arXiv subjects

Rubén Gómez González

Publications and source records attributed to Rubén Gómez González.

26 records · Page 2Linked to original sources

arXiv2020

Non-Newtonian rheology in inertial suspensions of inelastic rough hard spheres under simple shear flow

Non-Newtonian transport properties of an inertial suspension of inelastic rough hard spheres under simple shear flow are determined from the Boltzmann kinetic equation. The influence of the interstitial gas on rough hard spheres is modeled via a Fokker-Planck generalized equation for rotating spheres accounting for the coupling of both the translational and rotational degrees of freedom of grains with the background viscous gas. The generalized Fokker-Planck term is the sum of two ordinary Fokker-Planck differential operators in linear $\mathbf{v}$ and angular $\boldsymbolω$ velocity space. As usual, each Fokker-Planck operator is constituted by a drag force term (proportional to $\mathbf{v}$ and/or $\boldsymbolω$) plus a stochastic Langevin term defined in terms of the background temperature $T_\text{ex}$. The Boltzmann equation is solved by two different but complementary approaches: (i) by means of Grad's moment method, and (ii) by using a Bhatnagar-Gross-Krook (BGK)-type kinetic model adapted to inelastic rough hard spheres. As occurs in the case of \emph{smooth} inelastic hard spheres, our results show that both the temperature and the non-Newtonian viscosity increase drastically with increasing the shear rate (discontinuous shear thickening effect) while the fourth-degree velocity moments also exhibit an $S$-shape. In particular, while high levels of roughness may slightly attenuate the jump of the viscosity in comparison to the smooth case, the opposite happens for the rotational temperature. As an application of these results, a linear stability analysis of the steady simple shear flow solution is also carried out showing that there are regions of the parameter space where the steady solution becomes linearly unstable.

cond-mat.stat-mech↗

arXiv2019

Enskog kinetic theory for multicomponent granular suspensions

The Navier--Stokes transport coefficients of multicomponent granular suspensions at moderate densities are obtained in the context of the (inelastic) Enskog kinetic theory. The suspension is modeled as an ensemble of solid particles where the influence of the interstitial gas on grains is via a viscous drag force plus a stochastic Langevin-like term defined in terms of a background temperature. In the absence of spatial gradients, it is shown first that the system reaches a homogeneous steady state where the energy lost by inelastic collisions and viscous friction is compensated for by the energy injected by the stochastic force. Once the homogeneous steady state is characterized, a \emph{normal} solution to the set of Enskog equations is obtained by means of the Chapman--Enskog expansion around the \emph{local} version of the homogeneous state. To first-order in spatial gradients, the Chapman--Enskog solution allows us to identify the Navier--Stokes transport coefficients associated with the mass, momentum, and heat fluxes. In addition, the first-order contributions to the partial temperatures and the cooling rate are also calculated. Explicit forms for the diffusion coefficients, the shear and bulk viscosities, and the first-order contributions to the partial temperatures and the cooling rate are obtained in steady-state conditions by retaining the leading terms in a Sonine polynomial expansion. The results show that the dependence of the transport coefficients on inelasticity is clearly different from that found in its granular counterpart (no gas phase). The present work extends previous theoretical results for \emph{dilute} multicomponent granular suspensions [Khalil and Garzó, Phys. Rev. E \textbf{88}, 052201 (2013)] to higher densities.

cond-mat.stat-mech↗

arXiv2019

First-order contributions to the partial temperatures in binary granular suspensions at low density

The Boltzmann kinetic equation is considered to evaluate the first-order contributions $T_i^{(1)}$ to the partial temperatures in binary granular suspensions at low density. The influence of the surrounding gas on the solid particles is modeled via a drag force proportional to the particle velocity plus a stochastic Langevin-like term. The Boltzmann equation is solved by means of the Chapman--Enskog expansion around the local version of the reference homogeneous base state. To first-order in spatial gradients, the coefficients $T_i^{(1)}$ are computed by considering the leading terms in a Sonine polynomial expansion. In addition, the influence of $T_i^{(1)}$ on the first-order contribution $ζ^{(1)}$ to the cooling rate is also assessed. Our results show that the magnitude of both $T_i^{(1)}$ and $ζ^{(1)}$ can be relevant for some values of the parameter space of the system.

cond-mat.stat-mech↗

arXiv2019

Influence of the first-order contributions to the partial temperatures on transport properties in polydisperse dense granular mixtures

The Chapman--Enskog solution to the Enskog kinetic equation of polydisperse granular mixtures is revisited to determine the first-order contributions $\varpi_i$ to the partial temperatures. As expected, these quantities (which were neglected in previous attempts) are given in terms of the solution to a set of coupled integro-differential equations analogous to those for elastic collisions. The solubility condition for this set of equations is confirmed and the coefficients $\varpi_i$ are calculated by using the leading terms in a Sonine polynomial expansion. These coefficients are given as explicit functions of the sizes, masses, composition, density, and coefficients of restitution of the mixture. Within the context of small gradients, the results apply for arbitrary degree of inelasticity and are not restricted to specific values of the parameters of the mixture. In the case of elastic collisions, previous expressions of $\varpi_i$ for ordinary binary mixtures are recovered. Finally, the impact of the first-order coefficients $\varpi_i$ on the bulk viscosity $η_\text{b}$ and the first-order contribution $ζ^{(1)}$ to the cooling rate is assessed. It is shown that the effect of $\varpi_i$ on $η_\text{b}$ and $ζ^{(1)}$ is not negligible, specially for disparate mass ratios and strong inelasticity.

cond-mat.stat-mech↗

arXiv2019

Transport coefficients for granular suspensions at moderate densities

The Enskog kinetic theory for moderately dense granular suspensions is considered as a model to determine the Navier-Stokes transport coefficients. The influence of the interstitial gas on solid particles is modeled by a viscous drag force term plus a stochastic Langevin-like term. The suspension model is solved by means of the Chapman--Enskog method conveniently adapted to dissipative dynamics. The momentum and heat fluxes as well as the cooling rate are obtained to first order in the deviations of the hydrodynamic field gradients from their values in the homogeneous steady state. Since the cooling terms (arising from collisional dissipation and viscous friction) cannot be compensated for by the energy gained by grains due to collisions with the interstitial gas, the reference distribution (zeroth-order approximation of the Chapman--Enskog solution) depends on time through its dependence on temperature. On the other hand, to simplify the analysis and given that we are interested in computing transport properties in the first order of deviations from the reference state, the steady-state conditions are considered. This simplification allows us to get explicit expressions for the Navier--Stokes transport coefficients. As expected, the results show that the dependence of the transport coefficients on both inelasticity and density is clearly different from that found in its granular counterpart (no gas phase). Finally, a linear stability analysis of the hydrodynamic equations with respect to the homogeneous steady state is performed. In contrast to the granular case (no gas-phase), no instabilities are found and hence, the homogeneous steady state is (linearly) stable.

cond-mat.stat-mech↗

arXiv2019

An improved method for the estimation of the Gumbel distribution parameters

Usual estimation methods for the parameters of extreme values distribution employ only a few values, wasting a lot of information. More precisely, in the case of the Gumbel distribution, only the block maxima values are used. In this work, we propose a method to seize all the available information in order to increase the accuracy of the estimations. This intent can be achieved by taking advantage of the existing relationship between the parameters of the baseline distribution, which generates data from the full sample space, and the ones for the limit Gumbel distribution. In this way, an informative prior distribution can be obtained. Different statistical tests are used to compare the behaviour of our method with the standard one, showing that the proposed method performs well when dealing with very shortened available data. The empirical effectiveness of the approach is demonstrated through a simulation study and a case study. Reduction in the credible interval width and enhancement in parameter location show that the results with improved prior adapt to very shortened data better than standard method does.

physics.data-an↗

arXiv2018

Simple shear flow in granular suspensions: Inelastic Maxwell models and BGK-type kinetic model

The Boltzmann kinetic equation for low-density granular suspensions under simple shear flow is considered to determine the velocity moments through the fourth degree. The influence of the interstitial gas on solid particles is modeled by a viscous drag force term plus a stochastic Langevin-like term. Two independent but complementary approaches are followed to achieve exact results. First, to keep the structure of the Boltzmann collision operator, the so-called inelastic Maxwell models (IMM) are considered. In this model, since the collision rate is independent of the relative velocity of the two colliding particles, the forms of the collisional moments can be obtained without the knowledge of the velocity distribution function. As a complement of the previous effort, a BGK-type kinetic model adapted to granular gases is solved to get the velocity moments of the velocity distribution function. The analytical predictions of the rheological properties (which are \emph{exactly} obtained in terms of the coefficient of restitution $α$ and the reduced shear rate $a^*$) show in general an excellent agreement with event-driven simulations performed for inelastic hard spheres. In particular, both theoretical approaches show clearly that the temperature and non-Newtonian viscosity exhibit an $S$ shape in a plane of stress-strain rate (discontinuous shear thickening effect). With respect to the fourth-degree velocity moments, we find that while those moments have unphysical values for IMM in a certain region of the parameter space of the system, they are well defined functions of both $α$ and $a^*$ in the case of the BGK kinetic model. The explicit shear-rate dependence of the fourth-degree moments beyond this critical region is also obtained and compared against available computer simulations.

cond-mat.stat-mech↗

arXiv2017

Instabilities in granular gas-solid flows

A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is performed to study the conditions for stability of a suspension of solid particles immersed in a viscous gas. The dissipation in such systems arises from two different sources: inelasticity in particle collisions and viscous friction dissipation due to the influence of gas phase on solid particles. The starting point is a suspension model based on the (inelastic) Enskog kinetic equation where the effect of the interstitial gas phase on the dynamics of grains is modeled via a viscous drag force. The study is carried out in two different steps. First, the transport coefficients of the system are obtained by solving the Enskog equation by means of the Chapman-Enskog method up to first order in spatial gradients. Once the transport properties are known, then the corresponding linearized hydrodynamic equations are solved to get the dispersion relations. In contrast to previous studies [V. Garzó \emph{et al.}, Phys. Rev. E \textbf{93}, 012905 (2016)], the hydrodynamic modes are \emph{analytically} obtained as functions of the parameter space of the system. As expected, linear stability shows $d-1$ transversal (shear) modes (where $d$ is the dimensionality of the system) and a longitudinal "heat" mode to be unstable with respect to long enough wavelength excitations. The results also show that the main effect of gas phase is to decrease the value of the critical length $L_c$ (beyond which the system becomes unstable) with respect to its value for a dry granular fluid. Comparison with direct numerical simulations for $L_c$ shows a good agreement for conditions of practical interest.

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