and the equation of state. The dynamics of inhomogeneous states is then investigated using the Chapman–Enskog method, from which the Navier–Stokes transport coefficients are derived. The theory is further extended to granular mixtures, in which particles may differ in mass, size, restitution coefficient, or in the value of (Formula presented.). In this case, the phenomenology becomes richer; for example, energy equipartition is violated even in homogeneous steady states. The mixture dynamics is studied through the corresponding Navier–Stokes equations, and the associated transport coefficients are obtained in the low-density regime. The analysis of the hydrodynamic equations shows that, in agreement with simulations, the homogeneous state is linearly stable. Moreover, the intrinsically nonequilibrium nature of the model leads to the violation of Onsager reciprocity relations in granular mixtures. The theoretical predictions exhibit in general good agreement with both molecular dynamics simulations and direct simulation Monte Carlo results.
PB MDPI
YR 2026
FD 2026-04-15
LK https://hdl.handle.net/20.500.14352/136745
UL https://hdl.handle.net/20.500.14352/136745
LA eng
NO Brito, Ricardo, et al. «Dynamic Properties in a Collisional Model for Confined Granular Fluids: A Review». Entropy, vol. 28, n.o 4, abril de 2026, p. 454. DOI.org (Crossref), https://doi.org/10.3390/e28040454.
NO GR24022
NO European Commission
NO Gobierno de España
NO Ministerio de Ciencia e Innovación (España)
NO Fondo Nacional de Desarrollo Científico y Tecnológico (Chile)
NO Junta de Extremadura
DS Docta Complutense
RD 10 jun 2026