Showing papers by "Vicente Garzó published in 2020"

Enskog kinetic theory for multicomponent granular suspensions.

Abstract: 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 normal solution to the set of Enskog equations is obtained by means of the Chapman-Enskog expansion around the 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 dilute multicomponent granular suspensions [Khalil and Garzo, Phys. Rev. E 88, 052201 (2013)10.1103/PhysRevE.88.052201] to higher densities.

Mpemba-like effect in driven binary mixtures

Abstract: The Mpemba effect occurs when two samples at different initial temperatures evolve in such a way that the temperatures cross each other during the relaxation towards equilibrium. In this paper we show the emergence of a Mpemba-like effect in a molecular binary mixture in contact with a thermal reservoir (bath). The interaction between the gaseous particles of the mixture and the thermal reservoir is modeled via a viscous drag force plus a stochastic Langevin-like term. The presence of the external bath couples the time evolution of the total and partial temperatures of each component allowing the appearance of the Mpemba phenomenon, even when the initial temperature differences are of the same order of the temperatures themselves. Analytical results are obtained by considering multitemperature Maxwellian approximations for the velocity distribution functions of each component. The theoretical analysis is carried out for initial states close to and far away (large Mpemba-like effect) from equilibrium. The former situation allows us to develop a simple theory where the time evolution equation for the temperature is linearized around its asymptotic equilibrium solution. This linear theory provides an expression for the crossover time. We also provide a qualitative description of the large Mpemba effect. Our theoretical results agree very well with computer simulations obtained by numerically solving the Enskog kinetic equation by means of the direct simulation Monte Carlo method and by performing molecular dynamics simulations. Finally, preliminary results for driven granular mixtures also show the occurrence of a Mpemba-like effect for inelastic collisions.

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

Abstract: Non-Newtonian transport properties of an inertial suspension of inelastic rough hard spheres under simple shear flow are determined by 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 v and angular ω velocity space. As usual, each Fokker–Planck operator is constituted by a drag force term (proportional to v and/or ω) plus a stochastic Langevin term defined in terms of the background temperature Tex. 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 in the case of smooth inelastic hard spheres, our results show that both the temperature and the non-Newtonian viscosity increase drastically with an increase in 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. The present work extends previous theoretical results (H. Hayakawa and S. Takada, “Kinetic theory of discontinuous rheological phase transition for a dilute inertial suspension,” Prog. Theor. Exp. Phys. 2019, 083J01 and R. G. Gonzalez and V. Garzo, “Simple shear flow in granular suspensions: Inelastic Maxwell models and BGK-type kinetic model,” J. Stat. Mech. 2019, 013206) to rough spheres.

Enskog kinetic theory of rheology for a moderately dense inertial suspension.

Abstract: The Enskog kinetic theory for moderately dense inertial suspensions under simple shear flow is considered as a model to analyze the rheological properties of the system. The influence of the background fluid on suspended particles is modeled via a viscous drag force plus a Langevin-like term defined in terms of the background temperature. In a previous paper [Hayakawa et al., Phys. Rev. E 96, 042903 (2017)10.1103/PhysRevE.96.042903], Grad's moment method with the aid of a linear shear-rate expansion was employed to obtain a theory which gave good agreement with the results of event-driven Langevin simulations of hard spheres for low densities and/or small shear rates. Nevertheless, the previous approach had a limitation of not being applicable to the high-shear-rate and high-density regime. Thus, in the present paper, we extend the previous work and develop Grad's theory including higher-order terms in the shear rate. This improves significantly the theoretical predictions, a quantitative agreement between theory and simulation being found in the high-density region (volume fractions smaller than or equal to 0.4).

Energy nonequipartition in a collisional model of a confined quasi-two-dimensional granular mixture.

Abstract: Spanish Ministerio de Economia y Competitividad FIS2016-76359-P FIS2017-83709-R Fondecyt of ANID (Chile) 1180791 Junta de Extremadura (Spain) - "Fondo Europeo de Desarrollo Regional" funds IB16013 GR18079

Anomalous Mpemba effect in binary molecular suspensions

Abstract: The Mpemba effect is a phenomenon in which an initially hotter sample cools sooner. In this paper, we show the emergence of a anomalous Mpemba-like effect in a molecular binary mixture immersed in a viscous gas. Namely, a crossover in the temperature evolution when at least one of the samples presents non-monotonic relaxation. The influence of the bath on the dynamics of the particles is modeled via a viscous drag force plus a stochastic Langevin-like term. Each component of the mixture interchanges energy with the bath depending on the mechanical properties of its particles. This discrimination causes the coupling between the time evolution of temperature with that of the partial temperatures of each component. The anomalous Mpemba effect---and its inverse and mixed counterparts---stems from this coupling. In order to obtain analytical results, the velocity distribution functions of each component are approximated by considering multitemperature Maxwellian distributions. The theoretical results derived from the Enskog kinetic theory show an excellent agreement with direct simulation Monte Carlo (DMSC) data.

Erratum: Kinetic theory of shear thickening for a moderately dense gas-solid suspension: From discontinuous thickening to continuous thickening [Phys. Rev. E 96 , 042903 (2017)]

Abstract: This corrects the article DOI: 10.1103/PhysRevE.96.042903.

Unified hydrodynamic description for driven and undriven inelastic Maxwell mixtures at low density

Abstract: A hydrodynamic description for inelastic Maxwell mixtures driven by a stochastic bath with friction is derived Contrary to previous works where constitutive relations for the fluxes were restricted to states near the homogeneous steady state, here the set of Boltzmann kinetic equations is solved by means of the Chapman--Enskog method by considering a more general time-dependent reference state Due to this choice, the transport coefficients are given in terms of the solutions of a set of nonlinear differential equations which must be in general numerically solved The solution to these equations gives the transport coefficients in terms of the parameters of the mixture (masses, diameters, concentration, and coefficients of restitution) and the time-dependent (scaled) parameter $\xi^*$ which determines the influence of the thermostat on the system The Navier--Stokes transport coefficients are exactly obtained in the special cases of undriven mixtures ($\xi^*=0$) and driven mixtures under steady conditions ($\xi^*=\xi_\text{st}^*$, where $\xi_\text{st}^*$ is the value of the reduced noise strength at the steady state) As a complement, the results for inelastic Maxwell models (IMM) in both undriven and driven steady states are compared against approximate results for inelastic hard spheres (IHS) [Khalil and Garzo, Phys Rev E \textbf{88}, 052201 (2013)] While the IMM predictions for the diffusion transport coefficients show an excellent agreement with those derived for IHS, significant quantitative differences are specially found in the case of the heat flux transport coefficients

Mpemba-like effect in a molecular binary mixture in contact with a thermal reservoir

Abstract: The Mpemba effect occurs when two samples at different initial temperatures evolve in such a way that the temperatures cross each other during the relaxation towards equilibrium. In this paper we show the emergence of a Mpemba-like effect in a molecular binary mixture in contact with a thermal reservoir (bath). The interaction between the gaseous particles of the mixture and the thermal reservoir is modeled via a viscous drag force plus a stochastic Langevin-like term. The presence of the external bath couples the time evolution of the total and partial temperatures of each component allowing the appearance of the Mpemba phenomenon, even when the initial temperature differences are of the same order of the temperatures themselves. Analytical results are obtained by considering multitemperature Maxwellian approximations for the velocity distribution functions of each component. The theoretical analysis is carried out for initial states close to and far away (large Mpemba-like effect) from equilibrium. The former situation allows us to develop a simple theory where the time evolution equation for the temperature is linearized around its asymptotic equilibrium solution. This linear theory provides an expression for the crossover time. We also provide a qualitative description of the large Mpemba effect. Our theoretical results agree very well with computer simulations obtained by numerically solving the Enskog kinetic equation by means of the direct simulation Monte Carlo method and by performing molecular dynamics simulations.

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

Abstract: 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 $\boldsymbol{\omega}$ velocity space. As usual, each Fokker-Planck operator is constituted by a drag force term (proportional to $\mathbf{v}$ and/or $\boldsymbol{\omega}$) 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.

First-Order Contributions to the Partial Temperatures in Dilute Binary Granular Suspensions

Abstract: 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 \(\zeta ^{(1)}\) to the cooling rate is also assessed. Our results show that the magnitude of both \(T_i^{(1)}\) and \(\zeta ^{(1)}\) can be relevant for some values of the parameter space of the system.

Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture

Abstract: The Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture of inelastic hard spheres are determined from the Boltzmann kinetic equation. A normal or hydrodynamic solution to the Boltzmann equation is obtained via the Chapman--Enskog method for states near the local version of the homogeneous time-dependent state. 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. As expected, they are given in terms of the solutions of a set of coupled linear integral equations. In addition, in contrast to previous results obtained for low-density granular mixtures, there are also nonzero contributions to the first-order approximations to the partial temperatures $T_i^{(1)}$ and the cooling rate $\zeta^{(1)}$. Explicit forms for the diffusion transport coefficients, the shear viscosity coefficient, and the quantities $T_i^{(1)}$ and $\zeta^{(1)}$ are obtained by assuming the steady-state conditions and by considering the leading terms in a Sonine polynomial expansion. The above transport coefficients are given in terms of the coefficients of restitution, concentration, and the masses and diameters of the components of the mixture. The results apply in principle for arbitrary degree of inelasticity and are not limited to specific values of concentration, mass and/or size ratios. As a simple application of these results, the violation of the Onsager reciprocal relations for a confined granular mixture is quantified in terms of the parameter space of the problem.

Stability of the homogeneous steady state for a model of a confined quasi-two-dimensional granular fluid

Abstract: A linear stability analysis of the hydrodynamic equations of a model for confined quasi-two-dimensional granular gases is carried out. The stability analysis is performed around the homogeneous steady state (HSS) reached eventually by the system after a transient regime. In contrast to previous studies (which considered dilute or quasielastic systems), our analysis is based on the results obtained from the inelastic Enskog kinetic equation, which takes into account the (nonlinear) dependence of the transport coefficients and the cooling rate on dissipation and applies to moderate densities. As in earlier studies, the analysis shows that the HSS is linearly stable with respect to long enough wavelength excitations.

Non-monotonic Mpemba effect in binary molecular suspensions

Abstract: The Mpemba effect is a phenomenon in which an initially hotter sample cools sooner. In this paper, we show the emergence of a non-monotonic Mpemba-like effect in a molecular binary mixture immersed in a viscous gas. Namely, a crossover in the temperature evolution when at least one of the samples presents non-monotonic relaxation. The influence of the bath on the dynamics of the particles is modeled via a viscous drag force plus a stochastic Langevin-like term. Each component of the mixture interchanges energy with the bath depending on the mechanical properties of its particles. This discrimination causes the coupling between the time evolution of temperature with that of the partial temperatures of each component. The non-monotonic Mpemba effect -- and its inverse and mixed counterparts -- stems from this coupling. In order to obtain analytical results, the velocity distribution functions of each component are approximated by considering multitemperature Maxwellian distributions. The theoretical results derived from the Enskog kinetic theory show an excellent agreement with direct simulation Monte Carlo (DMSC) data.