arXiv subjects

Vicente Garzó

Publications and source records attributed to Vicente Garzó.

At least 73 records · Page 4Linked to original sources

arXiv2014

Transport coefficients of a granular gas of inelastic rough hard spheres

The Boltzmann equation for inelastic and rough hard spheres is considered as a model of a dilute granular gas. In this model, the collisions are characterized by constant coefficients of normal and tangential restitution and hence the translational and rotational degrees of freedom are coupled. A normal solution to the Boltzmann equation is obtained by means of the Chapman-Enskog method for states near the homogeneous cooling state. The analysis is carried out to first order in the spatial gradients of the number density, the flow velocity, and the granular temperature. The constitutive equations for the momentum and heat fluxes and for the cooling rate are derived and the associated transport coefficients are expressed in terms of the solutions of linear integral equations. For practical purposes, a first Sonine approximation is used to obtain explicit expressions of the transport coefficients as nonlinear functions of both coefficients of restitution and the moment of inertia. Known results for purely smooth inelastic spheres and perfectly elastic and rough spheres are recovered in the appropriate limits.

cond-mat.stat-mech↗

arXiv2014

Thermal diffusion segregation of an impurity in a driven granular fluid

We study segregation of an impurity in a driven granular fluid under two types of \emph{steady} states. In the first state, the granular gas is driven by a stochastic volume force field with a Fourier-type profile while in the second state, the granular gas is sheared in such a way that inelastic cooling is balanced by viscous heating. We compare theoretical results derived from a solution of the (inelastic) Boltzmann equation at Navier-Stokes (NS) order with those obtained from the Direct Monte Carlo simulation (DSMC) method and molecular dynamics (MD) simulations. Good agreement is found between theory and simulation, which provides strong evidence of the reliability of NS granular hydrodynamics for these steady states (including the dynamics of the impurity), even at high inelasticities. In addition, preliminary results for thermal diffusion in granular fluids at moderate densitis are also presented. As for dilute gases \cite{VGK14}, excellent agreement is also found in this more general case.

cond-mat.soft↗

arXiv2014

Influence of a drag force on linear transport in low-density gases. Stability analysis

The transport coefficients of a dilute classical gas in the presence of a drag force proportional to the velocity of the particle are determined from the Boltzmann equation. The viscous drag force could model the friction of solid particles with a surrounding fluid (interstitial gas phase). First, when the drag force is the only external action on the state of the system, the Boltzmann equation admits a Maxwellian solution $f_0(\mathbf{v},t)$ with a time-dependent temperature. Then, the Boltzmann equation is solved by means of the Chapman-Enskog expansion around the local version of the distribution $f_0$ to obtain the relevant transport coefficients of the system: the shear viscosity $η$, the thermal conductivity $κ$, and a new transport coefficient $μ$ (which is also present in granular gases) relating the heat flux with the density gradient. The results indicate that while $η$ is not affected by the drag force, the impact of this force on the transport coefficients $κ$ and $μ$ may be significant. Finally, a stability analysis of the linear hydrodynamic equations with respect to the time-dependent equilibrium state is performed, showing that the onset of instability is associated with the transversal shear mode that could be unstable for wave numbers smaller than a certain critical wave number.

cond-mat.stat-mech↗

arXiv2014

Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases

The hydrodynamic Burnett equations and the associated transport coefficients are exactly evaluated for generalized inelastic Maxwell models. In those models, the one-particle distribution function obeys the inelastic Boltzmann equation, with a velocity-independent collision rate proportional to the $γ$ power of the temperature. The pressure tensor and the heat flux are obtained to second order in the spatial gradients of the hydrodynamic fields with explicit expressions for all the Burnett transport coefficients as functions of $γ$, the coefficient of normal restitution, and the dimensionality of the system. Some transport coefficients that are related in a simple way in the elastic limit become decoupled in the inelastic case. As a byproduct, existing results in the literature for three-dimensional elastic systems are recovered, and a generalization to any dimension of the system is given. The structure of the present results is used to estimate the Burnett coefficients for inelastic hard spheres.

cond-mat.soft↗

arXiv2014

Hydrodynamic granular segregation induced by boundary heating and shear

Segregation induced by a thermal gradient of an impurity in a driven low-density granular gas is studied. The system is enclosed between two parallel walls from which we input thermal energy to the gas. We study here steady states occurring when the inelastic cooling is exactly balanced by some external energy input (stochastic force or viscous heating), resulting in a uniform heat flux. A segregation criterion based on Navier-Stokes granular hydrodynamics is written in terms of the tracer diffusion transport coefficients, whose dependence on the parameters of the system (masses, sizes and coefficients of restitution) is explicitly determined from a solution of the inelastic Boltzmann equation. The theoretical predictions are validated by means of Monte Carlo and molecular dynamics simulations, showing that Navier-Stokes hydrodynamics produces accurate segregation criteria even under strong shearing and/or inelasticity.

cond-mat.stat-mech↗

arXiv2014

Navier-Stokes transport coefficients for driven inelastic Maxwell models

We calculate in this work the Navier-Stokes transport coefficients from the Boltzmann equation for $d$-dimensional inelastic Maxwell models. By granular gas we mean here a low density system of identical spheres that lose a fraction of their kinetic energy after collisions. In the present work, the granular gas is fluidized by the presence of a thermostat that aides the system to reach a steady state. The thermostat is composed by two terms: a random force and a drag force. The combined action of both forces, that act homogeneously on the granular gas, tries to mimic the interaction of the set of particles with a surrounding fluid. The Chapman-Enskog method is applied to solve the inelastic Boltzmann equation to first order in the deviations of the hydrodynamic fields from their values in the homogeneous steady state. Since the collisional cooling cannot be compensated locally for by the heat produced by the driving forces, the reference (zeroth-order) distribution function $f^{(0)}$ depends on time through its dependence on the granular temperature. To simplify the analysis and obtain explicit forms for the transport coefficients, the steady state conditions are considered. A comparison with previous results obtained for inelastic hard spheres is also carried out.

cond-mat.stat-mech↗

arXiv2014

Homogeneous states in driven granular mixtures: Enskog kinetic theory versus molecular dynamics simulations

The homogeneous state of a binary mixture of smooth inelastic hard disks or spheres is analyzed. The mixture is driven by a thermostat composed by two terms: a stochastic force and a drag force proportional to the particle velocity. The combined action of both forces attempts to model the interaction of the mixture with a bath or surrounding fluid. The problem is studied by means of two independent and complementary routes. First, the Enskog kinetic equation with a Fokker-Planck term describing interactions of particles with thermostat is derived. The ratio of kinetic temperatures $T_1/T_2$ and the fourth-degree velocity moments $λ_1$ and $λ_2$ (which measure non-Gaussian properties of $φ_i$) are explicitly determined as a function of the mass ratio, size ratio, composition, density and coefficients of restitution. Secondly, to assess the reliability of the theoretical results, molecular dynamics simulations of a binary granular mixture of spheres are performed for two values of the coefficient of restitution ($α=0.9$ and 0.8) and three different solid volume fractions ($ϕ=0.00785$, 0.1 and 0.2). Comparison between kinetic theory and computer simulations for the temperature ratio shows excellent agreement, even for moderate densities and strong dissipation. In the case of the cumulants $λ_1$ and $λ_2$, good agreement is found for the lower densities although significant discrepancies between theory and simulation are observed with increasing density.

cond-mat.stat-mech↗

arXiv2014

Instabilities in moderately dense granular binary mixtures

A linear stability analysis of the Navier-Stokes (NS) granular hydrodynamic equations is performed to determine the critical length scale for the onset of vortices and clusters instabilities in granular dense binary mixtures. In contrast to previous attempts, our results (which are based on the solution to the inelastic Enskog equation to NS order) are not restricted to nearly elastic systems since they take into account the complete nonlinear dependence of the NS transport coefficients on the coefficients of restitution $α_{ij}$. The theoretical predictions for the critical length scales are compared to molecular dynamics (MD) simulations in flows of strong dissipation ($α_{ij}\geq 0.7$) and moderate solid volume fractions ($ϕ\leq 0.2$). We find excellent agreement between MD and kinetic theory for the onset of velocity vortices, indicating the applicability of NS hydrodynamics to polydisperse flows even for strong inelasticity, finite density, and particle dissimilarity.

cond-mat.stat-mech↗

arXiv2013

Transport coefficients for driven granular mixtures at low-density

The transport coefficients of a granular binary mixture driven by a stochastic bath with friction are determined from the inelastic Boltzmann kinetic equation. A normal solution is obtained via the Chapman-Enskog method for states near homogeneous steady states. 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. As in the monocomponent case, since the collisional cooling cannot be compensated locally for by the heat produced by the external driving, the reference distributions (zeroth-order approximations) $f_i^{(0)}$ ($i=1,2$) for each species depend on time through their dependence on the pressure and the temperature. Explicit forms for the diffusion transport coefficients and the shear viscosity coefficient are obtained by assuming the steady state conditions and by considering the leading terms in a Sonine polynomial expansion. A comparison with previous results obtained for granular Brownian motion and by using a (local) stochastic thermostat is also carried out. The present work extends previous theoretical results derived for monocomponent dense gases [V. Garzó, M. G. Chamorro, and F. Vega Reyes, Phys. Rev. E \textbf{87}, 032201 (2013)] to granular mixtures at low density.

cond-mat.stat-mech↗

arXiv2013

Homogeneous steady states in a granular fluid driven by a stochastic bath with friction

The homogeneous state of a granular flow of smooth inelastic hard spheres or disks described by the Enskog-Boltzmann kinetic equation is analyzed. The granular gas is fluidized by the presence of a random force and a drag force. The combined action of both forces, that act homogeneously on the granular gas, tries to mimic the interaction of the set of particles with a surrounding fluid. The first stochastic force thermalizes the system, providing for the necessary energy recovery to keep the system in its gas state at all times, whereas the second force allows us to mimic the action of the surrounding fluid viscosity. After a transient regime, the gas reaches a steady state characterized by a \emph{scaled} distribution function $φ$ that does not only depend on the dimensionless velocity $\mathbf{c}\equiv \mathbf{v}/v_0$ ($v_0$ being the thermal velocity) but also on the dimensionless driving force parameters. The dependence of $φ$ and its first relevant velocity moments $a_2$ and $a_3$ (which measure non-Gaussian properties of $φ$) on both the coefficient of restitution $\al$ and the driven parameters is widely investigated by means of the direct simulation Monte Carlo method. In addition, approximate forms for $a_2$ and $a_3$ are also derived from an expansion of $φ$ in Sonine polynomials. The theoretical expressions of the above Sonine coefficients agree well with simulation data, even for quite small values of $α$. Moreover, the third order expansion of the distribution function makes a significant accuracy improvement for larger velocities and inelasticities. Results also show that the non-Gaussian corrections to the distribution function $φ$ are smaller than those observed for undriven granular gases.

cond-mat.stat-mech↗

arXiv2013

Diffusion transport coefficients for granular binary mixtures at low density. Thermal diffusion segregation

The mass flux of a low-density granular binary mixture obtained previously by solving the Boltzmann equation by means of the Chapman-Enskog method is considered further. As in the elastic case, the associated transport coefficients $D$, $D_p$ and $D'$ are given in terms of the solutions of a set of coupled linear integral equations which are approximately solved by considering the first and second Sonine approximations. The diffusion coefficients are explicitly obtained as functions of the coefficients of restitution and the parameters of the mixture (masses, diameters and concentration) and their expressions hold for an arbitrary number of dimensions. In order to check the accuracy of the second Sonine correction for highly inelastic collisions, the Boltzmann equation is also numerically solved by means of the direct simulation Monte Carlo (DSMC) method to determine the mutual diffusion coefficient $D$ in some special situations (self-diffusion problem and tracer limit). The comparison with DSMC results reveals that the second Sonine approximation to $D$ improves the predictions made from the first Sonine approximation. We also study the granular segregation driven by a uni-directional thermal gradient. The segregation criterion is obtained from the so-called thermal diffusion factor $Λ$, which measures the amount of segregation parallel to the temperature gradient. The factor $Λ$ is determined here by considering the second-order Sonine forms of the diffusion coefficients and its dependence on the coefficients of restitution is widely analyzed across the parameter space of the system. The results obtained in this paper extend previous works carried out in the tracer limit (vanishing mole fraction of one of the species) by some of the authors of the present paper.

cond-mat.stat-mech↗

arXiv2013

Grad's moment method for a granular fluid at moderate densities. Navier-Stokes transport coefficients

The Navier-Stokes transport coefficients of a granular dense fluid of smooth inelastic hard disks or spheres are explicitly determined by solving the inelastic Enskog equation by means of Grad's moment method. The transport coefficients are explicitly determined as functions of the (constant) coefficient of restitution and the solid volume fraction. In addition, the cooling rate is also calculated to first order in the spatial gradients. The calculations are performed for an arbitrary number of dimensions. The results are not limited to small dissipation and are expected to apply at moderate densities. It is found that the expressions of the Navier-Stokes transport coefficients and the cooling rate agree with those previously obtained from the Chapman-Enskog method by using the leading terms in a Sonine polynomial expansion. This shows the equivalence between both methods for granular fluids in the Navier-Stokes approximation. A comparison with previous results derived from Grad's moment method for inelastic disks and spheres is also carried out.

cond-mat.stat-mech↗

arXiv2013

A numerical study of the Navier-Stokes transport coefficients for 2D granular hydrodynamics

A numerical study is presented to analyze the thermal mechanisms of unsteady, supersonic granular flow, by means of hydrodynamic simulations of the Navier-Stokes granular equations. For this purpose a paradigmatic problem in granular dynamics such as the Faraday instability is selected. Two different approaches for the Navier-Stokes transport coefficients for granular materials are considered, namely the traditional Jenkins-Richman theory for moderately dense quasi-elastic grains, and the improved Garzó-Dufty-Lutsko theory for arbitrary inelasticity, which we also present here. Both solutions are compared with event-driven simulations of the same system under the same conditions, by analyzing the density, the temperature and the velocity field. Important differences are found between the two approaches leading to interesting implications. In particular, the heat transfer mechanism coupled to the density gradient which is a distinctive feature of inelastic granular gases, is responsible for a major discrepancy in the temperature field and hence in the diffusion mechanisms.

physics.flu-dyn↗

arXiv2012

Enskog kinetic theory for $d$-dimensional dense granular gases

The goal of this note is to provide most of the technical details involved in the application of the Chapman-Enskog method to solve the revised Enskog equation to Navier-Stokes order. Explicit expressions for the transport coefficients and the cooling rate are obtained in terms of the coefficient of restitution and the solid volume fraction by using a new Sonine approach. This new approach consists of replacing, where appropriate in the Chapman-Enskog procedure, the local equilibrium distribution (used in the standard first Sonine approximation) by the homogeneous cooling state distribution. The calculations are performed in an arbitrary number of dimensions.

cond-mat.stat-mech↗

arXiv2012

Collisional rates for the inelastic Maxwell model: application to the divergence of anisotropic high-order velocity moments in the homogeneous cooling state

The collisional rates associated with the isotropic velocity moments $ $ and the anisotropic moments $ $ and $ $ are exactly derived in the case of the inelastic Maxwell model as functions of the exponent $r$, the coefficient of restitution $α$, and the dimensionality $d$. The results are applied to the evolution of the moments in the homogeneous free cooling state. It is found that, at a given value of $α$, not only the isotropic moments of a degree higher than a certain value diverge but also the anisotropic moments do. This implies that, while the scaled distribution function has been proven in the literature to converge to the isotropic self-similar solution in well-defined mathematical terms, nonzero initial anisotropic moments do not decay with time. On the other hand, our results show that the ratio between an anisotropic moment and the isotropic moment of the same degree tends to zero.

cond-mat.soft↗

arXiv2012

Assessing a Hydrodynamic Description for Instabilities in Highly Dissipative, Freely Cooling Granular Gases

An intriguing phenomenon displayed by granular flows and predicted by kinetic-theory-based models is the instability known as particle "clustering," which refers to the tendency of dissipative grains to form transient, loose regions of relatively high concentration. In this work, we assess a modified-Sonine approximation recently proposed [Garzó et al., Physica A 376, 94 (2007)] for a granular gas via an examination of system stability. In particular, we determine the critical length scale associated with the onset of two types of instabilities -vortices and clusters- via stability analyses of the Navier-Stokes-order hydrodynamic equations by using the expressions of the transport coefficients obtained from both the standard and the modified-Sonine approximations. We examine the impact of both Sonine approximations over a range of solids fraction ϕ<0.2 for small restitution coefficients e=0.25--0.4, where the standard and modified theories exhibit discrepancies. The theoretical predictions for the critical length scales are compared to molecular dynamics (MD) simulations, of which a small percentage were not considered due to inelastic collapse. Results show excellent quantitative agreement between MD and the modified-Sonine theory, while the standard theory loses accuracy for this highly dissipative parameter space. The modified theory also remedies a (highdissipation) qualitative mismatch between the standard theory and MD for the instability that forms more readily. Furthermore, the evolution of cluster size is briefly examined via MD, indicating that domain-size clusters may remain stable or halve in size, depending on system parameters.

cond-mat.stat-mech↗

arXiv2012

Segregation of an intruder in a heated granular dense gas

A recent segregation criterion [V. Garzó, Phys. Rev. E \textbf{78}, 020301(R) (2008)] based on the thermal diffusion factor $Λ$ of an intruder in a heated granular gas described by the inelastic Enskog equation is revisited. The sign of $Λ$ provides a criterion for the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE). The present theory incorporates two extra ingredients not accounted for by the previous theoretical attempt. First, the theory is based upon the second Sonine approximation to the transport coefficients of the mass flux of intruder. Second, the dependence of the temperature ratio (intruder temperature over that of the host granular gas) on the solid volume fraction is taken into account in the first and second Sonine approximations. In order to check the accuracy of the Sonine approximation considered, the Enskog equation is also numerically solved by means of the direct simulation Monte Carlo (DSMC) method to get the kinetic diffusion coefficient $D_0$. The comparison between theory and simulation shows that the second Sonine approximation to $D_0$ yields an improvement over the first Sonine approximation when the intruder is lighter than the gas particles in the range of large inelasticity. With respect to the form of the phase diagrams for the BNE/RBNE transition, the kinetic theory results for the factor $Λ$ indicate that while the form of these diagrams depends sensitively on the order of the Sonine approximation considered when gravity is absent, no significant differences between both Sonine solutions appear in the opposite limit (gravity dominates the thermal gradient). In the former case (no gravity), the first Sonine approximation overestimates both the RBNE region and the influence of dissipation on thermal diffusion segregation.

cond-mat.stat-mech↗

arXiv2011

Transport coefficients of driven granular fluids at moderate volume fractions

In a recent publication [Phys. Rev. E \textbf{83}, 011301 (2011)], Vollmayr--Lee \emph{et al.} have determined by computer simulations the thermal diffusivity and the longitudinal viscosity coefficients of a driven granular fluid of hard spheres at intermediate volume fractions. Although they compare their simulation results with the predictions of kinetic theory, they use the dilute expressions for the driven system and the modified Sonine approximations for the undriven system. The goal here is to carry out this comparison by proposing a modified Sonine approximation to the Enskog equation for driven granular fluids that leads to a better quantitative agreement.

cond-mat.stat-mech↗