arXiv subjects

David González Méndez

Publications and source records attributed to David González Méndez.

5 recordsLinked to original sources

arXiv2026

Enskog kinetic theory in a model of confined granular mixtures. Heat flux and some applications

This work considers the Enskog kinetic theory for moderately dense confined granular mixtures within the framework of the $Δ$-model, an effective collisional model that accounts for the transfer of energy from the vertical to the horizontal degrees of freedom of grains through an additional velocity increment during collisions. The main objective is to complete the Navier--Stokes hydrodynamic description of dense binary granular mixtures by explicitly determining the heat-flux transport coefficients, namely the Dufour and thermal conductivity coefficients, together with the first-order contributions to the partial temperatures and the cooling rate. These quantities are determined in the steady state from the Enskog kinetic equation by means of the Chapman--Enskog method and are expressed in terms of the masses and diameters of the particles, mixture composition, density, and coefficients of restitution. The results show that finite-density effects have a significant influence on transport, leading to behaviors that differ markedly from those observed in the dilute regime. The complete set of transport coefficients is considered further to study two different problems. First, we perform a linear stability analysis of the homogeneous steady state (HSS). The analysis demonstrates that no unstable transverse or longitudinal hydrodynamic modes are found over the parameter space explored, indicating that the HSS is linearly stable even at moderate densities. As a second problem, the violation of the Onsager reciprocal relations for a confined dense granular mixture is quantified in terms of the parameter space of the problem.

cond-mat.soft↗

arXiv2026

Dynamic properties in a collisional model of a confined quasi-two-dimensional granular fluid driven by a stochastic bath with friction

This paper investigates the dynamic properties of a confined quasi-two-dimensional granular fluid at moderate densities, modeled within the framework of the Enskog kinetic equation. The confinement is not treated explicitly at the geometrical level; instead, it is incorporated in an effective way through the so-called $Δ$-model (a collisional model that includes energy injection through modified collision rules). The referred model is extended in this paper to account for the influence of an interstitial gas via a viscous drag force and a stochastic Langevin-like term. By applying the Chapman--Enskog method, the Navier--Stokes transport coefficients and the cooling rate are derived analytically considering the leading terms in a Sonine polynomial expansion. The study focuses on steady-state conditions and examines how the combined effects of inelastic collisions and external driving influence transport properties such as the viscosity and the thermal conductivity. Theoretical predictions for the steady temperature and the kurtosis are validated against direct simulation Monte Carlo (DSMC) results, showing excellent agreement. The findings reveal that the external driving significantly alters the transport coefficients compared to dry (no gas phase) granular systems, challenging previous assumptions that neglected these effects. Additionally, a linear stability analysis demonstrates that the homogeneous steady state is stable across the explored parameter space.

cond-mat.soft↗

arXiv2026

Transport properties in a model of confined granular mixtures at moderate densities

This work derives the Navier--Stokes hydrodynamic equations for a model of a confined, quasi-two-dimensional, $s$-component mixture of inelastic, smooth, hard spheres. Using the inelastic version of the revised Enskog theory, macroscopic balance equations for mass, momentum, and energy are obtained, and constitutive equations for the fluxes are determined through a first-order Chapman--Enskog expansion. As for elastic collisions, the transport coefficients are given in terms of the solutions of a set of coupled linear integral equations. Approximate solutions to these equations for diffusion transport coefficients and shear viscosity are achieved by assuming steady-state conditions and considering leading terms in a Sonine polynomial expansion. These transport coefficients are expressed in terms of the coefficients of restitution, concentration, the masses and diameters of the mixture's components, and the system's density. The results apply to moderate densities and are not limited to particular values of the coefficients of restitution, concentration, mass, and/or diameter ratios. As an application, the thermal diffusion factor is evaluated to analyze segregation driven by temperature gradients and gravity, providing criteria that distinguish whether larger particles accumulate near the hotter or colder boundaries.

cond-mat.soft↗

arXiv2025

Nonlinear transport of tracer particles immersed in a strongly sheared dilute gas with inelastic collisions

The diffusion of tracer particles immersed in a granular gas under uniform shear flow (USF) is analyzed within the framework of the inelastic Boltzmann equation. Two different but complementary approaches are followed to achieve exact results. First, we maintain the structure of the Boltzmann collision operator but consider inelastic Maxwell models (IMM). Using IMM allows us to compute the collisional moments of the Boltzmann operator without knowing the velocity distribution functions of the granular binary mixture explicitly. Second, we consider a kinetic model of the Boltzmann equation for inelastic hard spheres (IHS). This kinetic model is based on the equivalence between a gas of elastic hard spheres subjected to a drag force proportional to the particle velocity and a gas of IHS. We solve the Boltzmann--Lorentz kinetic equation for tracer particles using a generalized Chapman--Enskog--like expansion around the shear flow distribution. This reference distribution retains all hydrodynamic orders in the shear rate. The mass flux is obtained to first order in the deviations of the concentration, pressure, and temperature from their values in the reference state. Due to the velocity space anisotropy induced by the shear flow, the mass flux is expressed in terms of tensorial quantities rather than the conventional scalar diffusion coefficients. The exact results derived here are compared with those previously obtained for IHS by using different approximations [JSTAT P02012 (2007)]. The comparison generally shows reasonable quantitative agreement, especially for IMM results. Finally, we study segregation by thermal diffusion as an application of the theory. The phase diagrams illustrating segregation are shown and compared with IHS results, demonstrating qualitative agreement.

cond-mat.soft↗

arXiv2025

Kinetic model for transport in granular mixtures

A kinetic model for granular mixtures is considered to study three different non-equilibrium situations. The model is based on the equivalence between a gas of elastic hard spheres subjected to a drag force proportional to the particle velocity and a gas of inelastic hard spheres. As a first problem, the relaxation of the velocity moments to their forms in the homogeneous cooling state (HCS) is studied. Then, taking the HCS as the reference state, the kinetic model is solved by the Chapman-Enskog method, which is conveniently adapted to inelastic collisions. For small spatial gradients, the mass, momentum and heat fluxes of the mixture are determined and exact expressions for the Navier-Stokes transport coefficients are obtained. As a third nonequilibrium problem, the kinetic model is solved exactly in the uniform shear flow (USF) state, where the rheological properties of the mixture are computed in terms of the parameter space of the mixture. In addition to the transport properties, the velocity distribution functions of each species are also explicitly obtained. To assess the reliability of the model, its theoretical predictions are compared with both (approximate) analytical results and computer simulations of the original Boltzmann equation. In general, the comparison shows a reasonable agreement between the two kinetic equations. While the diffusion transport coefficients show excellent agreement with the Boltzmann results, more quantitative differences appear in the case of the shear viscosity coefficient and the heat flux transport coefficients. In the case of the USF, although the model qualitatively captures the shear rate dependence of the rheological properties well, the discrepancies increase with increasing inelasticity in collisions.

cond-mat.soft↗